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We study online learning in episodic constrained Markov decision processes(CMDPs), where the goal of the learner is to collect as much reward as possibleover the episodes, while guaranteeing that some long-term constraints aresatisfied during the learning process. Rewards and constraints can be selectedeither stochastically or adversarially, and the transition function is notknown to the learner. While online learning in classical unconstrained MDPs hasreceived considerable attention over the last years, the setting of CMDPs isstill largely unexplored. This is surprising, since in real-world applications,such as, e.g., autonomous driving, automated bidding, and recommender systems,there are usually additional constraints and specifications that an agent hasto obey during the learning process. In this paper, we provide the firstbest-of-both-worlds algorithm for CMDPs with long-term constraints. Ouralgorithm is capable of handling settings in which rewards and constraints areselected either stochastically or adversarially, without requiring anyknowledge of the underling process. Moreover, our algorithm matchesstate-of-the-art regret and constraint violation bounds for settings in whichconstraints are selected stochastically, while it is the first to provideguarantees in the case in which they are chosen adversarially.

A Best-of-Both-Worlds Algorithm for Constrained MDPs with Long-Term Constraints