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<p>学习RL至今(2020年04月02日21:30:19)，一直没有系统地看过这本被誉为RL界“圣经”的教科书，也没有对从该书中学到的知识点进行整理与记录，本文将记录重读《Reinforcement Learning: An Introduction》这本书时所学到的关键知识点和受到的启发。</p>
<a id="more"></a>
<h1 id="Introduction"><a href="#Introduction" class="headerlink" title="Introduction"></a>Introduction</h1><h2 id="Chapter-1-Introduction"><a href="#Chapter-1-Introduction" class="headerlink" title="Chapter 1 Introduction"></a>Chapter 1 Introduction</h2><h3 id="Reinforcement-Learning"><a href="#Reinforcement-Learning" class="headerlink" title="Reinforcement Learning"></a>Reinforcement Learning</h3><h3 id="Examples"><a href="#Examples" class="headerlink" title="Examples"></a>Examples</h3><h3 id="Elements-of-Reinforcement-Learning"><a href="#Elements-of-Reinforcement-Learning" class="headerlink" title="Elements of Reinforcement Learning"></a>Elements of Reinforcement Learning</h3><h3 id="Limitations-and-Scope"><a href="#Limitations-and-Scope" class="headerlink" title="Limitations and Scope"></a>Limitations and Scope</h3><h3 id="An-Extended-Example-Tic-Tac-Toe"><a href="#An-Extended-Example-Tic-Tac-Toe" class="headerlink" title="An Extended Example: Tic-Tac-Toe"></a>An Extended Example: Tic-Tac-Toe</h3><h3 id="Summary"><a href="#Summary" class="headerlink" title="Summary"></a>Summary</h3><h3 id="Early-History-of-Reinforcement-Learning"><a href="#Early-History-of-Reinforcement-Learning" class="headerlink" title="Early History of Reinforcement Learning"></a>Early History of Reinforcement Learning</h3><h1 id="Tabular-Solution-Methods"><a href="#Tabular-Solution-Methods" class="headerlink" title="Tabular Solution Methods"></a>Tabular Solution Methods</h1><h2 id="Chapter-2-Multi-armed-Bandits"><a href="#Chapter-2-Multi-armed-Bandits" class="headerlink" title="Chapter 2 Multi-armed Bandits"></a>Chapter 2 Multi-armed Bandits</h2><h3 id="A-k-armed-Bandit-Problem"><a href="#A-k-armed-Bandit-Problem" class="headerlink" title="A k-armed Bandit Problem"></a>A k-armed Bandit Problem</h3><h3 id="Action-value-Methods"><a href="#Action-value-Methods" class="headerlink" title="Action-value Methods"></a>Action-value Methods</h3><h3 id="The-10-armed-Testbed"><a href="#The-10-armed-Testbed" class="headerlink" title="The 10-armed Testbed"></a>The 10-armed Testbed</h3><h3 id="Incremental-Implementation"><a href="#Incremental-Implementation" class="headerlink" title="Incremental Implementation"></a>Incremental Implementation</h3><h3 id="Tracking-a-Nonstationary-Problem"><a href="#Tracking-a-Nonstationary-Problem" class="headerlink" title="Tracking a Nonstationary Problem"></a>Tracking a Nonstationary Problem</h3><h3 id="Optimistic-Initial-Values"><a href="#Optimistic-Initial-Values" class="headerlink" title="Optimistic Initial Values"></a>Optimistic Initial Values</h3><h3 id="Upper-Confidence-Bound-ActionSelection"><a href="#Upper-Confidence-Bound-ActionSelection" class="headerlink" title="Upper-Confidence-Bound ActionSelection"></a>Upper-Confidence-Bound ActionSelection</h3><h3 id="Gradient-Bandit-Algorithms"><a href="#Gradient-Bandit-Algorithms" class="headerlink" title="Gradient Bandit Algorithms"></a>Gradient Bandit Algorithms</h3><h3 id="Associative-Search-Contextual-Bandits"><a href="#Associative-Search-Contextual-Bandits" class="headerlink" title="Associative Search(Contextual Bandits)"></a>Associative Search(Contextual Bandits)</h3><h3 id="Summary-1"><a href="#Summary-1" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-3-Finite-Markov-Decision-Processes"><a href="#Chapter-3-Finite-Markov-Decision-Processes" class="headerlink" title="Chapter 3 Finite Markov Decision Processes"></a>Chapter 3 Finite Markov Decision Processes</h2><h3 id="The-Agent-Environment-Interface"><a href="#The-Agent-Environment-Interface" class="headerlink" title="The Agent-Environment Interface"></a>The Agent-Environment Interface</h3><h3 id="Goals-and-Rewards"><a href="#Goals-and-Rewards" class="headerlink" title="Goals and Rewards"></a>Goals and Rewards</h3><h3 id="Returns-and-Episodes"><a href="#Returns-and-Episodes" class="headerlink" title="Returns and Episodes"></a>Returns and Episodes</h3><h3 id="Unified-Nation-for-Episodic-and-Continuing-Tasks"><a href="#Unified-Nation-for-Episodic-and-Continuing-Tasks" class="headerlink" title="Unified Nation for Episodic and Continuing Tasks"></a>Unified Nation for Episodic and Continuing Tasks</h3><h3 id="Policies-and-Value-Functions"><a href="#Policies-and-Value-Functions" class="headerlink" title="Policies and Value Functions"></a>Policies and Value Functions</h3><h3 id="Optimial-Policies-and-Optimal-Value-Functions"><a href="#Optimial-Policies-and-Optimal-Value-Functions" class="headerlink" title="Optimial Policies and Optimal Value Functions"></a>Optimial Policies and Optimal Value Functions</h3><h3 id="Optimality-and-Approximation"><a href="#Optimality-and-Approximation" class="headerlink" title="Optimality and Approximation"></a>Optimality and Approximation</h3><h3 id="Summary-2"><a href="#Summary-2" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-4-Dynamic-Programming"><a href="#Chapter-4-Dynamic-Programming" class="headerlink" title="Chapter 4 Dynamic Programming"></a>Chapter 4 Dynamic Programming</h2><h3 id="Policy-Evaluation-Prediction"><a href="#Policy-Evaluation-Prediction" class="headerlink" title="Policy Evaluation(Prediction)"></a>Policy Evaluation(Prediction)</h3><h3 id="Policy-Improvement"><a href="#Policy-Improvement" class="headerlink" title="Policy Improvement"></a>Policy Improvement</h3><h3 id="Policy-Iteration"><a href="#Policy-Iteration" class="headerlink" title="Policy Iteration"></a>Policy Iteration</h3><h3 id="Value-Iteration"><a href="#Value-Iteration" class="headerlink" title="Value Iteration"></a>Value Iteration</h3><h3 id="Asynchronous-Dynamic-Programming"><a href="#Asynchronous-Dynamic-Programming" class="headerlink" title="Asynchronous Dynamic Programming"></a>Asynchronous Dynamic Programming</h3><h3 id="Generalized-Policy-Iteration"><a href="#Generalized-Policy-Iteration" class="headerlink" title="Generalized Policy Iteration"></a>Generalized Policy Iteration</h3><h3 id="Efficiency-of-Dynamic-Programming"><a href="#Efficiency-of-Dynamic-Programming" class="headerlink" title="Efficiency of Dynamic Programming"></a>Efficiency of Dynamic Programming</h3><h3 id="Summary-3"><a href="#Summary-3" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-5-Monte-Carlo-Methods"><a href="#Chapter-5-Monte-Carlo-Methods" class="headerlink" title="Chapter 5 Monte Carlo Methods"></a>Chapter 5 Monte Carlo Methods</h2><h3 id="Monte-Carlo-Prediction"><a href="#Monte-Carlo-Prediction" class="headerlink" title="Monte Carlo Prediction"></a>Monte Carlo Prediction</h3><h3 id="Monte-Carlo-Estimation-of-Action-Values"><a href="#Monte-Carlo-Estimation-of-Action-Values" class="headerlink" title="Monte Carlo Estimation of Action Values"></a>Monte Carlo Estimation of Action Values</h3><h3 id="Monte-Carlo-Control"><a href="#Monte-Carlo-Control" class="headerlink" title="Monte Carlo Control"></a>Monte Carlo Control</h3><h3 id="Monte-Carlo-Control-without-Exploring-Starts"><a href="#Monte-Carlo-Control-without-Exploring-Starts" class="headerlink" title="Monte Carlo Control without Exploring Starts"></a>Monte Carlo Control without Exploring Starts</h3><h3 id="Off-policy-Prediction-via-Improtance-Sampling"><a href="#Off-policy-Prediction-via-Improtance-Sampling" class="headerlink" title="Off-policy Prediction via Improtance Sampling"></a>Off-policy Prediction via Improtance Sampling</h3><h3 id="Incremental-Implementation-1"><a href="#Incremental-Implementation-1" class="headerlink" title="Incremental Implementation"></a>Incremental Implementation</h3><h3 id="Off-policy-Monte-Carlo-Control"><a href="#Off-policy-Monte-Carlo-Control" class="headerlink" title="Off-policy Monte Carlo Control"></a>Off-policy Monte Carlo