Learning Adversarial Markov Decision Processes with Delayed Feedback

TL;DR

This paper develops algorithms for reinforcement learning in Markov decision processes where feedback on actions is delayed arbitrarily, achieving near-optimal regret bounds in both full-information and bandit feedback scenarios.

Contribution

It introduces the first algorithms for MDPs with delayed feedback, providing regret bounds that adapt to total delay and work under adversarial and stochastic costs.

Findings

Achieves near-optimal regret of √(K+D) with full information.

Proves regret bounds of √(K+D) in stochastic bandit setting.

Establishes (K+D)^{2/3} regret in general bandit case.

Abstract

Reinforcement learning typically assumes that agents observe feedback for their actions immediately, but in many real-world applications (like recommendation systems) feedback is observed in delay. This paper studies online learning in episodic Markov decision processes (MDPs) with unknown transitions, adversarially changing costs and unrestricted delayed feedback. That is, the costs and trajectory of episode $k$ are revealed to the learner only in the end of episode $k + d^k$, where the delays $d^k$ are neither identical nor bounded, and are chosen by an oblivious adversary. We present novel algorithms based on policy optimization that achieve near-optimal high-probability regret of $\sqrt{K + D}$ under full-information feedback, where $K$ is the number of episodes and $D = \sum_{k} d^k$ is the total delay. Under bandit feedback, we prove similar $\sqrt{K + D}$ regret assuming the costs are stochastic, and $(K + D)^{2/3}$ regret in the general case. We are the first to consider regret minimization in the important setting of MDPs with delayed feedback.