Behavior-Induced Mirror-Prox Temporal-Difference Learning for Faster Off-Policy Prediction

Computer Science > Artificial Intelligence [Submitted on 16 May 2026] Behavior-Induced Mirror-Prox Temporal-Difference Learning for Faster Off-Policy Prediction Xingguo Chen, Yuchen Shen, Shangdong Yang, Chao Li, Guang Yang, Wenhao Wang Gradient temporal-difference methods provide stable off-policy prediction with linear function approximation, but their practical performance is strongly affected by the geometry induced by the auxiliary-variable metric. Existing Mirror-Prox TD methods typically use the feature covariance metric, whereas hybrid TD methods suggest that behavior-policy transition information can provide a more informative update geometry. This paper proposes a behavior-induced Mirror-Prox temporal-difference method, called STHTD-MP, which replaces the covariance metric in the primal-dual saddle-point formulation with the symmetric part of the behavior-policy Bellman matrix. The method keeps a single learning rate for the primal and auxiliary variables and applies a Mirror-Prox prediction-correction step to the resulting hybrid saddle-point operator. We provide a formal convergence analysis for fixed-policy linear prediction under standard stochastic approximation assumptions: the behavior-induced metric is positive definite, the joint mean system is Hurwitz, boundedness follows from a Lyapunov argument, and the stochastic recursion converges by the ODE method. We further derive projected-oracle ergodic gap bounds and an exact mean-operator comparison with GTD2-MP based on the spectral radius of the deterministic Mirror-Prox error matrix. The analysis shows that STHTD-MP can have a smaller mean contraction factor than GTD2-MP when the behavior-induced metric improves the saddle-point geometry. Exact numerical mean-operator analysis on two-state, Random Walk, and Boyan Chain benchmarks supports this condition, while Baird's counterexample is identified as a singular boundary case where the strict assumptions fail. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2605.28849 [cs.AI]   (or arXiv:2605.28849v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2605.28849 Focus to learn more Submission history From: Xingguo Chen [view email] [v1] Sat, 16 May 2026 11:33:44 UTC (4,782 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-05 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)