Control</h3><h3 id="Discounting-aware-Importance-Sampling"><a href="#Discounting-aware-Importance-Sampling" class="headerlink" title="Discounting-aware Importance Sampling"></a>Discounting-aware Importance Sampling</h3><h3 id="Per-decision-Importance-Sampling"><a href="#Per-decision-Importance-Sampling" class="headerlink" title="Per-decision Importance Sampling"></a>Per-decision Importance Sampling</h3><h3 id="Summary-4"><a href="#Summary-4" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-6-Temporal-Difference-Learning"><a href="#Chapter-6-Temporal-Difference-Learning" class="headerlink" title="Chapter 6 Temporal-Difference Learning"></a>Chapter 6 Temporal-Difference Learning</h2><h3 id="TD-Prediction"><a href="#TD-Prediction" class="headerlink" title="TD Prediction"></a>TD Prediction</h3><h3 id="Advantages-of-TD-Prediction-Methods"><a href="#Advantages-of-TD-Prediction-Methods" class="headerlink" title="Advantages of TD Prediction Methods"></a>Advantages of TD Prediction Methods</h3><h3 id="Optimality-of-TD-0"><a href="#Optimality-of-TD-0" class="headerlink" title="Optimality of TD(0)"></a>Optimality of TD(0)</h3><h3 id="Sarsa-On-policy-TD-Control"><a href="#Sarsa-On-policy-TD-Control" class="headerlink" title="Sarsa: On-policy TD Control"></a>Sarsa: On-policy TD Control</h3><h3 id="Q-learning-Off-policy-TD-Control"><a href="#Q-learning-Off-policy-TD-Control" class="headerlink" title="Q-learning: Off-policy TD Control"></a>Q-learning: Off-policy TD Control</h3><h3 id="Expected-Sarsa"><a href="#Expected-Sarsa" class="headerlink" title="Expected Sarsa"></a>Expected Sarsa</h3><h3 id="Maximization-Bias-and-Double-Learning"><a href="#Maximization-Bias-and-Double-Learning" class="headerlink" title="Maximization Bias and Double Learning"></a>Maximization Bias and Double Learning</h3><h3 id="Games-Afterstates-and-Other-Special-Cases"><a href="#Games-Afterstates-and-Other-Special-Cases" class="headerlink" title="Games, Afterstates, and Other Special Cases"></a>Games, Afterstates, and Other Special Cases</h3><h3 id="Summary-5"><a href="#Summary-5" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-7-n-step-Bootstrapping"><a href="#Chapter-7-n-step-Bootstrapping" class="headerlink" title="Chapter 7 n-step Bootstrapping"></a>Chapter 7 n-step Bootstrapping</h2><h3 id="n-step-TD-Prediction"><a href="#n-step-TD-Prediction" class="headerlink" title="n-step TD Prediction"></a>n-step TD Prediction</h3><h3 id="n-step-Sarsa"><a href="#n-step-Sarsa" class="headerlink" title="n-step Sarsa"></a>n-step Sarsa</h3><h3 id="n-step-Off-policy-Learning"><a href="#n-step-Off-policy-Learning" class="headerlink" title="n-step Off-policy Learning"></a>n-step Off-policy Learning</h3><h3 id="Per-decision-Methods-with-Control-Variates"><a href="#Per-decision-Methods-with-Control-Variates" class="headerlink" title="Per-decision Methods with Control Variates"></a>Per-decision Methods with Control Variates</h3><h3 id="Off-policy-Learning-Without-Importance-Sampling-The-n-step-Tree-Backup-Algorithm"><a href="#Off-policy-Learning-Without-Importance-Sampling-The-n-step-Tree-Backup-Algorithm" class="headerlink" title="Off-policy Learning Without Importance Sampling: The n-step Tree Backup Algorithm"></a>Off-policy Learning Without Importance Sampling: The n-step Tree Backup Algorithm</h3><h3 id="A-Unifying-Algorithm-n-step-Q-sigma"><a href="#A-Unifying-Algorithm-n-step-Q-sigma" class="headerlink" title="A Unifying Algorithm: n-step $Q(\sigma)$"></a>A Unifying Algorithm: n-step $Q(\sigma)$</h3><h3 id="Summary-6"><a href="#Summary-6" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-8-Planning-and-Learning-with-Tabular-Methods"><a href="#Chapter-8-Planning-and-Learning-with-Tabular-Methods" class="headerlink" title="Chapter 8 Planning and Learning with Tabular Methods"></a>Chapter 8 Planning and Learning with Tabular Methods</h2><h3 id="Models-and-Planning"><a href="#Models-and-Planning" class="headerlink" title="Models and Planning"></a>Models and Planning</h3><h3 id="Dyna-Integrated-Planning-Acting-and-Learning"><a href="#Dyna-Integrated-Planning-Acting-and-Learning" class="headerlink" title="Dyna: Integrated Planning, Acting, and Learning"></a>Dyna: Integrated Planning, Acting, and Learning</h3><h3 id="When-the-Model-Is-Wrong"><a href="#When-the-Model-Is-Wrong" class="headerlink" title="When the Model Is Wrong"></a>When the Model Is Wrong</h3><h3 id="Prioritized-Sweeping"><a href="#Prioritized-Sweeping" class="headerlink" title="Prioritized Sweeping"></a>Prioritized Sweeping</h3><h3 id="Expected-vs-Sample-Updates"><a href="#Expected-vs-Sample-Updates" class="headerlink" title="Expected vs. Sample Updates"></a>Expected vs. Sample Updates</h3><h3 id="Trajectory-Sampling"><a href="#Trajectory-Sampling" class="headerlink" title="Trajectory Sampling"></a>Trajectory Sampling</h3><h3 id="Real-time-Dynamic-Programming"><a href="#Real-time-Dynamic-Programming" class="headerlink" title="Real-time Dynamic Programming"></a>Real-time Dynamic Programming</h3><h3 id="Planning-at-Decision-Time"><a href="#Planning-at-Decision-Time" class="headerlink" title="Planning at Decision Time"></a>Planning at Decision Time</h3><h3 id="Heuristic-Search"><a href="#Heuristic-Search" class="headerlink" title="Heuristic Search"></a>Heuristic Search</h3><h3 id="Rollout-Algorithms"><a href="#Rollout-Algorithms" class="headerlink" title="Rollout Algorithms"></a>Rollout Algorithms</h3><h3 id="Monte-Carlo-Tree-Search"><a href="#Monte-Carlo-Tree-Search" class="headerlink" title="Monte Carlo Tree Search"></a>Monte Carlo Tree Search</h3><h3 id="Summary-7"><a href="#Summary-7" class="headerlink" title="Summary"></a>Summary</h3><h1 id="Approximate-Solution-Methods"><a href="#Approximate-Solution-Methods" class="headerlink" title="Approximate Solution Methods"></a>Approximate Solution Methods</h1><h2 id="Chapter-9-On-policy-Prediction-with-Approximation"><a href="#Chapter-9-On-policy-Prediction-with-Approximation" class="headerlink" title="Chapter 9 On-policy Prediction with Approximation"></a>Chapter 9 On-policy Prediction with Approximation</h2><h3 id="Value-function-Approximation"><a href="#Value-function-Approximation" class="headerlink" title="Value-function Approximation"></a>Value-function Approximation</h3><h3 id="The-Prediction-Objective-VE"><a href="#The-Prediction-Objective-VE" class="headerlink" title="The Prediction Objective(VE)"></a>The Prediction Objective(VE)</h3><h3 id="Stochastic-gradient-and-Semi-gradient-Methods"><a href="#Stochastic-gradient-and-Semi-gradient-Methods" class="headerlink" title="Stochastic-gradient and Semi-gradient Methods"></a>Stochastic-gradient and Semi-gradient Methods</h3><h3 id="Linear-Methods"><a href="#Linear-Methods" class="headerlink" title="Linear Methods"></a>Linear Methods</h3><h3 id="Feature-Construction-for-Linear-Methods"><a href="#Feature-Construction-for-Linear-Methods" class="headerlink" title="Feature Construction for Linear Methods"></a>Feature Construction for Linear Methods</h3><h4 id="Polynomials"><a href="#Polynomials" class="headerlink" title="Polynomials"></a>Polynomials</h4><h4 id="Fourier-Basis"><a href="#Fourier-Basis" class="headerlink" title="Fourier Basis"></a>Fourier Basis</h4><h4 id="Coarse-Coding"><a href="#Coarse-Coding" class="headerlink" title="Coarse Coding"></a>Coarse Coding</h4><h4 id="Tile-Coding"><a href="#Tile-Coding" class="headerlink" title="Tile Coding"></a>Tile Coding</h4><h4 id="Radial-Basis-Functions"><a href="#Radial-Basis-Functions" class="headerlink" title="Radial Basis Functions"></a>Radial Basis Functions</h4><h3 id="Selecting-Step-size-Parameters-Manually"><a href="#Selecting-Step-size-Parameters-Manually" class="headerlink" title="Selecting Step-size Parameters Manually"></a>Selecting Step-size Parameters Manually</h3><h3 id="Nonlinear-Function-Approximation-Artificial-Neural-Networks"><a