Polynomial-Time Approximability of Constrained Reinforcement Learning

• URL: http://arxiv.org/abs/2502.07764v1
• Date: Tue, 11 Feb 2025 18:47:53 GMT
• Title: Polynomial-Time Approximability of Constrained Reinforcement Learning
• Authors: Jeremy McMahan,
• Abstract summary: We study the computational complexity of approximating general constrained Markov decision processes. Our contribution is the design of a time $(0,epsilon)$-additive approximation for finding optimal constrained policies.
• Score: 1.223779595809275
• License:
• Abstract: We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as $P \neq NP$. The generality of our approach results in answers to several long-standing open complexity questions in the constrained reinforcement learning literature. Specifically, we are the first to prove polynomial-time approximability for the following settings: policies under chance constraints, deterministic policies under multiple expectation constraints, policies under non-homogeneous constraints (i.e., constraints of different types), and policies under constraints for continuous-state processes.

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