A Covering Framework for Offline POMDPs Learning using Belief Space Metric
This work addresses sample efficiency challenges in offline reinforcement learning for partially observable environments, offering a novel theoretical framework that could benefit researchers and practitioners in AI and robotics, though it is incremental in refining existing methods.
The paper tackles the problem of off-policy evaluation in partially observable Markov decision processes, where hidden states exacerbate errors, by introducing a covering analysis framework that leverages the belief space metric to relax coverage assumptions and derive error bounds that mitigate exponential blow-ups in horizon and memory length, yielding tighter bounds for algorithms like double sampling Bellman error minimization and memory-based future dependent value functions.
In off policy evaluation (OPE) for partially observable Markov decision processes (POMDPs), an agent must infer hidden states from past observations, which exacerbates both the curse of horizon and the curse of memory in existing OPE methods. This paper introduces a novel covering analysis framework that exploits the intrinsic metric structure of the belief space (distributions over latent states) to relax traditional coverage assumptions. By assuming value relevant functions are Lipschitz continuous in the belief space, we derive error bounds that mitigate exponential blow ups in horizon and memory length. Our unified analysis technique applies to a broad class of OPE algorithms, yielding concrete error bounds and coverage requirements expressed in terms of belief space metrics rather than raw history coverage. We illustrate the improved sample efficiency of this framework via case studies: the double sampling Bellman error minimization algorithm, and the memory based future dependent value functions (FDVF). In both cases, our coverage definition based on the belief space metric yields tighter bounds.