href="#Nonlinear-Function-Approximation-Artificial-Neural-Networks" class="headerlink" title="Nonlinear Function Approximation: Artificial Neural Networks"></a>Nonlinear Function Approximation: Artificial Neural Networks</h3><h3 id="Least-Squares-TD"><a href="#Least-Squares-TD" class="headerlink" title="Least-Squares TD"></a>Least-Squares TD</h3><h3 id="Memory-based-Function-Approximation"><a href="#Memory-based-Function-Approximation" class="headerlink" title="Memory-based Function Approximation"></a>Memory-based Function Approximation</h3><h3 id="Kernel-based-Function-Approximation"><a href="#Kernel-based-Function-Approximation" class="headerlink" title="Kernel-based Function Approximation"></a>Kernel-based Function Approximation</h3><h3 id="Looking-Deeper-at-On-policy-Learning-Interest-and-Emphasis"><a href="#Looking-Deeper-at-On-policy-Learning-Interest-and-Emphasis" class="headerlink" title="Looking Deeper at On-policy Learning: Interest and Emphasis"></a>Looking Deeper at On-policy Learning: Interest and Emphasis</h3><h3 id="Summary-8"><a href="#Summary-8" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-10-On-policy-Control-with-Approximation"><a href="#Chapter-10-On-policy-Control-with-Approximation" class="headerlink" title="Chapter 10 On-policy Control with Approximation"></a>Chapter 10 On-policy Control with Approximation</h2><h3 id="Episodic-Semi-gradient-Control"><a href="#Episodic-Semi-gradient-Control" class="headerlink" title="Episodic Semi-gradient Control"></a>Episodic Semi-gradient Control</h3><h3 id="Semi-gradient-n-step-Sarsa"><a href="#Semi-gradient-n-step-Sarsa" class="headerlink" title="Semi-gradient n-step Sarsa"></a>Semi-gradient n-step Sarsa</h3><h3 id="Average-Reward-A-New-Problem-Setting-for-Continuing-Tasks"><a href="#Average-Reward-A-New-Problem-Setting-for-Continuing-Tasks" class="headerlink" title="Average Reward: A New Problem Setting for Continuing Tasks"></a>Average Reward: A New Problem Setting for Continuing Tasks</h3><h3 id="Deprecating-the-Discounted-Setting"><a href="#Deprecating-the-Discounted-Setting" class="headerlink" title="Deprecating the Discounted Setting"></a>Deprecating the Discounted Setting</h3><h3 id="Differential-Semi-gradient-n-step-Sarsa"><a href="#Differential-Semi-gradient-n-step-Sarsa" class="headerlink" title="Differential Semi-gradient n-step Sarsa"></a>Differential Semi-gradient n-step Sarsa</h3><h3 id="Summary-9"><a href="#Summary-9" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-11-Off-policy-Methods-with-Approximation"><a href="#Chapter-11-Off-policy-Methods-with-Approximation" class="headerlink" title="Chapter 11 Off-policy Methods with Approximation"></a>Chapter 11 Off-policy Methods with Approximation</h2><h3 id="Semi-gradient-Methods"><a href="#Semi-gradient-Methods" class="headerlink" title="Semi-gradient Methods"></a>Semi-gradient Methods</h3><h3 id="Examples-of-Off-policy-Divergence"><a href="#Examples-of-Off-policy-Divergence" class="headerlink" title="Examples of Off-policy Divergence"></a>Examples of Off-policy Divergence</h3><h3 id="The-Deadly-Triad"><a href="#The-Deadly-Triad" class="headerlink" title="The Deadly Triad"></a>The Deadly Triad</h3><h3 id="Linear-Value-function-Geometry"><a href="#Linear-Value-function-Geometry" class="headerlink" title="Linear Value-function Geometry"></a>Linear Value-function Geometry</h3><h3 id="Gradient-Descent-in-the-Bellman-Error"><a href="#Gradient-Descent-in-the-Bellman-Error" class="headerlink" title="Gradient Descent in the Bellman Error"></a>Gradient Descent in the Bellman Error</h3><h3 id="The-Bellman-Error-is-Not-Learnable"><a href="#The-Bellman-Error-is-Not-Learnable" class="headerlink" title="The Bellman Error is Not Learnable"></a>The Bellman Error is Not Learnable</h3><h3 id="Gradient-TD-Methods"><a href="#Gradient-TD-Methods" class="headerlink" title="Gradient-TD Methods"></a>Gradient-TD Methods</h3><h3 id="Emphatic-TD-Methods"><a href="#Emphatic-TD-Methods" class="headerlink" title="Emphatic-TD Methods"></a>Emphatic-TD Methods</h3><h3 id="Reducing-Variance"><a href="#Reducing-Variance" class="headerlink" title="Reducing Variance"></a>Reducing Variance</h3><h3 id="Summary-10"><a href="#Summary-10" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-12-Eligibility-Traces"><a href="#Chapter-12-Eligibility-Traces" class="headerlink" title="Chapter 12 Eligibility Traces"></a>Chapter 12 Eligibility Traces</h2><h3 id="The-lambda-return"><a href="#The-lambda-return" class="headerlink" title="The $\lambda$-return"></a>The $\lambda$-return</h3><h3 id="TD-lambda"><a href="#TD-lambda" class="headerlink" title="TD($\lambda$)"></a>TD($\lambda$)</h3><h3 id="n-step-Truncated-lambda-return-Methods"><a href="#n-step-Truncated-lambda-return-Methods" class="headerlink" title="n-step Truncated $\lambda$-return Methods"></a>n-step Truncated $\lambda$-return Methods</h3><h3 id="Redoing-Updates-Online-lambda-return-Algorithm"><a href="#Redoing-Updates-Online-lambda-return-Algorithm" class="headerlink" title="Redoing Updates: Online $\lambda$-return Algorithm"></a>Redoing Updates: Online $\lambda$-return Algorithm</h3><h3 id="True-Online-TD-lambda"><a href="#True-Online-TD-lambda" class="headerlink" title="True Online TD($\lambda$)"></a>True Online TD($\lambda$)</h3><h3 id="Dutch-Traces-in-Monte-Carlo-Learning"><a href="#Dutch-Traces-in-Monte-Carlo-Learning" class="headerlink" title="Dutch Traces in Monte Carlo Learning"></a>Dutch Traces in Monte Carlo Learning</h3><h3 id="Sarsa-lambda"><a href="#Sarsa-lambda" class="headerlink" title="Sarsa($\lambda$)"></a>Sarsa($\lambda$)</h3><h3 id="Variable-lambda-and-gamma"><a href="#Variable-lambda-and-gamma" class="headerlink" title="Variable $\lambda$ and $\gamma$"></a>Variable $\lambda$ and $\gamma$</h3><h3 id="Off-policy-Traces-with-Control-Variates"><a href="#Off-policy-Traces-with-Control-Variates" class="headerlink" title="Off-policy Traces with Control Variates"></a>Off-policy Traces with Control Variates</h3><h3 id="Watkins’s-Q-lambda-to-Tree-Backup-lambda"><a href="#Watkins’s-Q-lambda-to-Tree-Backup-lambda" class="headerlink" title="Watkins’s Q($\lambda$) to Tree-Backup( $\lambda$)"></a>Watkins’s Q($\lambda$) to Tree-Backup( $\lambda$)</h3><h3 id="Stable-Off-policy-Methods-with-Traces"><a href="#Stable-Off-policy-Methods-with-Traces" class="headerlink" title="Stable Off-policy Methods with Traces"></a>Stable Off-policy Methods with Traces</h3><h3 id="Implementation-Issues"><a href="#Implementation-Issues" class="headerlink" title="Implementation Issues"></a>Implementation Issues</h3><h3 id="Conclusions"><a href="#Conclusions" class="headerlink" title="Conclusions"></a>Conclusions</h3><h2 id="Chapter-13-Policy-Gradient-Methods"><a href="#Chapter-13-Policy-Gradient-Methods" class="headerlink" title="Chapter 13 Policy Gradient Methods"></a>Chapter 13 Policy Gradient Methods</h2><h3 id="Policy-Approximation-and-its-Advantages"><a href="#Policy-Approximation-and-its-Advantages" class="headerlink" title="Policy Approximation and its Advantages"></a>Policy Approximation and its Advantages</h3><h3 id="The-Policy-Gradient-Theorem"><a href="#The-Policy-Gradient-Theorem" class="headerlink" title="The Policy Gradient Theorem"></a>The Policy Gradient Theorem</h3><h3 id="REINFORCE-Monte-Carlo-Policy-Gradient"><a href="#REINFORCE-Monte-Carlo-Policy-Gradient" class="headerlink" title="REINFORCE: Monte Carlo Policy Gradient"></a>REINFORCE: Monte Carlo Policy Gradient</h3><h3 id="REINFORCE-with-Baseline"><a href="#REINFORCE-with-Baseline" class="headerlink" title="REINFORCE with Baseline"></a>REINFORCE with Baseline</h3><h3 id="Actor–Critic-Methods"><a href="#Actor–Critic-Methods" class="headerlink" title="Actor–Critic Methods"></a>Actor–Critic Methods</h3><h3 id="Policy-Gradient-for-Continuing-Problems"><a href="#Policy-Gradient-for-Continuing-Problems" class="headerlink" title="Policy Gradient for Continuing Problems"></a>Policy