Adaptive Stochastic Optimisation of Nonconvex Composite Objectives
This addresses computational efficiency challenges in high-dimensional optimization for machine learning and data science applications, representing a strong specific gain rather than a broad paradigm shift.
The paper tackles the problem of optimizing nonconvex composite objectives in high-dimensional settings by proposing a family of stochastic composite mirror descent algorithms with adaptive step sizes, achieving logarithmic complexity dependence on dimensionality for zeroth-order optimization problems.
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.