Multiobjective Stochastic Linear Bandits under Lexicographic Ordering
Primary Area: reinforcement learning
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Keywords: multiobjective, bandits, lexicographic ordering
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TL;DR: We develop an almost optimal algorithm for the multiobjective stochastic linear bandits under lexicographic ordering.
Abstract: This paper studies the multiobjective stochastic linear bandit (MOSLB) model under lexicographic ordering, where the agent aims to simultaneously maximize $m$ objectives in a hierarchical manner. This model has various real-world scenarios, including water resource planning and radiation treatment for cancer patients. However, there is no effort on the general MOSLB model except a special case called multiobjective multi-armed bandits. Previous literature provided a suboptimal algorithm for this special case, which enjoys a regret bound of $\widetilde{O}(T^{2/3})$ under a priority-based regret measure. In this paper, we propose an algorithm achieving the almost optimal regret bound $\widetilde{O}(d\sqrt{T})$ for the MOSLB model, and its metric is the general regret. Here, $d$ is the dimension of arm vector and $T$ is the time horizon. The major novelties of our algorithm include a new arm filter and a multiple trade-off approach for exploration and exploitation. Experiments confirm the merits of our algorithms and provide compelling evidence to support our analysis.
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Submission Number: 4018
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