Learning Adversarial Markov Decision Processes with Delayed Feedback
It addresses the challenge of delayed feedback in real-world applications like recommendation systems, presenting the first regret minimization results for this setting, which is a novel but incremental extension of existing MDP frameworks.
This paper tackles the problem of reinforcement learning in Markov decision processes with adversarially changing costs and unrestricted delayed feedback, achieving near-optimal regret bounds of √(K + D) under full-information feedback and similar or (K + D)^{2/3} under bandit feedback.
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.