Dueling Convex Optimization with General Preferences

• URL: http://arxiv.org/abs/2210.02562v1
• Date: Tue, 27 Sep 2022 11:10:41 GMT
• Title: Dueling Convex Optimization with General Preferences
• Authors: Aadirupa Saha, Tomer Koren, Yishay Mansour
• Abstract summary: We address the problem of emph optimization with dueling feedback, where the goal is to minimize a convex function given a weaker form of emphilonling feedback. Our main contribution is an efficient algorithm with convergence $smashwidetilde O(epsilon-4p)$ for a smooth convex objective function, and an efficient $smashwidetilde O(epsilon-2p) when the objective is smooth and convex.
• Score: 85.14061196945599
• License: http://creativecommons.org/licenses/by/4.0/
• 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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