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Reinforcement Learning: Theory and Algorithms

Reinforcement Learning: Theory and AlgorithmsAlekh AgarwalNan JiangSham M. KakadeWen SunJanuary 31, 2022 WORKING DRAFT:Please any typos or errors you appreciate it!iiContents1 Fundamentals31 Markov Decision (Infinite-Horizon) Markov Decision Processes .. objective, policies, and values .. Consistency Equations for Stationary Policies .. Optimality Equations .. Markov Decision Processes .. Complexity .. Iteration .. Iteration .. Iteration for Finite Horizon MDPs .. Linear Programming Approach .. Complexity and Sampling Models .. : Advantages and The Performance Difference Lemma .. Remarks and Further Reading ..202 Sample Complexity with a Generative : a naive model-based approach .. Sample Complexity .. Optimal Sample Complexity (and the Model Based Approach) .. Discounted Case .. Horizon Setting .. Lemmas .. the proof .. and Effective Horizon Dependencies .. Remarks and Further Readings ..293 Linear Bellman Linear Bellman Completeness Condition.

In reinforcement learning, the interactions between the agent and the environment are often described by an infinite-horizon, discounted Markov Decision Process (MDP) M= (S;A;P;r;; ), specified by: •A state space S, which may be finite or infinite. For mathematical convenience, we will assume that Sis finite or countably infinite.

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