## Abstract

Existing online learning algorithms for adversarial Markov Decision Processes achieve O(√T) regret after T rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the transition function has to be fixed. This is because it has been shown that adversarial transition functions make no-regret learning impossible. Despite such impossibility results, in this work, we develop algorithms that can handle both adversarial losses and adversarial transitions, with regret increasing smoothly in the degree of maliciousness of the adversary. More concretely, we first propose an algorithm that enjoys O(√T + C

measures how adversarial the transition functions are and can be at most O(T) . While this algorithm itself requires knowledge of C

) regret up to logarithmic factors, where U is some standard gap-dependent coefficient and C

^{P}) regret, up to logarithmic factors, where C^{P}measures how adversarial the transition functions are and can be at most O(T) . While this algorithm itself requires knowledge of C

^{P}, we further develop a black-box reduction approach that removes this requirement. Moreover, we also show that further refinements of the algorithm not only maintains the same regret bound, but also simultaneously adapts to easier environments (where losses are generated in a certain stochastically constrained manner as in [Jin et al. 2021]) and achieves O(U + √UC^{L }+ C^{P}) regret up to logarithmic factors, where U is some standard gap-dependent coefficient and C

^{L }is the amount of corruption on losses.Original language | English |
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Title of host publication | 37th Conference on Neural Information Processing Systems (NeurIPS 2023) |

Publication status | Published - 2023 |

## Keywords

- Machine Learning
- Reinforcement Learning
- Adversarial Reinforcement Learning
- Learning Theory
- No-Regret
- Reinforcement Learning with Corruptions