Statistics Papers

Document Type

Journal Article

Date of this Version

2013

Publication Source

SIAM Journal on Optimization

Volume

23

Issue

1

Start Page

213

Last Page

240

DOI

10.1137/110850827

Abstract

This paper addresses the problem of minimizing a convex, Lipschitz function f over a convex, compact set X under a stochastic bandit (i.e., noisy zeroth-order) feedback model. In this model, the algorithm is allowed to observe noisy realizations of the function value f(x) at any query point x ∈ X. The quantity of interest is the regret of the algorithm, which is the sum of the function values at algorithm's query points minus the optimal function value. We demonstrate a generalization of the ellipsoid algorithm that incurs O(poly(d) √T) regret. Since any algorithm has regret at least Ω(√T) on this problem, our algorithm is optimal in terms of the scaling with T.

Copyright/Permission Statement

Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Keywords

derivative-free optimization, bandit optimization, ellipsoid method

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Date Posted: 27 November 2017

This document has been peer reviewed.