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arXiv · 2210.02562

Dueling Convex Optimization with General Preferences

Aadirupa Saha·Tomer Koren·Yishay Mansour
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Abstract

We address the problem of \emph{convex optimization with dueling feedback}, where the goal is to minimize a convex function given a weaker form of \emph{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 \emph{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 $\smash{\widetilde O}(\epsilon^{-4p})$ for a smooth convex objective function, and an optimal rate of $\smash{\widetilde O}(\epsilon^{-2p})$ when the objective is smooth and strongly convex.

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Aadirupa Saha, Tomer Koren, Yishay Mansour. 2022-09-27. Dueling Convex Optimization with General Preferences. https://arxiv.org/abs/2210.02562

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