A One-Size-Fits-All Solution to Conservative Bandit Problems

• URL: http://arxiv.org/abs/2012.07341v3
• Date: Wed, 16 Dec 2020 08:15:50 GMT
• Title: A One-Size-Fits-All Solution to Conservative Bandit Problems
• Authors: Yihan Du, Siwei Wang, Longbo Huang
• Abstract summary: We study a family of conservative bandit problems (CBPs) with sample-path reward constraints. We propose a One-Size-Fits-All solution to CBPs and present its applications to three encompassed problems.
• Score: 32.907883501286
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we study a family of conservative bandit problems (CBPs) with sample-path reward constraints, i.e., the learner's reward performance must be at least as well as a given baseline at any time. We propose a One-Size-Fits-All solution to CBPs and present its applications to three encompassed problems, i.e. conservative multi-armed bandits (CMAB), conservative linear bandits (CLB) and conservative contextual combinatorial bandits (CCCB). Different from previous works which consider high probability constraints on the expected reward, we focus on a sample-path constraint on the actually received reward, and achieve better theoretical guarantees ($T$-independent additive regrets instead of $T$-dependent) and empirical performance. Furthermore, we extend the results and consider a novel conservative mean-variance bandit problem (MV-CBP), which measures the learning performance with both the expected reward and variability. For this extended problem, we provide a novel algorithm with $O(1/T)$ normalized additive regrets ($T$-independent in the cumulative form) and validate this result through empirical evaluation.

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