Gradient for Continuing Problems</h3><h3 id="Policy-Parameterization-for-Continuous-Actions"><a href="#Policy-Parameterization-for-Continuous-Actions" class="headerlink" title="Policy Parameterization for Continuous Actions"></a>Policy Parameterization for Continuous Actions</h3><h3 id="Summary-11"><a href="#Summary-11" class="headerlink" title="Summary"></a>Summary</h3><h1 id="Looking-Deeper"><a href="#Looking-Deeper" class="headerlink" title="Looking Deeper"></a>Looking Deeper</h1><h2 id="Chapter-14-Psychology"><a href="#Chapter-14-Psychology" class="headerlink" title="Chapter 14 Psychology"></a>Chapter 14 Psychology</h2><h3 id="Prediction-and-Control"><a href="#Prediction-and-Control" class="headerlink" title="Prediction and Control"></a>Prediction and Control</h3><h3 id="Classical-Conditioning"><a href="#Classical-Conditioning" class="headerlink" title="Classical Conditioning"></a>Classical Conditioning</h3><h4 id="Blocking-and-Higher-order-Conditioning"><a href="#Blocking-and-Higher-order-Conditioning" class="headerlink" title="Blocking and Higher-order Conditioning"></a>Blocking and Higher-order Conditioning</h4><h4 id="The-Rescorla–Wagner-Model"><a href="#The-Rescorla–Wagner-Model" class="headerlink" title="The Rescorla–Wagner Model"></a>The Rescorla–Wagner Model</h4><h4 id="The-TD-Model"><a href="#The-TD-Model" class="headerlink" title="The TD Model"></a>The TD Model</h4><h4 id="TD-Model-Simulations"><a href="#TD-Model-Simulations" class="headerlink" title="TD Model Simulations"></a>TD Model Simulations</h4><h3 id="Instrumental-Conditioning"><a href="#Instrumental-Conditioning" class="headerlink" title="Instrumental Conditioning"></a>Instrumental Conditioning</h3><h3 id="Delayed-Reinforcement"><a href="#Delayed-Reinforcement" class="headerlink" title="Delayed Reinforcement"></a>Delayed Reinforcement</h3><h3 id="Cognitive-Maps"><a href="#Cognitive-Maps" class="headerlink" title="Cognitive Maps"></a>Cognitive Maps</h3><h3 id="Habitual-and-Goal-directed-Behavior"><a href="#Habitual-and-Goal-directed-Behavior" class="headerlink" title="Habitual and Goal-directed Behavior"></a>Habitual and Goal-directed Behavior</h3><h3 id="Summary-12"><a href="#Summary-12" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-15-Neuroscience"><a href="#Chapter-15-Neuroscience" class="headerlink" title="Chapter 15 Neuroscience"></a>Chapter 15 Neuroscience</h2><h3 id="Neuroscience-Basics"><a href="#Neuroscience-Basics" class="headerlink" title="Neuroscience Basics"></a>Neuroscience Basics</h3><h3 id="Reward-Signals-Reinforcement-Signals-Values-and-Prediction-Errors"><a href="#Reward-Signals-Reinforcement-Signals-Values-and-Prediction-Errors" class="headerlink" title="Reward Signals, Reinforcement Signals, Values, and Prediction Errors"></a>Reward Signals, Reinforcement Signals, Values, and Prediction Errors</h3><h3 id="The-Reward-Prediction-Error-Hypothesis"><a href="#The-Reward-Prediction-Error-Hypothesis" class="headerlink" title="The Reward Prediction Error Hypothesis"></a>The Reward Prediction Error Hypothesis</h3><h3 id="Dopamine"><a href="#Dopamine" class="headerlink" title="Dopamine"></a>Dopamine</h3><h3 id="Experimental-Support-for-the-Reward-Prediction-Error-Hypothesis"><a href="#Experimental-Support-for-the-Reward-Prediction-Error-Hypothesis" class="headerlink" title="Experimental Support for the Reward Prediction Error Hypothesis"></a>Experimental Support for the Reward Prediction Error Hypothesis</h3><h3 id="TD-Error-Dopamine-Correspondence"><a href="#TD-Error-Dopamine-Correspondence" class="headerlink" title="TD Error/Dopamine Correspondence"></a>TD Error/Dopamine Correspondence</h3><h3 id="Neural-Actor–Critic"><a href="#Neural-Actor–Critic" class="headerlink" title="Neural Actor–Critic"></a>Neural Actor–Critic</h3><h3 id="Actor-and-Critic-Learning-Rules"><a href="#Actor-and-Critic-Learning-Rules" class="headerlink" title="Actor and Critic Learning Rules"></a>Actor and Critic Learning Rules</h3><h3 id="Hedonistic-Neurons"><a href="#Hedonistic-Neurons" class="headerlink" title="Hedonistic Neurons"></a>Hedonistic Neurons</h3><h3 id="Collective-Reinforcement-Learning"><a href="#Collective-Reinforcement-Learning" class="headerlink" title="Collective Reinforcement Learning"></a>Collective Reinforcement Learning</h3><h3 id="Model-based-Methods-in-the-Brain"><a href="#Model-based-Methods-in-the-Brain" class="headerlink" title="Model-based Methods in the Brain"></a>Model-based Methods in the Brain</h3><h3 id="Addiction"><a href="#Addiction" class="headerlink" title="Addiction"></a>Addiction</h3><h3 id="Summary-13"><a href="#Summary-13" class="headerlink" title="Summary"></a>Summary</h3><h2 id="Chapter-16-Applications-and-Case-Studies"><a href="#Chapter-16-Applications-and-Case-Studies" class="headerlink" title="Chapter 16 Applications and Case Studies"></a>Chapter 16 Applications and Case Studies</h2><h3 id="TD-Gammon"><a href="#TD-Gammon" class="headerlink" title="TD-Gammon"></a>TD-Gammon</h3><h3 id="Samuel’s-Checkers-Player"><a href="#Samuel’s-Checkers-Player" class="headerlink" title="Samuel’s Checkers Player"></a>Samuel’s Checkers Player</h3><h3 id="Watson’s-Daily-Double-Wagering"><a href="#Watson’s-Daily-Double-Wagering" class="headerlink" title="Watson’s Daily-Double Wagering"></a>Watson’s Daily-Double Wagering</h3><h3 id="Optimizing-Memory-Control"><a href="#Optimizing-Memory-Control" class="headerlink" title="Optimizing Memory Control"></a>Optimizing Memory Control</h3><h3 id="Human-level-Video-Game-Play"><a href="#Human-level-Video-Game-Play" class="headerlink" title="Human-level Video Game Play"></a>Human-level Video Game Play</h3><h3 id="Mastering-the-Game-of-Go"><a href="#Mastering-the-Game-of-Go" class="headerlink" title="Mastering the Game of Go"></a>Mastering the Game of Go</h3><h4 id="AlphaGo"><a href="#AlphaGo" class="headerlink" title="AlphaGo"></a>AlphaGo</h4><h4 id="AlphaGo-Zero"><a href="#AlphaGo-Zero" class="headerlink" title="AlphaGo Zero"></a>AlphaGo Zero</h4><h3 id="Personalized-Web-Services"><a href="#Personalized-Web-Services" class="headerlink" title="Personalized Web Services"></a>Personalized Web Services</h3><h3 id="Thermal-Soaring"><a href="#Thermal-Soaring" class="headerlink" title="Thermal Soaring"></a>Thermal Soaring</h3><h2 id="Chapter-17-Frontiers"><a href="#Chapter-17-Frontiers" class="headerlink" title="Chapter 17 Frontiers"></a>Chapter 17 Frontiers</h2><h3 id="General-Value-Functions-and-Auxiliary-Tasks"><a href="#General-Value-Functions-and-Auxiliary-Tasks" class="headerlink" title="General Value Functions and Auxiliary Tasks"></a>General Value Functions and Auxiliary Tasks</h3><h3 id="Temporal-Abstraction-via-Options"><a href="#Temporal-Abstraction-via-Options" class="headerlink" title="Temporal Abstraction via Options"></a>Temporal Abstraction via Options</h3><h3 id="Observations-and-State"><a href="#Observations-and-State" class="headerlink" title="Observations and State"></a>Observations and State</h3><h3 id="Designing-Reward-Signals"><a href="#Designing-Reward-Signals" class="headerlink" title="Designing Reward Signals"></a>Designing Reward Signals</h3><h3 id="Remaining-Issues"><a href="#Remaining-Issues" class="headerlink" title="Remaining Issues"></a>Remaining Issues</h3><h3 id="The-Future-of-Artificial-Intelligence"><a href="#The-Future-of-Artificial-Intelligence" class="headerlink" title="The Future of Artificial Intelligence"></a>The Future of Artificial Intelligence</h3>
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<div style="text-align:center;color: #ccc;font-size:14px;">-------------本文结束<i class="fa fa-heart"></i>感谢您的阅读-------------</div>
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<p><span>本文标题:</span><a href="/rl-an-introduction.html">《Reinforcement Learning: An Introduction》阅读笔记</a></p>
