Fairness and Welfare Quantification for Regret in Multi-Armed Bandits

We extend the notion of regret with a welfarist perspective. Focussing on classic multi-armed bandit (MAB) framework, current work quantifies performance algorithms by applying fundamental welfare function, namely Nash social (NSW) function. This corresponds to equating algorithm's geometric mean its expected rewards and leads us study regret, defined as difference between - priori unknown optimal (among arms) performance. Since NSW is known satisfy fairness axioms, our approach complements utilitarian considerations average (cumulative) wherein algorithm evaluated via arithmetic rewards. develops an that, given horizon play T, achieves O ( sqrt{(k log T)/T} ), here k denotes number arms in MAB instance. Since, for any algorithm, at least much (the AM-GM inequality), lower bound holds well. Therefore, guarantee essentially tight. In addition, we develop anytime O( T ).