Provably Efficient Reinforcement Learning via Surprise Bound

Hanlin Zhu, Ruosong Wang, Jason D. Lee

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


Value function approximation is important in modern reinforcement learning (RL) problems especially when the state space is (infinitely) large. Despite the importance and wide applicability of value function approximation, its theoretical understanding is still not as sophisticated as its empirical success, especially in the context of general function approximation. In this paper, we propose a provably efficient RL algorithm (both computationally and statistically) with general value function approximations. We show that if the value functions can be approximated by a function class F which satisfies the Bellman-completeness assumption, our algorithm achieves an Oe(poly(ιH)T) regret bound where ι is the product of the surprise bound and log-covering numbers, H is the planning horizon, K is the number of episodes and T = HK is the total number of steps the agent interacts with the environment. Our algorithm achieves reasonable regret bounds when applied to both the linear setting and the sparse high-dimensional linear setting. Moreover, our algorithm only needs to solve O(H log K) empirical risk minimization (ERM) problems, which is far more efficient than previous algorithms that need to solve ERM problems for Ω(HK) times.

Original languageEnglish (US)
Pages (from-to)4006-4032
Number of pages27
JournalProceedings of Machine Learning Research
StatePublished - 2023
Externally publishedYes
Event26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 - Valencia, Spain
Duration: Apr 25 2023Apr 27 2023

All Science Journal Classification (ASJC) codes

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


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