# Copeland Dueling Bandits

arXiv: https://arxiv.org/abs/1506.00312 · HTML: https://mlsanity.com/paper/1506.00312/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2015.

## Built on by (most cited first, 30 of 36)

- [Dueling RL: Reinforcement Learning with Trajectory Preferences](https://mlsanity.com/paper/2111.04850/) (2021)
- [Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability](https://mlsanity.com/paper/2111.12306/) (2021)
- [Feel-Good Thompson Sampling for Contextual Dueling Bandits](https://mlsanity.com/paper/2404.06013/) (2024)
- [Variance-Aware Regret Bounds for Stochastic Contextual Dueling Bandits](https://mlsanity.com/paper/2310.00968/) (2023)
- [Borda Regret Minimization for Generalized Linear Dueling Bandits](https://mlsanity.com/paper/2303.08816/) (2023)
- [Batched Dueling Bandits](https://mlsanity.com/paper/2202.10660/) (2022)
- [Active Evaluation: Efficient NLG Evaluation with Few Pairwise Comparisons](https://mlsanity.com/paper/2203.06063/) (2022)
- [Preference learning along multiple criteria: A game-theoretic perspective](https://mlsanity.com/paper/2105.01850/) (2021)
- [Optimal and Efficient Dynamic Regret Algorithms for Non-Stationary Dueling Bandits](https://mlsanity.com/paper/2111.03917/) (2021)
- [Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback](https://mlsanity.com/paper/2404.10776/) (2024)
- [ANACONDA: An Improved Dynamic Regret Algorithm for Adaptive Non-Stationary Dueling Bandits](https://mlsanity.com/paper/2210.14322/) (2022)
- [Dueling Convex Optimization with General Preferences](https://mlsanity.com/paper/2210.02562/) (2022)
- [Dueling Bandits with Adversarial Sleeping](https://mlsanity.com/paper/2107.02274/) (2021)
- [Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences](https://mlsanity.com/paper/2202.06694/) (2022)
- [When Can We Track Significant Preference Shifts in Dueling Bandits?](https://mlsanity.com/paper/2302.06595/) (2023)
- [Dueling Bandits: From Two-dueling to Multi-dueling](https://mlsanity.com/paper/2211.10293/) (2022)
- [Stop Relying on No-Choice and Do not Repeat the Moves: Optimal, Efficient and Practical Algorithms for Assortment Optimization](https://mlsanity.com/paper/2402.18917/) (2024)
- [FraPPE: Fast and Efficient Preference-based Pure Exploration](https://mlsanity.com/paper/2508.16487/) (2025)
- [One Arrow, Two Kills: An Unified Framework for Achieving Optimal Regret Guarantees in Sleeping Bandits](https://mlsanity.com/paper/2210.14998/) (2022)
- [Think Before You Duel: Understanding Complexities of Preference Learning under Constrained Resources](https://mlsanity.com/paper/2312.17229/) (2023)
- [Biased Dueling Bandits with Stochastic Delayed Feedback](https://mlsanity.com/paper/2408.14603/) (2024)
- [An Asymptotically Optimal Batched Algorithm for the Dueling Bandit Problem](https://mlsanity.com/paper/2209.12108/) (2022)
- [Non-Stationary Dueling Bandits Under a Weighted Borda Criterion](https://mlsanity.com/paper/2403.12950/) (2024)
- [Multi-Player Approaches for Dueling Bandits](https://mlsanity.com/paper/2405.16168/) (2024)
- [Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options](https://mlsanity.com/paper/2510.18713/) (2025)
- [Multi-Armed Bandits With Best-Action Queries](https://mlsanity.com/paper/2605.08287/) (2026)
- [DP-Dueling: Learning from Preference Feedback without Compromising User Privacy](https://mlsanity.com/paper/2403.15045/) (2024)
- [Adversarial Multi-dueling Bandits](https://mlsanity.com/paper/2406.12475/) (2024)
- [QuACK: A Multipurpose Queuing Algorithm for Cooperative k-Armed Bandits](https://mlsanity.com/paper/2410.23867/) (2024)
- [Active Evaluation of General Agents: Problem Definition and Comparison of Baseline Algorithms](https://mlsanity.com/paper/2601.07651/) (2026)

## Abstract (arXiv)

A version of the dueling bandit problem is addressed in which a Condorcet winner may not exist. Two algorithms are proposed that instead seek to minimize regret with respect to the Copeland winner, which, unlike the Condorcet winner, is guaranteed to exist. The first, Copeland Confidence Bound (CCB), is designed for small numbers of arms, while the second, Scalable Copeland Bandits (SCB), works better for large-scale problems. We provide theoretical results bounding the regret accumulated by CCB and SCB, both substantially improving existing results. Such existing results either offer bounds of the form O(K log T) but require restrictive assumptions, or offer bounds of the form O(K2 log T) without requiring such assumptions. Our results offer the best of both worlds: O(K log T) bounds without restrictive assumptions.