A one-bit, comparison-based gradient estimator

نویسندگان

چکیده

We study zeroth-order optimization for convex functions where we further assume that function evaluations are unavailable. Instead, one only has access to a comparison oracle, which given two points x and y returns single bit of information indicating point larger value, f(x) or f(y). By treating the gradient as an unknown signal be recovered, show how can use tools from one-bit compressed sensing construct robust reliable estimator normalized gradient. then propose algorithm, coined SCOBO, uses this within descent scheme. when some low dimensional structure exploited, SCOBO outperforms state-of-the-art in terms query complexity. Our theoretical claims verified by extensive numerical experiments.

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ژورنال

عنوان ژورنال: Applied and Computational Harmonic Analysis

سال: 2022

ISSN: ['1096-603X', '1063-5203']

DOI: https://doi.org/10.1016/j.acha.2022.03.003