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This paper advances distributionally robust reinforcement learning by establishing finite-time convergence guarantees for single-trajectory Q-learning with linear function approximation. The authors resolve estimation challenges in the $\chi^2$ uncertainty framework through a variational reformulation and blockwise frozen-target scheme, validated via neural network experiments on continuous-state control tasks. This work is significant for improving policy robustness in real-world deployment scenarios where training data distributions may diverge from operational environments.
Finite-Time Convergence of Single-Trajectory Chi-Square Robust Q-Learning With Linear Function Approximation
arXiv:2510.01721v4 Announce Type: replace Abstract: Distributionally robust reinforcement learning seeks policies that remain effective when the deployment environment differs from the one that generated the training data. We study model-free robust Q-learning with $\chi^2$ uncertainty sets and linear function approximation, using data from a single trajectory of an unknown nominal MDP. Evaluating the $\chi^2$ robust Bellman target introduces the square root of a conditional second moment, which cannot be estimated unbiasedly from one transition, while the projected robust Bellman operator need not be contractive. We address these obstacles through a variational reformulation of the robust Bellman target and a blockwise frozen-target scheme, and establish a finite-time error bound relative to the optimal robust Q-function for every $\gamma\in(0,1)$. A neural-network experiment illustrates how the variational target can be used in a continuous-state nonlinear-control task.
Abstract:Distributionally robust reinforcement learning seeks policies that remain effective when the deployment environment differs from the one that generated the training data. We study model-free robust Q-learning with $\chi^2$ uncertainty sets and linear function approximation, using data from a single trajectory of an unknown nominal MDP. Evaluating the $\chi^2$ robust Bellman target introduces the square root of a conditional second moment, which cannot be estimated unbiasedly from one transition, while the projected robust Bellman operator need not be contractive. We address these obstacles through a variational reformulation of the robust Bellman target and a blockwise frozen-target scheme, and establish a finite-time error bound relative to the optimal robust Q-function for every $\gamma\in(0,1)$. A neural-network experiment illustrates how the variational target can be used in a continuous-state nonlinear-control task.
Machine Learning (cs.LG)
arXiv:2510.01721 [cs.LG]
(or arXiv:2510.01721v4 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2510.01721 Focus to learn more arXiv-issued DOI via DataCite
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