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We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To this end, we have developed Full-Low Evaluation methods, organized around two main types of iterations. The first iteration type is expensive in function evaluations, but exhibits good performance in the smooth and non-noisy cases. For the theory, we consider a line search based on an approximate gradient, backtracking until a sufficient decrease condition is satisfied. In practice, the gradient was approximated via finite differences, and the direction was calculated by a quasi-Newton step (BFGS). The second iteration type is cheap in function evaluations, yet more robust in the presence of noise or non-smoothness. For the theory, we consider direct search, and in practice we use probabilistic direct search with one random direction and its negative. A switch condition from Full-Eval to Low-Eval iterations was developed based on the values of the line-search and direct-search stepsizes. If enough Full-Eval steps are taken, we derive a complexity result of gradient-descent type. Under failure of Full-Eval, the Low-Eval iterations become the drivers of convergence yielding non-smooth convergence. Full-Low Evaluation methods are shown to be efficient and robust in practice across problems with different levels of smoothness and noise.
This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing interval $h
The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a sm
In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised zeroth-order oracle
A novel derivative-free algorithm, optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to accelerat
This paper addresses a distributed optimization problem in a communication network where nodes are active sporadically. Each active node applies some learning method to control its action to maximize the global utility function, which is defined as t