Is Q-learning provably efficient?

Chi Jin, Zeyuan Allen-Zhu, Sebastien Bubeck, Michael I. Jordan

Research output: Contribution to journalConference articlepeer-review

437 Scopus citations


Model-free reinforcement learning (RL) algorithms, such as Q-learning, directly parameterize and update value functions or policies without explicitly modeling the environment. They are typically simpler, more flexible to use, and thus more prevalent in modern deep RL than model-based approaches. However, empirical work has suggested that model-free algorithms may require more samples to learn [7, 22]. The theoretical question of “whether model-free algorithms can be made sample efficient” is one of the most fundamental questions in RL, and remains unsolved even in the basic scenario with finitely many states and actions. We prove that, in an episodic MDP setting, Q-learning with UCB exploration achieves regret Õ(H3SAT), where S and A are the numbers of states and actions, H is the number of steps per episode, and T is the total number of steps. This sample efficiency matches the optimal regret that can be achieved by any model-based approach, up to a single H factor. To the best of our knowledge, this is the first analysis in the model-free setting that establishes T regret without requiring access to a “simulator.”

Original languageEnglish (US)
Pages (from-to)4863-4873
Number of pages11
JournalAdvances in Neural Information Processing Systems
StatePublished - 2018
Externally publishedYes
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


Dive into the research topics of 'Is Q-learning provably efficient?'. Together they form a unique fingerprint.

Cite this