Near-Optimal Regret for Adversarial MDP with Delayed Bandit Feedback

TL;DR

This paper develops algorithms for reinforcement learning in adversarial episodic MDPs with unknown, changing delays in feedback, achieving near-optimal regret bounds that significantly improve over previous methods.

Contribution

It introduces the first algorithms that attain near-optimal  regret in adversarial MDPs with arbitrary, changing delays in feedback.

Findings

Achieved  regret bound proportional to  +D.

Improved regret bounds from  to near-optimal levels.

Demonstrated effectiveness in adversarial, delayed feedback scenarios.

Abstract

The standard assumption in reinforcement learning (RL) is that agents observe feedback for their actions immediately. However, in practice feedback is often observed in delay. This paper studies online learning in episodic Markov decision process (MDP) with unknown transitions, adversarially changing costs, and unrestricted delayed bandit feedback. More precisely, the feedback for the agent in episode $k$ is revealed only in the end of episode $k + d^k$, where the delay $d^k$ can be changing over episodes and chosen by an oblivious adversary. We present the first algorithms that achieve near-optimal $\sqrt{K + D}$ regret, where $K$ is the number of episodes and $D = \sum_{k=1}^K d^k$ is the total delay, significantly improving upon the best known regret bound of $(K + D)^{2/3}$.