Budgeted Bayesian Bandits for Future Utilization

Sudipto Guha

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arXiv · 2610.24156

Budgeted Bayesian Bandits for Future Utilization

Sudipto Guha

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Abstract

The multi-armed bandit problem models the trade-off between exploration and exploitation. In this paper, we study the variant where exploration has a hard budget and precedes exploitation. Prior guarantees include a 1/3 approximation by Guha and Munagala using Lagrangian duality, and a 4/27 approximation by Ma against a primal linear programming relaxation for a more general model. We show that the analyses of both algorithms are tight, even when their relaxations are asymptotically exact. We provide a different efficient algorithm that achieves a 0.43 approximation. We then provide an efficient algorithm whose guarantee approaches 1-e^{-1} approx 0.63 for bounded exchangeable reward observations in a non-vanishing regime, which is asymptotically tight against natural linear programming relaxations. The technique also gives certificates for stopping sequential model evaluation.

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Sudipto Guha. 2026-10-16. Budgeted Bayesian Bandits for Future Utilization. https://arxiv.org/abs/2610.24156

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