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arXiv · 1402.2667

On Zeroth-Order Stochastic Convex Optimization via Random Walks

Tengyuan Liang·Hariharan Narayanan·Alexander Rakhlin
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Abstract

We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of $\tilde{\mathcal{O}}(n^{7}T^{-1/2})$ after $T$ queries for a convex bounded function $f:{\mathbb R}^n\to{\mathbb R}$. The method is based on a random walk (the \emph{Ball Walk}) on the epigraph of the function. The randomized approach circumvents the problem of gradient estimation, and appears to be less sensitive to noisy function evaluations compared to noiseless zeroth order methods.

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Tengyuan Liang, Hariharan Narayanan, Alexander Rakhlin. 2014-02-11. On Zeroth-Order Stochastic Convex Optimization via Random Walks. https://arxiv.org/abs/1402.2667

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