Learning Constrained Markov Decision Processes With Non-stationary Rewards and Constraints

• URL: http://arxiv.org/abs/2405.14372v2
• Date: Thu, 26 Sep 2024 13:23:54 GMT
• Title: Learning Constrained Markov Decision Processes With Non-stationary Rewards and Constraints
• Authors: Francesco Emanuele Stradi, Anna Lunghi, Matteo Castiglioni, Alberto Marchesi, Nicola Gatti,
• Abstract summary: In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining sublinear regret and sublinear constraint violation. We show that this negative result can be eased in CMDPs with non-stationary rewards and constraints, by providing algorithms whose performances smoothly degrade as non-stationarity increases.
• Score: 34.7178680288326
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In constrained Markov decision processes (CMDPs) with adversarial rewards and constraints, a well-known impossibility result prevents any algorithm from attaining both sublinear regret and sublinear constraint violation, when competing against a best-in-hindsight policy that satisfies constraints on average. In this paper, we show that this negative result can be eased in CMDPs with non-stationary rewards and constraints, by providing algorithms whose performances smoothly degrade as non-stationarity increases. Specifically, we propose algorithms attaining $\tilde{\mathcal{O}} (\sqrt{T} + C)$ regret and positive constraint violation under bandit feedback, where $C$ is a corruption value measuring the environment non-stationarity. This can be $\Theta(T)$ in the worst case, coherently with the impossibility result for adversarial CMDPs. First, we design an algorithm with the desired guarantees when $C$ is known. Then, in the case $C$ is unknown, we show how to obtain the same results by embedding such an algorithm in a general meta-procedure. This is of independent interest, as it can be applied to any non-stationary constrained online learning setting.

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