Model-based RL in Contextual Decision Processes: PAC bounds and Exponential Improvements over Model-free Approaches

Wen Sun, Nan Jiang, Akshay Krishnamurthy, Alekh Agarwal, John Langford

Research output: Contribution to journalConference articlepeer-review


We study the sample complexity of model-based reinforcement learning (henceforth RL) in general contextual decision processes that require strategic exploration to find a near-optimal policy. We design new algorithms for RL with a generic model class and analyze their statistical properties. Our algorithms have sample complexity governed by a new structural parameter called the witness rank, which we show to be small in several settings of interest, including factored MDPs. We also show that the witness rank is never larger than the recently proposed Bellman rank parameter governing the sample complexity of the model-free algorithm OLIVE (Jiang et al., 2017), the only other provably sample-efficient algorithm for global exploration at this level of generality. Focusing on the special case of factored MDPs, we prove an exponential lower bound for a general class of model-free approaches, including OLIVE, which, when combined with our algorithmic results, demonstrates exponential separation between model-based and model-free RL in some rich-observation settings.

Original languageEnglish (US)
Pages (from-to)2898-2933
Number of pages36
JournalProceedings of Machine Learning Research
StatePublished - 2019
Event32nd Conference on Learning Theory, COLT 2019 - Phoenix, United States
Duration: Jun 25 2019Jun 28 2019


  • Reinforcement Learning
  • exploration

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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