"Direct Search Methods for Stochastic Zeroth-Order Problems"Rinaldi, FrancescoOptimizing a function without using derivatives is a challenging task, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization offers a large number of algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct search, is particularly popular thanks to its simplicity of implementation and interesting theoretical properties. In this talk, we describe direct search algorithms that handle Stochastic Zeroth-Order problems, i.e., problems whose objective is not computable in practice, with the only information available obtained by a stochastic zeroth-order oracle calculating an estimate of the function for any given point. Under standard assumptions on the accuracy and the variance of the random estimates used, we establish global convergence to stationary points. Finally, we report some numerical results to show the practical effectiveness of the methods. |
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