Dueling Bandits With Weak Regret

TL;DR

This paper introduces the Winner Stays (WS) algorithm for dueling bandits, effectively minimizing weak and strong regret in content recommendation tasks with pairwise feedback, outperforming existing methods in simulations and real data.

Contribution

The paper proposes the first weak regret-optimized dueling bandit algorithm, Winner Stays, with theoretical guarantees and practical efficiency for both weak and strong regret settings.

Findings

WS-W achieves constant weak regret over time.

WS outperforms existing algorithms in simulations.

WS is computationally simple for many arms.

Abstract

We consider online content recommendation with implicit feedback through pairwise comparisons, formalized as the so-called dueling bandit problem. We study the dueling bandit problem in the Condorcet winner setting, and consider two notions of regret: the more well-studied strong regret, which is 0 only when both arms pulled are the Condorcet winner; and the less well-studied weak regret, which is 0 if either arm pulled is the Condorcet winner. We propose a new algorithm for this problem, Winner Stays (WS), with variations for each kind of regret: WS for weak regret (WS-W) has expected cumulative weak regret that is $O(N^2)$, and $O(N\log(N))$ if arms have a total order; WS for strong regret (WS-S) has expected cumulative strong regret of $O(N^2 + N \log(T))$, and $O(N\log(N)+N\log(T))$ if arms have a total order. WS-W is the first dueling bandit algorithm with weak regret that is constant in time. WS is simple to compute, even for problems with many arms, and we demonstrate through numerical experiments on simulated and real data that WS has significantly smaller regret than existing algorithms in both the weak- and strong-regret settings.