How Expert Confidence Can Improve Collective Decision-Making in Contextual Multi-Armed Bandit Problems

In collective decision-making (CDM) a group of experts with a shared set of values and a common goal must combine their knowledge to make a collectively optimal decision. Whereas existing research on CDM primarily focuses on making binary decisions, we focus here on CDM applied to solving contextual multi-armed bandit (CMAB) problems, where the goal is to exploit contextual information to select the best arm among a set. To address the limiting assumptions of prior work, we introduce confidence estimates and propose a novel approach to deciding with expert advice which can take advantage of these estimates. We further show that, when confidence estimates are imperfect, the proposed approach is more robust than the classical confidence-weighted majority vote.