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In this paper, we consider reinforcement learning of Markov DecisionProcesses (MDP) with peak constraints, where an agent chooses a policy tooptimize an objective and at the same time satisfy additional constraints. Theagent has to take actions based on the observed states, reward outputs, andconstraint-outputs, without any knowledge about the dynamics, reward functions,and/or the knowledge of the constraint-functions. We introduce a game theoreticapproach to construct reinforcement learning algorithms where the agentmaximizes an unconstrained objective that depends on the simulated action ofthe minimizing opponent which acts on a finite set of actions and the outputdata of the constraint functions (rewards). We show that the policies obtainedfrom maximin Q-learning converge to the optimal policies. To the best of ourknowledge, this is the first time learning algorithms guarantee convergence tooptimal stationary policies for the MDP problem with peak constraints for bothdiscounted and expected average rewards.

Reinforcement Learning of Markov Decision Processes with Peak Constraints