Adaptive Zeroth-Order Optimisation of Nonconvex Composite Objectives

• URL: http://arxiv.org/abs/2208.04579v1
• Date: Tue, 9 Aug 2022 07:36:25 GMT
• Title: Adaptive Zeroth-Order Optimisation of Nonconvex Composite Objectives
• Authors: Weijia Shao, Sahin Albayrak
• Abstract summary: We analyze algorithms for zeroth-order entropy composite objectives, focusing on dependence on dimensionality. This is achieved by exploiting low dimensional structure of the decision set using the mirror descent method with an estimation alike function. To improve the gradient, we replace the classic sampling method based on Rademacher and show that the mini-batch method copes with non-Eucli geometry.
• Score: 1.7640556247739623
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose and analyze algorithms for zeroth-order optimization of non-convex composite objectives, focusing on reducing the complexity dependence on dimensionality. This is achieved by exploiting the low dimensional structure of the decision set using the stochastic mirror descent method with an entropy alike function, which performs gradient descent in the space equipped with the maximum norm. To improve the gradient estimation, we replace the classic Gaussian smoothing method with a sampling method based on the Rademacher distribution and show that the mini-batch method copes with the non-Euclidean geometry. To avoid tuning hyperparameters, we analyze the adaptive stepsizes for the general stochastic mirror descent and show that the adaptive version of the proposed algorithm converges without requiring prior knowledge about the problem.

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