Leveraging priors on distribution functions for multi-arm bandits

Sumit Vashishtha; Odalric-Ambrym Maillard

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arXiv · 2503.04518

Leveraging priors on distribution functions for multi-arm bandits

Sumit Vashishtha·Odalric-Ambrym Maillard

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Abstract

We introduce Dirichlet Process Posterior Sampling (DPPS), a Bayesian non-parametric algorithm for multi-arm bandits based on Dirichlet Process (DP) priors. Like Thompson-sampling, DPPS is a probability-matching algorithm, i.e., it plays an arm based on its posterior-probability of being optimal. Instead of assuming a parametric class for the reward generating distribution of each arm, and then putting a prior on the parameters, in DPPS the reward generating distribution is directly modeled using DP priors. DPPS provides a principled approach to incorporate prior belief about the bandit environment, and in the noninformative limit of the DP posteriors (i.e. Bayesian Bootstrap), we recover Non Parametric Thompson Sampling (NPTS), a popular non-parametric bandit algorithm, as a special case of DPPS. We employ stick-breaking representation of the DP priors, and show excellent empirical performance of DPPS in challenging synthetic and real world bandit environments. Finally, using an information-theoretic analysis, we show non-asymptotic optimality of DPPS in the Bayesian regret setup.

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Sumit Vashishtha, Odalric-Ambrym Maillard. 2025-03-06. Leveraging priors on distribution functions for multi-arm bandits. https://arxiv.org/abs/2503.04518

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