Dueling Bandits with Team Comparisons

Abstract

We introduce the dueling teams problem, a new online-learning setting in which the learner observes noisy comparisons of disjoint pairs of k-sized teams from a universe of n players. The goal of the learner is to minimize the number of duels required to identify, with high probability, a Condorcet winning team, i.e., a team which wins against any other disjoint team (with probability at least 1/2). Noisy comparisons are linked to a total order on the teams. We formalize our model by building upon the dueling bandits setting [23] and provide several algorithms, both for stochastic and deterministic settings. For the stochastic setting, we provide a reduction to the classical dueling bandits setting, yielding an algorithm that identifies a Condorcet winning team within O((n + k log(k)) max(log log n,log k)) duels, where ∆ is a gap parameter. For deterministic feedback, we additionally present a gap-independent algorithm that identifies a Condorcet winning team within O(nk log(k) + k 5 ) duels.