# Dueling Convex Optimization with General Preferences

arXiv: https://arxiv.org/abs/2210.02562 · HTML: https://mlsanity.com/paper/2210.02562/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 27 Sep 2022.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Preference-based Online Learning with Dueling Bandits: A Survey](https://mlsanity.com/paper/1807.11398/) (2018)
- [Contextual Dueling Bandits](https://mlsanity.com/paper/1502.06362/) (2015)
- [Preferential Bayesian Optimization](https://mlsanity.com/paper/1704.03651/) (2017)
- [Reducing Dueling Bandits to Cardinal Bandits](https://mlsanity.com/paper/1405.3396/) (2014)
- [Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability](https://mlsanity.com/paper/2111.12306/) (2021)
- [Copeland Dueling Bandits](https://mlsanity.com/paper/1506.00312/) (2015)
- [Multi-dueling Bandits with Dependent Arms](https://mlsanity.com/paper/1705.00253/) (2017)
- [Adversarial Dueling Bandits](https://mlsanity.com/paper/2010.14563/) (2020)
- [A Relative Exponential Weighing Algorithm for Adversarial Utility-based Dueling Bandits](https://mlsanity.com/paper/1601.03855/) (2016)
- [Sparse Dueling Bandits](https://mlsanity.com/paper/1502.00133/) (2015)
- [Minimax-optimal Inference from Partial Rankings](https://mlsanity.com/paper/1406.5638/) (2014)
- [Regret Analysis for Continuous Dueling Bandit](https://mlsanity.com/paper/1711.07693/) (2017)
- [Multi-Dueling Bandits and Their Application to Online Ranker Evaluation](https://mlsanity.com/paper/1608.06253/) (2016)
- [Data-driven Rank Breaking for Efficient Rank Aggregation](https://mlsanity.com/paper/1601.05495/) (2016)

## Built on by (most cited first, 6 of 6)

- [Think Before You Duel: Understanding Complexities of Preference Learning under Constrained Resources](https://mlsanity.com/paper/2312.17229/) (2023)
- [Online Convex Optimization with Dueling Feedback](https://mlsanity.com/paper/2608.15050/) (2026)
- [DP-Dueling: Learning from Preference Feedback without Compromising User Privacy](https://mlsanity.com/paper/2403.15045/) (2024)
- [Lipschitz Dueling Bandits over Continuous Action Spaces](https://mlsanity.com/paper/2604.00523/) (2026)
- [Finding Stationary Points by Comparisons](https://mlsanity.com/paper/2606.27082/) (2026)
- [Learning in Continuous Games from Pairwise Preference Feedback](https://mlsanity.com/paper/2610.05428/) (2026)

## Abstract (arXiv)

We address the problem of convex optimization with dueling feedback, where the goal is to minimize a convex function given a weaker form of dueling feedback. Each query consists of two points and the dueling feedback returns a (noisy) single-bit binary comparison of the function values of the two queried points. The translation of the function values to the single comparison bit is through a transfer function. This problem has been addressed previously for some restricted classes of transfer functions, but here we consider a very general transfer function class which includes all functions that can be approximated by a finite polynomial with a minimal degree p. Our main contribution is an efficient algorithm with convergence rate of smashwidetilde O(ε-4p) for a smooth convex objective function, and an optimal rate of smashwidetilde O(ε-2p) when the objective is smooth and strongly convex.