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2019

Stochastic Three Points Method for Unconstrained Smooth Minimization

Bergou, El Houcine, Gorbunov, Eduard, Richtárik, Peter

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In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible.

We design a novel randomized derivative-free algorithm --- the stochastic three points (STP) method --- and analyze its iteration complexity.
At each iteration, STP generates a random search direction according to a certain fixed probability law.
Our assumptions on this law are very mild: roughly speaking, all laws which do not concentrate all measure on any halfspace passing through the origin will work.

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