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<div class="post-toc-content"><ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#Introduction"><span class="nav-number">1.</span> <span class="nav-text">Introduction</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-1-Introduction"><span class="nav-number">1.1.</span> <span class="nav-text">Chapter 1 Introduction</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Reinforcement-Learning"><span class="nav-number">1.1.1.</span> <span class="nav-text">Reinforcement Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Examples"><span class="nav-number">1.1.2.</span> <span class="nav-text">Examples</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Elements-of-Reinforcement-Learning"><span class="nav-number">1.1.3.</span> <span class="nav-text">Elements of Reinforcement Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Limitations-and-Scope"><span class="nav-number">1.1.4.</span> <span class="nav-text">Limitations and Scope</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#An-Extended-Example-Tic-Tac-Toe"><span class="nav-number">1.1.5.</span> <span class="nav-text">An Extended Example: Tic-Tac-Toe</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary"><span class="nav-number">1.1.6.</span> <span class="nav-text">Summary</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Early-History-of-Reinforcement-Learning"><span class="nav-number">1.1.7.</span> <span class="nav-text">Early History of Reinforcement Learning</span></a></li></ol></li></ol></li><li class="nav-item nav-level-1"><a class="nav-link" href="#Tabular-Solution-Methods"><span class="nav-number">2.</span> <span class="nav-text">Tabular Solution Methods</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-2-Multi-armed-Bandits"><span class="nav-number">2.1.</span> <span class="nav-text">Chapter 2 Multi-armed Bandits</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#A-k-armed-Bandit-Problem"><span class="nav-number">2.1.1.</span> <span class="nav-text">A k-armed Bandit Problem</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Action-value-Methods"><span class="nav-number">2.1.2.</span> <span class="nav-text">Action-value Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-10-armed-Testbed"><span class="nav-number">2.1.3.</span> <span class="nav-text">The 10-armed Testbed</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Incremental-Implementation"><span class="nav-number">2.1.4.</span> <span class="nav-text">Incremental Implementation</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Tracking-a-Nonstationary-Problem"><span class="nav-number">2.1.5.</span> <span class="nav-text">Tracking a Nonstationary Problem</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Optimistic-Initial-Values"><span class="nav-number">2.1.6.</span> <span class="nav-text">Optimistic Initial Values</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Upper-Confidence-Bound-ActionSelection"><span class="nav-number">2.1.7.</span> <span class="nav-text">Upper-Confidence-Bound ActionSelection</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Gradient-Bandit-Algorithms"><span class="nav-number">2.1.8.</span> <span class="nav-text">Gradient Bandit Algorithms</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Associative-Search-Contextual-Bandits"><span class="nav-number">2.1.9.</span> <span class="nav-text">Associative Search(Contextual Bandits)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-1"><span class="nav-number">2.1.10.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-3-Finite-Markov-Decision-Processes"><span class="nav-number">2.2.</span> <span class="nav-text">Chapter 3 Finite Markov Decision Processes</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Agent-Environment-Interface"><span class="nav-number">2.2.1.</span> <span class="nav-text">The Agent-Environment Interface</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Goals-and-Rewards"><span class="nav-number">2.2.2.</span> <span class="nav-text">Goals and Rewards</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Returns-and-Episodes"><span class="nav-number">2.2.3.</span> <span class="nav-text">Returns and Episodes</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Unified-Nation-for-Episodic-and-Continuing-Tasks"><span class="nav-number">2.2.4.</span> <span class="nav-text">Unified Nation for Episodic and Continuing Tasks</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Policies-and-Value-Functions"><span class="nav-number">2.2.5.</span> <span class="nav-text">Policies and Value Functions</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Optimial-Policies-and-Optimal-Value-Functions"><span class="nav-number">2.2.6.</span> <span class="nav-text">Optimial Policies and Optimal Value Functions</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Optimality-and-Approximation"><span class="nav-number">2.2.7.</span> <span class="nav-text">Optimality and Approximation</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-2"><span class="nav-number">2.2.8.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-4-Dynamic-Programming"><span class="nav-number">2.3.</span> <span class="nav-text">Chapter 4 Dynamic Programming</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Policy-Evaluation-Prediction"><span class="nav-number">2.3.1.</span> <span class="nav-text">Policy Evaluation(Prediction)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Policy-Improvement"><span class="nav-number">2.3.2.</span> <span class="nav-text">Policy Improvement</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Policy-Iteration"><span class="nav-number">2.3.3.</span> <span class="nav-text">Policy Iteration</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Value-Iteration"><span class="nav-number">2.3.4.</span> <span class="nav-text">Value Iteration</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Asynchronous-Dynamic-Programming"><span class="nav-number">2.3.5.</span> <span class="nav-text">Asynchronous Dynamic Programming</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Generalized-Policy-Iteration"><span class="nav-number">2.3.6.</span> <span class="nav-text">Generalized Policy Iteration</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Efficiency-of-Dynamic-Programming"><span class="nav-number">2.3.7.</span> <span class="nav-text">Efficiency of Dynamic Programming</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-3"><span class="nav-number">2.3.8.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-5-Monte-Carlo-Methods"><span class="nav-number">2.4.</span> <span class="nav-text">Chapter 5 Monte Carlo Methods</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Monte-Carlo-Prediction"><span class="nav-number">2.4.1.</span> <span class="nav-text">Monte Carlo Prediction</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Monte-Carlo-Estimation-of-Action-Values"><span class="nav-number">2.4.2.</span> <span class="nav-text">Monte Carlo Estimation of Action Values</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Monte-Carlo-Control"><span class="nav-number">2.4.3.</span> <span class="nav-text">Monte Carlo Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Monte-Carlo-Control-without-Exploring-Starts"><span class="nav-number">2.4.4.</span> <span class="nav-text">Monte Carlo Control without Exploring Starts</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Off-policy-Prediction-via-Improtance-Sampling"><span class="nav-number">2.4.5.</span> <span class="nav-text">Off-policy Prediction via Improtance Sampling</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Incremental-Implementation-1"><span class="nav-number">2.4.6.</span> <span class="nav-text">Incremental Implementation</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Off-policy-Monte-Carlo-Control"><span class="nav-number">2.4.7.</span> <span class="nav-text">Off-policy Monte Carlo Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Discounting-aware-Importance-Sampling"><span class="nav-number">2.4.8.