Bayesian Design Principles for Frequentist Sequential Learning

Yunbei Xu*, Assaf Zeevi

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


We develop a general theory to optimize the frequentist regret for sequential learning problems, where efficient bandit and reinforcement learning algorithms can be derived from unified Bayesian principles. We propose a novel optimization approach to create “algorithmic beliefs” at each round, and use Bayesian posteriors to make decisions. This is the first approach to make Bayesian-type algorithms prior-free and applicable to adversarial settings, in a generic and optimal manner. Moreover, the algorithms are simple and often efficient to implement. As a major application, we present a novel algorithm for multi-armed bandits that achieves the “best-of-all-worlds” empirical performance in the stochastic, adversarial, and non-stationary environments. And we illustrate how these principles can be used in linear bandits, convex bandits, and reinforcement learning.

Original languageEnglish
Pages (from-to)38768-38800
Number of pages33
JournalProceedings of Machine Learning Research
StatePublished - 2023
Externally publishedYes
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: 23 Jul 202329 Jul 2023


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