TL;DR
This paper introduces SCOBO, a novel zeroth-order optimization algorithm that estimates gradients using only comparison-based one-bit feedback, outperforming existing methods when the function has low-dimensional structure.
Contribution
The paper develops a gradient estimator from comparison oracle data using one-bit compressed sensing, and proposes SCOBO, a new algorithm that leverages this estimator for efficient optimization.
Findings
SCOBO outperforms state-of-the-art methods in low-dimensional structured settings.
The gradient estimator is robust and reliable despite limited one-bit comparison data.
Extensive experiments verify the theoretical advantages of SCOBO.
Abstract
We study zeroth-order optimization for convex functions where we further assume that function evaluations are unavailable. Instead, one only has access to a , which given two points and returns a single bit of information indicating which point has larger function value, or . By treating the gradient as an unknown signal to be recovered, we show how one can use tools from one-bit compressed sensing to construct a robust and reliable estimator of the normalized gradient. We then propose an algorithm, coined SCOBO, that uses this estimator within a gradient descent scheme. We show that when has some low dimensional structure that can be exploited, SCOBO outperforms the state-of-the-art in terms of query complexity. Our theoretical claims are verified by extensive numerical experiments.
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