</span> <span class="nav-text">Discounting-aware Importance Sampling</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Per-decision-Importance-Sampling"><span class="nav-number">2.4.9.</span> <span class="nav-text">Per-decision Importance Sampling</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-4"><span class="nav-number">2.4.10.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-6-Temporal-Difference-Learning"><span class="nav-number">2.5.</span> <span class="nav-text">Chapter 6 Temporal-Difference Learning</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#TD-Prediction"><span class="nav-number">2.5.1.</span> <span class="nav-text">TD Prediction</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Advantages-of-TD-Prediction-Methods"><span class="nav-number">2.5.2.</span> <span class="nav-text">Advantages of TD Prediction Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Optimality-of-TD-0"><span class="nav-number">2.5.3.</span> <span class="nav-text">Optimality of TD(0)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Sarsa-On-policy-TD-Control"><span class="nav-number">2.5.4.</span> <span class="nav-text">Sarsa: On-policy TD Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Q-learning-Off-policy-TD-Control"><span class="nav-number">2.5.5.</span> <span class="nav-text">Q-learning: Off-policy TD Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Expected-Sarsa"><span class="nav-number">2.5.6.</span> <span class="nav-text">Expected Sarsa</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Maximization-Bias-and-Double-Learning"><span class="nav-number">2.5.7.</span> <span class="nav-text">Maximization Bias and Double Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Games-Afterstates-and-Other-Special-Cases"><span class="nav-number">2.5.8.</span> <span class="nav-text">Games, Afterstates, and Other Special Cases</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-5"><span class="nav-number">2.5.9.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-7-n-step-Bootstrapping"><span class="nav-number">2.6.</span> <span class="nav-text">Chapter 7 n-step Bootstrapping</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#n-step-TD-Prediction"><span class="nav-number">2.6.1.</span> <span class="nav-text">n-step TD Prediction</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#n-step-Sarsa"><span class="nav-number">2.6.2.</span> <span class="nav-text">n-step Sarsa</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#n-step-Off-policy-Learning"><span class="nav-number">2.6.3.</span> <span class="nav-text">n-step Off-policy Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Per-decision-Methods-with-Control-Variates"><span class="nav-number">2.6.4.</span> <span class="nav-text">Per-decision Methods with Control Variates</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Off-policy-Learning-Without-Importance-Sampling-The-n-step-Tree-Backup-Algorithm"><span class="nav-number">2.6.5.</span> <span class="nav-text">Off-policy Learning Without Importance Sampling: The n-step Tree Backup Algorithm</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#A-Unifying-Algorithm-n-step-Q-sigma"><span class="nav-number">2.6.6.</span> <span class="nav-text">A Unifying Algorithm: n-step $Q(\sigma)$</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-6"><span class="nav-number">2.6.7.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-8-Planning-and-Learning-with-Tabular-Methods"><span class="nav-number">2.7.</span> <span class="nav-text">Chapter 8 Planning and Learning with Tabular Methods</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Models-and-Planning"><span class="nav-number">2.7.1.</span> <span class="nav-text">Models and Planning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Dyna-Integrated-Planning-Acting-and-Learning"><span class="nav-number">2.7.2.</span> <span class="nav-text">Dyna: Integrated Planning, Acting, and Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#When-the-Model-Is-Wrong"><span class="nav-number">2.7.3.</span> <span class="nav-text">When the Model Is Wrong</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Prioritized-Sweeping"><span class="nav-number">2.7.4.</span> <span class="nav-text">Prioritized Sweeping</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Expected-vs-Sample-Updates"><span class="nav-number">2.7.5.</span> <span class="nav-text">Expected vs. Sample Updates</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Trajectory-Sampling"><span class="nav-number">2.7.6.</span> <span class="nav-text">Trajectory Sampling</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Real-time-Dynamic-Programming"><span class="nav-number">2.7.7.</span> <span class="nav-text">Real-time Dynamic Programming</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Planning-at-Decision-Time"><span class="nav-number">2.7.8.</span> <span class="nav-text">Planning at Decision Time</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Heuristic-Search"><span class="nav-number">2.7.9.</span> <span class="nav-text">Heuristic Search</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Rollout-Algorithms"><span class="nav-number">2.7.10.</span> <span class="nav-text">Rollout Algorithms</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Monte-Carlo-Tree-Search"><span class="nav-number">2.7.11.</span> <span class="nav-text">Monte Carlo Tree Search</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-7"><span class="nav-number">2.7.12.</span> <span class="nav-text">Summary</span></a></li></ol></li></ol></li><li class="nav-item nav-level-1"><a class="nav-link" href="#Approximate-Solution-Methods"><span class="nav-number">3.</span> <span class="nav-text">Approximate Solution Methods</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-9-On-policy-Prediction-with-Approximation"><span class="nav-number">3.1.</span> <span class="nav-text">Chapter 9 On-policy Prediction with Approximation</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Value-function-Approximation"><span class="nav-number">3.1.1.</span> <span class="nav-text">Value-function Approximation</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Prediction-Objective-VE"><span class="nav-number">3.1.2.</span> <span class="nav-text">The Prediction Objective(VE)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Stochastic-gradient-and-Semi-gradient-Methods"><span class="nav-number">3.1.3.</span> <span class="nav-text">Stochastic-gradient and Semi-gradient Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Linear-Methods"><span class="nav-number">3.1.4.</span> <span class="nav-text">Linear Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Feature-Construction-for-Linear-Methods"><span class="nav-number">3.1.5.</span> <span class="nav-text">Feature Construction for Linear Methods</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Polynomials"><span class="nav-number">3.1.5.1.</span> <span class="nav-text">Polynomials</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Fourier-Basis"><span class="nav-number">3.1.5.2.</span> <span class="nav-text">Fourier Basis</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Coarse-Coding"><span class="nav-number">3.1.5.3.</span> <span class="nav-text">Coarse Coding</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Tile-Coding"><span class="nav-number">3.1.5.4.</span> <span class="nav-text">Tile Coding</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Radial-Basis-Functions"><span class="nav-number">3.1.5.5.</span> <span class="nav-text">Radial Basis Functions</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Selecting-Step-size-Parameters-Manually"><span class="nav-number">3.1.6.</span> <span class="nav-text">Selecting Step-size Parameters Manually</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Nonlinear-Function-Approximation-Artificial-Neural-Networks"><span class="nav-number">3.1.7.