Budgeted Multi-Armed Bandits with Asymmetric Confidence Intervals

• URL: http://arxiv.org/abs/2306.07071v2
• Date: Tue, 15 Aug 2023 10:55:53 GMT
• Title: Budgeted Multi-Armed Bandits with Asymmetric Confidence Intervals
• Authors: Marco Heyden, Vadim Arzamasov, Edouard Fouch\'e, Klemens B\"ohm
• Abstract summary: We study the Budgeted Multi-Armed Bandit (MAB) problem, where a player chooses from $K$ arms with unknown expected rewards and costs. 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.
• Score: 0.9831489366502302
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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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