Simultaneously Learning Stochastic and Adversarial Episodic MDPs with Known Transition

• URL: http://arxiv.org/abs/2006.05606v2
• Date: Mon, 2 Nov 2020 07:21:00 GMT
• Title: Simultaneously Learning Stochastic and Adversarial Episodic MDPs with Known Transition
• Authors: Tiancheng Jin, Haipeng Luo
• Abstract summary: We develop the first algorithm with a best-of-both-worlds'' guarantee. It achieves $mathcalO(log T)$ regret when the losses are adversarial. More generally, it achieves $tildemathcalO(sqrtC)$ regret in an intermediate setting.
• Score: 38.28925339231888
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work studies the problem of learning episodic Markov Decision Processes with known transition and bandit feedback. We develop the first algorithm with a ``best-of-both-worlds'' guarantee: it achieves $\mathcal{O}(log T)$ regret when the losses are stochastic, and simultaneously enjoys worst-case robustness with $\tilde{\mathcal{O}}(\sqrt{T})$ regret even when the losses are adversarial, where $T$ is the number of episodes. More generally, it achieves $\tilde{\mathcal{O}}(\sqrt{C})$ regret in an intermediate setting where the losses are corrupted by a total amount of $C$. Our algorithm is based on the Follow-the-Regularized-Leader method from Zimin and Neu (2013), with a novel hybrid regularizer inspired by recent works of Zimmert et al. (2019a, 2019b) for the special case of multi-armed bandits. Crucially, our regularizer admits a non-diagonal Hessian with a highly complicated inverse. Analyzing such a regularizer and deriving a particular self-bounding regret guarantee is our key technical contribution and might be of independent interest.

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