</span> <span class="nav-text">Nonlinear Function Approximation: Artificial Neural Networks</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Least-Squares-TD"><span class="nav-number">3.1.8.</span> <span class="nav-text">Least-Squares TD</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Memory-based-Function-Approximation"><span class="nav-number">3.1.9.</span> <span class="nav-text">Memory-based Function Approximation</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Kernel-based-Function-Approximation"><span class="nav-number">3.1.10.</span> <span class="nav-text">Kernel-based Function Approximation</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Looking-Deeper-at-On-policy-Learning-Interest-and-Emphasis"><span class="nav-number">3.1.11.</span> <span class="nav-text">Looking Deeper at On-policy Learning: Interest and Emphasis</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-8"><span class="nav-number">3.1.12.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-10-On-policy-Control-with-Approximation"><span class="nav-number">3.2.</span> <span class="nav-text">Chapter 10 On-policy Control with Approximation</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Episodic-Semi-gradient-Control"><span class="nav-number">3.2.1.</span> <span class="nav-text">Episodic Semi-gradient Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Semi-gradient-n-step-Sarsa"><span class="nav-number">3.2.2.</span> <span class="nav-text">Semi-gradient n-step Sarsa</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Average-Reward-A-New-Problem-Setting-for-Continuing-Tasks"><span class="nav-number">3.2.3.</span> <span class="nav-text">Average Reward: A New Problem Setting for Continuing Tasks</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Deprecating-the-Discounted-Setting"><span class="nav-number">3.2.4.</span> <span class="nav-text">Deprecating the Discounted Setting</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Differential-Semi-gradient-n-step-Sarsa"><span class="nav-number">3.2.5.</span> <span class="nav-text">Differential Semi-gradient n-step Sarsa</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-9"><span class="nav-number">3.2.6.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-11-Off-policy-Methods-with-Approximation"><span class="nav-number">3.3.</span> <span class="nav-text">Chapter 11 Off-policy Methods with Approximation</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Semi-gradient-Methods"><span class="nav-number">3.3.1.</span> <span class="nav-text">Semi-gradient Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Examples-of-Off-policy-Divergence"><span class="nav-number">3.3.2.</span> <span class="nav-text">Examples of Off-policy Divergence</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Deadly-Triad"><span class="nav-number">3.3.3.</span> <span class="nav-text">The Deadly Triad</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Linear-Value-function-Geometry"><span class="nav-number">3.3.4.</span> <span class="nav-text">Linear Value-function Geometry</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Gradient-Descent-in-the-Bellman-Error"><span class="nav-number">3.3.5.</span> <span class="nav-text">Gradient Descent in the Bellman Error</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Bellman-Error-is-Not-Learnable"><span class="nav-number">3.3.6.</span> <span class="nav-text">The Bellman Error is Not Learnable</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Gradient-TD-Methods"><span class="nav-number">3.3.7.</span> <span class="nav-text">Gradient-TD Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Emphatic-TD-Methods"><span class="nav-number">3.3.8.</span> <span class="nav-text">Emphatic-TD Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Reducing-Variance"><span class="nav-number">3.3.9.</span> <span class="nav-text">Reducing Variance</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-10"><span class="nav-number">3.3.10.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-12-Eligibility-Traces"><span class="nav-number">3.4.</span> <span class="nav-text">Chapter 12 Eligibility Traces</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#The-lambda-return"><span class="nav-number">3.4.1.</span> <span class="nav-text">The $\lambda$-return</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#TD-lambda"><span class="nav-number">3.4.2.</span> <span class="nav-text">TD($\lambda$)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#n-step-Truncated-lambda-return-Methods"><span class="nav-number">3.4.3.</span> <span class="nav-text">n-step Truncated $\lambda$-return Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Redoing-Updates-Online-lambda-return-Algorithm"><span class="nav-number">3.4.4.</span> <span class="nav-text">Redoing Updates: Online $\lambda$-return Algorithm</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#True-Online-TD-lambda"><span class="nav-number">3.4.5.</span> <span class="nav-text">True Online TD($\lambda$)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Dutch-Traces-in-Monte-Carlo-Learning"><span class="nav-number">3.4.6.</span> <span class="nav-text">Dutch Traces in Monte Carlo Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Sarsa-lambda"><span class="nav-number">3.4.7.</span> <span class="nav-text">Sarsa($\lambda$)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Variable-lambda-and-gamma"><span class="nav-number">3.4.8.</span> <span class="nav-text">Variable $\lambda$ and $\gamma$</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Off-policy-Traces-with-Control-Variates"><span class="nav-number">3.4.9.</span> <span class="nav-text">Off-policy Traces with Control Variates</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Watkins’s-Q-lambda-to-Tree-Backup-lambda"><span class="nav-number">3.4.10.</span> <span class="nav-text">Watkins’s Q($\lambda$) to Tree-Backup( $\lambda$)</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Stable-Off-policy-Methods-with-Traces"><span class="nav-number">3.4.11.</span> <span class="nav-text">Stable Off-policy Methods with Traces</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Implementation-Issues"><span class="nav-number">3.4.12.</span> <span class="nav-text">Implementation Issues</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Conclusions"><span class="nav-number">3.4.13.</span> <span class="nav-text">Conclusions</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-13-Policy-Gradient-Methods"><span class="nav-number">3.5.</span> <span class="nav-text">Chapter 13 Policy Gradient Methods</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Policy-Approximation-and-its-Advantages"><span class="nav-number">3.5.1.</span> <span class="nav-text">Policy Approximation and its Advantages</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Policy-Gradient-Theorem"><span class="nav-number">3.5.2.</span> <span class="nav-text">The Policy Gradient Theorem</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#REINFORCE-Monte-Carlo-Policy-Gradient"><span class="nav-number">3.5.3.</span> <span class="nav-text">REINFORCE: Monte Carlo Policy Gradient</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#REINFORCE-with-Baseline"><span class="nav-number">3.5.4.</span> <span class="nav-text">REINFORCE with Baseline</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Actor–Critic-Methods"><span class="nav-number">3.5.5.</span> <span class="nav-text">Actor–Critic Methods</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Policy-Gradient-for-Continuing-Problems"><span class="nav-number">3.5.6.</span> <span class="nav-text">Policy Gradient for Continuing Problems</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Policy-Parameterization-for-Continuous-Actions"><span class="nav-number">3.5.7.