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Mathematics > Optimization and Control

arXiv:2309.02082 (math)
[Submitted on 5 Sep 2023]

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

Authors: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.
Comments: 15 pages; 3 figures
Subjects: Optimization and Control (math.OC); Numerical Analysis (math.NA); Machine Learning (stat.ML)
Cite as: arXiv:2309.02082 [math.OC]
  (or arXiv:2309.02082v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2309.02082

Submission history

From: Konstantinos Zygalakis [view email]
[v1] Tue, 5 Sep 2023 09:39:56 UTC (66 KB)
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