Minimax Optimal Regret Bound for Reinforcement Learning with Trajectory Feedback
Keywords: Reinforcement learning theory, regret analysis, trajectory feedback
TL;DR: We prove a nearly optimal regret bound for reinforcement learning with trajectory feedback.
Abstract: We study the reinforcement learning (RL) problem with trajectory feedback. The trajectory feedback based reinforcement learning problem, where the learner can only observe the accumulative noised reward along the trajectory, is particularly suitable for the practical scenarios where the agent suffers extensively from querying the reward in each single step. For a finite-horizon Markov Decision Process (MDP) with $S$ states, $A$ actions and a horizon length of $H$, we develop an algorithm that enjoys an optimal regret of $\tilde{O}\left(\sqrt{SAH^3K}\right)$ in $K$ episodes for sufficiently large $K$. To achieve this, our technical contributions are two-fold: (1) we incorporate reinforcement learning with linear bandits problem to construct a tighter confidence region for the reward function; (2) we construct a reference transition model to better guide the exploration process.
Primary Area: learning theory
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Submission Number: 12876
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