Learning Sequential Decisions from Multiple Sources via Group-Robust Markov Decision Processes

• URL: http://arxiv.org/abs/2602.01825v1
• Date: Mon, 02 Feb 2026 08:58:55 GMT
• Title: Learning Sequential Decisions from Multiple Sources via Group-Robust Markov Decision Processes
• Authors: Mingyuan Xu, Zongqi Xia, Tianxi Cai, Doudou Zhou, Nian Si,
• Abstract summary: This paper aims to learn robust sequential decision-making policies from offline, multi-site datasets.<n>To model cross-site uncertainty, we study distributionally robust MDPs with a group-linear structure.<n>We introduce feature-wise (d-rectangular) uncertainty sets, which preserve tractable robust Bellman recursions while maintaining key cross-site structure.
• Score: 9.088701245020479
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We often collect data from multiple sites (e.g., hospitals) that share common structure but also exhibit heterogeneity. This paper aims to learn robust sequential decision-making policies from such offline, multi-site datasets. To model cross-site uncertainty, we study distributionally robust MDPs with a group-linear structure: all sites share a common feature map, and both the transition kernels and expected reward functions are linear in these shared features. We introduce feature-wise (d-rectangular) uncertainty sets, which preserve tractable robust Bellman recursions while maintaining key cross-site structure. Building on this, we then develop an offline algorithm based on pessimistic value iteration that includes: (i) per-site ridge regression for Bellman targets, (ii) feature-wise worst-case (row-wise minimization) aggregation, and (iii) a data-dependent pessimism penalty computed from the diagonals of the inverse design matrices. We further propose a cluster-level extension that pools similar sites to improve sample efficiency, guided by prior knowledge of site similarity. Under a robust partial coverage assumption, we prove a suboptimality bound for the resulting policy. Overall, our framework addresses multi-site learning with heterogeneous data sources and provides a principled approach to robust planning without relying on strong state-action rectangularity assumptions.

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