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arXiv · 2309.02082

Backward error analysis and the qualitative behaviour of stochastic optimization algorithms: Application to stochastic coordinate descent

Stefano Di Giovacchino·Desmond J. Higham·Konstantinos Zygalakis
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Abstract

Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical integrators, we propose a class of stochastic differential equations that approximate the dynamics of general stochastic optimization methods more closely than the original gradient flow. Analyzing a modified stochastic differential equation can reveal qualitative insights about the associated optimization method. Here, we study mean-square stability of the modified equation in the case of stochastic coordinate descent.

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Stefano Di Giovacchino, Desmond J. Higham, Konstantinos Zygalakis. 2023-09-05. Backward error analysis and the qualitative behaviour of stochastic optimization algorithms: Application to stochastic coordinate descent. https://arxiv.org/abs/2309.02082

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