Jul 12, 2020

In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank Wolfe) methods to solve the problem of constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an accelerated stochastic zeroth-order Frank Wolfe (Acc-SZOFW) method based on the variance reduced technique and a novel momentum technique. Moreover, under some mild conditions, we prove that the Acc-SZOFW has the function query complexity of O(d√(n)ϵ^-2) for finding an ϵ-stationary point in the finite-sum problem, which improves the exiting best result by a factor of O(√(n)ϵ^-2), and has the function query complexity of O(dϵ^-3) in the stochastic problem, which improves the exiting best result by a factor of O(ϵ^-1). Further, we propose a novel accelerated stochastic zeroth-order Frank Wolfe (Acc-SZOFW*) to relax the large mini-batch size required in the Acc-SZOFW. In particular, we prove that the Acc-SZOFW* still has the function query complexity of O(dϵ^-3) in the stochastic problem. Finally, we use extensive experiments including black-box adversarial attack and robust black-box classification to verify the efficiency of our algorithms.

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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