Mostly Exploration-free Algorithms for Multi-Objective Linear Bandits

ICLR 2025 Conference Submission9801 Authors

Keywords: multi-objective, free exploration, linear bandit

TL;DR: We developed mostly exploration free algorithms for multi-objective linear bandits.

Abstract: We address the challenge of solving multi-objective bandit problems, which are increasingly relevant in real-world applications where multiple possibly conflicting objectives must be optimized simultaneously. Existing multi-objective algorithms often rely on complex, computationally intensive methods, making them impractical for real-world use. In this paper, we propose a novel perspective by showing that objective diversity can naturally induce free exploration, allowing for simpler, near-greedy algorithms to achieve optimal regret bounds up to logarithmic factors with respect to the number of rounds. We introduce simple and efficient algorithms for multi-objective linear bandits, which do not require constructing empirical Pareto fronts and achieve a regret bound of $\tilde{\mathcal{O}}(\sqrt{T})$ under sufficient objective diversity and suitable regularity. We also introduce the concept of objective fairness, ensuring equal treatment of all objectives, and show that our algorithms satisfy this criterion. Numerical experiments validate our theoretical findings, demonstrating that objective diversity can enhance algorithm performance while simplifying the solution process.

Primary Area: learning theory

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Submission Number: 9801