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arXiv · 1107.1744

Stochastic convex optimization with bandit feedback

Alekh Agarwal·Dean P. Foster·Daniel Hsu·Sham M. Kakade·Alexander Rakhlin
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Abstract

This paper addresses the problem of minimizing a convex, Lipschitz function $f$ over a convex, compact set $\xset$ under a stochastic bandit feedback model. In this model, the algorithm is allowed to observe noisy realizations of the function value $f(x)$ at any query point $x \in \xset$. 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 $\otil(\poly(d)\sqrt{T})$ regret. Since any algorithm has regret at least $\Omega(\sqrt{T})$ on this problem, our algorithm is optimal in terms of the scaling with $T$.

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BibTeXRIS

Alekh Agarwal, Dean P. Foster, Daniel Hsu, Sham M. Kakade, Alexander Rakhlin. 2011-07-08. Stochastic convex optimization with bandit feedback. https://arxiv.org/abs/1107.1744

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