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arXiv · 2410.24128

Q-learning for Quantile MDPs: A Decomposition, Performance, and Convergence Analysis

Jia Lin Hau·Erick Delage·Esther Derman·Mohammad Ghavamzadeh·Marek Petrik
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Abstract

In Markov decision processes (MDPs), quantile risk measures such as Value-at-Risk are a standard metric for modeling RL agents' preferences for certain outcomes. This paper proposes a new Q-learning algorithm for quantile optimization in MDPs with strong convergence and performance guarantees. The algorithm leverages a new, simple dynamic program (DP) decomposition for quantile MDPs. Compared with prior work, our DP decomposition requires neither known transition probabilities nor solving complex saddle point equations and serves as a suitable foundation for other model-free RL algorithms. Our numerical results in tabular domains show that our Q-learning algorithm converges to its DP variant and outperforms earlier algorithms.

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Jia Lin Hau, Erick Delage, Esther Derman, Mohammad Ghavamzadeh, Marek Petrik. 2024-10-31. Q-learning for Quantile MDPs: A Decomposition, Performance, and Convergence Analysis. https://arxiv.org/abs/2410.24128

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