Batch Value-function Approximation with Only Realizability
This addresses a long-standing challenge in batch RL for researchers and practitioners, offering a novel solution that overcomes prior negative evidence, though it is incremental in requiring stronger data assumptions.
The paper tackles the problem of batch reinforcement learning from a polynomial-sized dataset using only a realizable function class, breaking a previous hardness conjecture. The proposed BVFT algorithm achieves this under a stronger notion of exploratory data, though specific numerical results are not provided.
We make progress in a long-standing problem of batch reinforcement learning (RL): learning $Q^\star$ from an exploratory and polynomial-sized dataset, using a realizable and otherwise arbitrary function class. In fact, all existing algorithms demand function-approximation assumptions stronger than realizability, and the mounting negative evidence has led to a conjecture that sample-efficient learning is impossible in this setting (Chen and Jiang, 2019). Our algorithm, BVFT, breaks the hardness conjecture (albeit under a stronger notion of exploratory data) via a tournament procedure that reduces the learning problem to pairwise comparison, and solves the latter with the help of a state-action partition constructed from the compared functions. We also discuss how BVFT can be applied to model selection among other extensions and open problems.