Efficiently Solving Discounted MDPs with Predictions on Transition Matrices

• URL: http://arxiv.org/abs/2502.15345v1
• Date: Fri, 21 Feb 2025 09:59:46 GMT
• Title: Efficiently Solving Discounted MDPs with Predictions on Transition Matrices
• Authors: Lixing Lyu, Jiashuo Jiang, Wang Chi Cheung,
• Abstract summary: We study Discounted Markov Decision Processes (DMDPs) under a generative model.<n>We propose a novel framework to investigate how a prediction on the transition matrix can enhance the sample efficiency in solving DMDPs.
• Score: 6.199300239433395
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study infinite-horizon Discounted Markov Decision Processes (DMDPs) under a generative model. Motivated by the Algorithm with Advice framework Mitzenmacher and Vassilvitskii 2022, we propose a novel framework to investigate how a prediction on the transition matrix can enhance the sample efficiency in solving DMDPs and improve sample complexity bounds. We focus on the DMDPs with $N$ state-action pairs and discounted factor $\gamma$. Firstly, we provide an impossibility result that, without prior knowledge of the prediction accuracy, no sampling policy can compute an $\epsilon$-optimal policy with a sample complexity bound better than $\tilde{O}((1-\gamma)^{-3} N\epsilon^{-2})$, which matches the state-of-the-art minimax sample complexity bound with no prediction. In complement, we propose an algorithm based on minimax optimization techniques that leverages the prediction on the transition matrix. Our algorithm achieves a sample complexity bound depending on the prediction error, and the bound is uniformly better than $\tilde{O}((1-\gamma)^{-4} N \epsilon^{-2})$, the previous best result derived from convex optimization methods. These theoretical findings are further supported by our numerical experiments.

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