Directional Optimism for Safe Linear Bandits

• URL: http://arxiv.org/abs/2308.15006v2
• Date: Mon, 11 Mar 2024 23:32:33 GMT
• Title: Directional Optimism for Safe Linear Bandits
• Authors: Spencer Hutchinson, Berkay Turan, Mahnoosh Alizadeh
• Abstract summary: The safe linear bandit problem is a version of the classical linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. We find that it is possible to achieve improved regret guarantees for both well-separated problem instances and action sets that are finite star convex sets. Lastly, we introduce a generalization of the safe linear bandit setting where the constraints are convex and adapt our algorithms and analyses to this setting by leveraging a novel convex-analysis based approach.
• Score: 4.84955052297084
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The safe linear bandit problem is a version of the classical stochastic linear bandit problem where the learner's actions must satisfy an uncertain constraint at all rounds. Due its applicability to many real-world settings, this problem has received considerable attention in recent years. By leveraging a novel approach that we call directional optimism, we find that it is possible to achieve improved regret guarantees for both well-separated problem instances and action sets that are finite star convex sets. Furthermore, we propose a novel algorithm for this setting that improves on existing algorithms in terms of empirical performance, while enjoying matching regret guarantees. Lastly, we introduce a generalization of the safe linear bandit setting where the constraints are convex and adapt our algorithms and analyses to this setting by leveraging a novel convex-analysis based approach.

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