Concave Utility Reinforcement Learning with Zero-Constraint Violations

• URL: http://arxiv.org/abs/2109.05439v3
• Date: Fri, 17 Nov 2023 02:20:40 GMT
• Title: Concave Utility Reinforcement Learning with Zero-Constraint Violations
• Authors: Mridul Agarwal, Qinbo Bai, Vaneet Aggarwal
• Abstract summary: We consider the problem of concave utility reinforcement learning (CURL) with convex constraints. We propose a model-based learning algorithm that also achieves zero constraint violations.
• Score: 43.29210413964558
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of tabular infinite horizon concave utility reinforcement learning (CURL) with convex constraints. For this, we propose a model-based learning algorithm that also achieves zero constraint violations. Assuming that the concave objective and the convex constraints have a solution interior to the set of feasible occupation measures, we solve a tighter optimization problem to ensure that the constraints are never violated despite the imprecise model knowledge and model stochasticity. We use Bellman error-based analysis for tabular infinite-horizon setups which allows analyzing stochastic policies. Combining the Bellman error-based analysis and tighter optimization equation, for $T$ interactions with the environment, we obtain a high-probability regret guarantee for objective which grows as $\Tilde{O}(1/\sqrt{T})$, excluding other factors. The proposed method can be applied for optimistic algorithms to obtain high-probability regret bounds and also be used for posterior sampling algorithms to obtain a loose Bayesian regret bounds but with significant improvement in computational complexity.

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