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Near-Optimal Regret Bounds for Multi-batch Reinforcement Learning
Zihan Zhang · Yuhang Jiang · Yuan Zhou · Xiangyang Ji

In this paper, we study the episodic reinforcement learning (RL) problem modeled by finite-horizon Markov Decision Processes (MDPs) with constraint on the number of batches. The multi-batch reinforcement learning framework, where the agent is required to provide a time schedule to update policy before everything, which is particularly suitable for the scenarios where the agent suffers extensively from changing the policy adaptively. Given a finite-horizon MDP with $S$ states, $A$ actions and planning horizon $H$, we design a computational efficient algorithm to achieve near-optimal regret of $\tilde{O}(\sqrt{SAH^3K\ln(1/\delta)})$\footnote{$\tilde{O}(\cdot)$ hides logarithmic terms of $(S,A,H,K)$} in $K$ episodes using $O\left(H+\log_2\log_2(K) \right)$ batches with confidence parameter $\delta$. To our best of knowledge, it is the first $\tilde{O}(\sqrt{SAH^3K})$ regret bound with $O(H+\log_2\log_2(K))$ batch complexity. Meanwhile, we show that to achieve $\tilde{O}(\mathrm{poly}(S,A,H)\sqrt{K})$ regret, the number of batches is at least $\Omega\left(H/\log_A(K)+ \log_2\log_2(K) \right)$, which matches our upper bound up to logarithmic terms.Our technical contribution are two-fold: 1) a near-optimal design scheme to explore over the unlearned states; 2) an computational efficient algorithm to explore certain directions with an approximated transition model.ion model.

Author Information

Zihan Zhang (Tsinghua University)
Yuhang Jiang (Department of Automation, Tsinghua University)
Yuan Zhou (University of Illinois, Urbana Champaign)
Xiangyang Ji (Tsinghua University)

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