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Adaptive Stochastic Optimisation of Nonconvex Composite Objectives

Author
Weijia Shao, Fikret Sivrikaya, Sahin Albayrak
Category
math.OC
Date Published
2022/11/21
Date Retrieved
2022/11/22
Date Updated
2022/11/22
Description
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an entropy-like update-generating function, these algorithms perform gradient descent in the space equipped with the maximum norm, which allows us to exploit the low-dimensional structure of the decision sets for high-dimensional problems. Together with a sampling method based on the Rademacher distribution and variance reduction techniques, the proposed algorithms guarantee a logarithmic complexity dependence on dimensionality for zeroth-order optimisation problems.
Posts
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Readers
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Score
0.75
Tweeters
3
URL
https://arxiv.org/abs/2211.11710
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