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arXiv · 2306.07071

Budgeted Multi-Armed Bandits with Asymmetric Confidence Intervals

Marco Heyden·Vadim Arzamasov·Edouard Fouché·Klemens Böhm
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Abstract

We study the stochastic Budgeted Multi-Armed Bandit (MAB) problem, where a player chooses from $K$ arms with unknown expected rewards and costs. The goal is to maximize the total reward under a budget constraint. A player thus seeks to choose the arm with the highest reward-cost ratio as often as possible. Current state-of-the-art policies for this problem have several issues, which we illustrate. To overcome them, we propose a new upper confidence bound (UCB) sampling policy, $\omega$-UCB, that uses asymmetric confidence intervals. These intervals scale with the distance between the sample mean and the bounds of a random variable, yielding a more accurate and tight estimation of the reward-cost ratio compared to our competitors. We show that our approach has logarithmic regret and consistently outperforms existing policies in synthetic and real settings.

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Marco Heyden, Vadim Arzamasov, Edouard Fouché, Klemens Böhm. 2023-06-12. Budgeted Multi-Armed Bandits with Asymmetric Confidence Intervals. https://arxiv.org/abs/2306.07071

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