</span> <span class="nav-text">Policy Parameterization for Continuous Actions</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-11"><span class="nav-number">3.5.8.</span> <span class="nav-text">Summary</span></a></li></ol></li></ol></li><li class="nav-item nav-level-1"><a class="nav-link" href="#Looking-Deeper"><span class="nav-number">4.</span> <span class="nav-text">Looking Deeper</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-14-Psychology"><span class="nav-number">4.1.</span> <span class="nav-text">Chapter 14 Psychology</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Prediction-and-Control"><span class="nav-number">4.1.1.</span> <span class="nav-text">Prediction and Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Classical-Conditioning"><span class="nav-number">4.1.2.</span> <span class="nav-text">Classical Conditioning</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Blocking-and-Higher-order-Conditioning"><span class="nav-number">4.1.2.1.</span> <span class="nav-text">Blocking and Higher-order Conditioning</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#The-Rescorla–Wagner-Model"><span class="nav-number">4.1.2.2.</span> <span class="nav-text">The Rescorla–Wagner Model</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#The-TD-Model"><span class="nav-number">4.1.2.3.</span> <span class="nav-text">The TD Model</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#TD-Model-Simulations"><span class="nav-number">4.1.2.4.</span> <span class="nav-text">TD Model Simulations</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Instrumental-Conditioning"><span class="nav-number">4.1.3.</span> <span class="nav-text">Instrumental Conditioning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Delayed-Reinforcement"><span class="nav-number">4.1.4.</span> <span class="nav-text">Delayed Reinforcement</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Cognitive-Maps"><span class="nav-number">4.1.5.</span> <span class="nav-text">Cognitive Maps</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Habitual-and-Goal-directed-Behavior"><span class="nav-number">4.1.6.</span> <span class="nav-text">Habitual and Goal-directed Behavior</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-12"><span class="nav-number">4.1.7.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-15-Neuroscience"><span class="nav-number">4.2.</span> <span class="nav-text">Chapter 15 Neuroscience</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Neuroscience-Basics"><span class="nav-number">4.2.1.</span> <span class="nav-text">Neuroscience Basics</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Reward-Signals-Reinforcement-Signals-Values-and-Prediction-Errors"><span class="nav-number">4.2.2.</span> <span class="nav-text">Reward Signals, Reinforcement Signals, Values, and Prediction Errors</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Reward-Prediction-Error-Hypothesis"><span class="nav-number">4.2.3.</span> <span class="nav-text">The Reward Prediction Error Hypothesis</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Dopamine"><span class="nav-number">4.2.4.</span> <span class="nav-text">Dopamine</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Experimental-Support-for-the-Reward-Prediction-Error-Hypothesis"><span class="nav-number">4.2.5.</span> <span class="nav-text">Experimental Support for the Reward Prediction Error Hypothesis</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#TD-Error-Dopamine-Correspondence"><span class="nav-number">4.2.6.</span> <span class="nav-text">TD Error/Dopamine Correspondence</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Neural-Actor–Critic"><span class="nav-number">4.2.7.</span> <span class="nav-text">Neural Actor–Critic</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Actor-and-Critic-Learning-Rules"><span class="nav-number">4.2.8.</span> <span class="nav-text">Actor and Critic Learning Rules</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Hedonistic-Neurons"><span class="nav-number">4.2.9.</span> <span class="nav-text">Hedonistic Neurons</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Collective-Reinforcement-Learning"><span class="nav-number">4.2.10.</span> <span class="nav-text">Collective Reinforcement Learning</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Model-based-Methods-in-the-Brain"><span class="nav-number">4.2.11.</span> <span class="nav-text">Model-based Methods in the Brain</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Addiction"><span class="nav-number">4.2.12.</span> <span class="nav-text">Addiction</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Summary-13"><span class="nav-number">4.2.13.</span> <span class="nav-text">Summary</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-16-Applications-and-Case-Studies"><span class="nav-number">4.3.</span> <span class="nav-text">Chapter 16 Applications and Case Studies</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#TD-Gammon"><span class="nav-number">4.3.1.</span> <span class="nav-text">TD-Gammon</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Samuel’s-Checkers-Player"><span class="nav-number">4.3.2.</span> <span class="nav-text">Samuel’s Checkers Player</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Watson’s-Daily-Double-Wagering"><span class="nav-number">4.3.3.</span> <span class="nav-text">Watson’s Daily-Double Wagering</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Optimizing-Memory-Control"><span class="nav-number">4.3.4.</span> <span class="nav-text">Optimizing Memory Control</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Human-level-Video-Game-Play"><span class="nav-number">4.3.5.</span> <span class="nav-text">Human-level Video Game Play</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Mastering-the-Game-of-Go"><span class="nav-number">4.3.6.</span> <span class="nav-text">Mastering the Game of Go</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#AlphaGo"><span class="nav-number">4.3.6.1.</span> <span class="nav-text">AlphaGo</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#AlphaGo-Zero"><span class="nav-number">4.3.6.2.</span> <span class="nav-text">AlphaGo Zero</span></a></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Personalized-Web-Services"><span class="nav-number">4.3.7.</span> <span class="nav-text">Personalized Web Services</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Thermal-Soaring"><span class="nav-number">4.3.8.</span> <span class="nav-text">Thermal Soaring</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#Chapter-17-Frontiers"><span class="nav-number">4.4.</span> <span class="nav-text">Chapter 17 Frontiers</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#General-Value-Functions-and-Auxiliary-Tasks"><span class="nav-number">4.4.1.</span> <span class="nav-text">General Value Functions and Auxiliary Tasks</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Temporal-Abstraction-via-Options"><span class="nav-number">4.4.2.</span> <span class="nav-text">Temporal Abstraction via Options</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Observations-and-State"><span class="nav-number">4.4.3.</span> <span class="nav-text">Observations and State</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Designing-Reward-Signals"><span class="nav-number">4.4.4.</span> <span class="nav-text">Designing Reward Signals</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Remaining-Issues"><span class="nav-number">4.4.5.</span> <span class="nav-text">Remaining Issues</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#The-Future-of-Artificial-Intelligence"><span class="nav-number">4.4.6.</span> <span class="nav-text">The Future of Artificial Intelligence</span></a></li></ol></li></ol></li></ol></div>
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