Bellman Eluder Dimension: New Rich Classes of RL Problems, and Sample-Efficient Algorithms
By Chi Jin, Qinghua Liu, Sobhan Miryoosefi. 2021
261 citations recorded by the source corpus.
Finding the minimal structural assumptions that empower sample-efficient learning is one of the most important research directions in Reinforcement Learning (RL). This paper advances our understanding of this fundamental question by introducing a new complexity measure -- Bellman Eluder (BE) dimension. We show that the family of RL problems of low BE dimension is remarkably rich, which subsumes a vast majority of existing tractable RL problems including but not limited to tabular MDPs, linear MDPs, reactive POMDPs, low Bellman rank problems as well as low Eluder dimension problems. This paper further designs a new optimization-based algorithm -- GOLF, and reanalyzes a hypothesis elimination-based algorithm -- OLIVE (proposed in Jiang et al., 2017). We prove that both algorithms learn the near-optimal policies of low BE dimension problems in a number of samples that is polynomial in all relevant parameters, but independent of the size of state-action space. Our regret and sample complexity results match or improve the best existing results for several well-known subclasses of low BE dimension problems.
Subfields: Artificial Intelligence
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Citations in the corpus
- Towards Continual Reinforcement Learning: A Review and Perspectives (2020, background): “Similarly, recent work has achieved proveable generalization for problems with low Bellman Eluder dimensions (Jin et al., 2021) and low dimensional underlying causal structure (Huang et al.”