Learning Sequential Decisions from Multiple Sources via Group-Robust Markov Decision Processes
Mingyuan Xu, Zongqi Xia, Tianxi Cai, Doudou Zhou, Nian Si
Learning a common policy from multiple source environments requires accounting for cross-source heterogeneity, and the offline setting introduces an additional challenge of limited data coverage. We formulate this problem as a distributionally robust Markov decision process under a shared linear MDP representation with source-specific transition and reward components. The uncertainty set is constructed through feature-wise mixtures of these components, yielding a $d$-rectangular structure that captures cross-source heterogeneity and admits a robust Bellman recursion. Building on this formulation, we develop Group-Robust Pessimistic Value Iteration (GR-PEVI), an offline policy-learning algorithm that combines feature-wise worst-case aggregation with a data-dependent pessimism penalty. Under a robust partial coverage condition, we establish finite-sample suboptimality guarantees for GR-PEVI and extend the analysis to clustered sources, characterizing the trade-off between the statistical gain from pooling similar sources and the approximation error induced by within-cluster heterogeneity. Simulation studies demonstrate the effectiveness of GR-PEVI, with empirical behavior consistent with the theoretical analysis. We apply GR-PEVI to a multi-source electronic health record study of multiple sclerosis treatment decisions to illustrate its use in a clinical setting.
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