Generalized Linear Markov Decision Process

• URL: http://arxiv.org/abs/2506.00818v1
• Date: Sun, 01 Jun 2025 03:50:41 GMT
• Title: Generalized Linear Markov Decision Process
• Authors: Sinian Zhang, Kaicheng Zhang, Ziping Xu, Tianxi Cai, Doudou Zhou,
• Abstract summary: Generalized Linear MDP (GLMDP) framework models rewards using generalized linear models (GLMs)<n>We develop two offline RL algorithms: Generalized Pessimistic Value Iteration (GPEVI) and a semi-supervised variant (SS-GPEVI)<n>Our algorithms achieve theoretical guarantees on policy suboptimality and demonstrate improved sample efficiency in settings where reward labels are expensive or limited.
• Score: 9.219628236765933
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The linear Markov Decision Process (MDP) framework offers a principled foundation for reinforcement learning (RL) with strong theoretical guarantees and sample efficiency. However, its restrictive assumption-that both transition dynamics and reward functions are linear in the same feature space-limits its applicability in real-world domains, where rewards often exhibit nonlinear or discrete structures. Motivated by applications such as healthcare and e-commerce, where data is scarce and reward signals can be binary or count-valued, we propose the Generalized Linear MDP (GLMDP) framework-an extension of the linear MDP framework-that models rewards using generalized linear models (GLMs) while maintaining linear transition dynamics. We establish the Bellman completeness of GLMDPs with respect to a new function class that accommodates nonlinear rewards and develop two offline RL algorithms: Generalized Pessimistic Value Iteration (GPEVI) and a semi-supervised variant (SS-GPEVI) that utilizes both labeled and unlabeled trajectories. Our algorithms achieve theoretical guarantees on policy suboptimality and demonstrate improved sample efficiency in settings where reward labels are expensive or limited.

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