Accelerated Stochastic Optimization Methods under Quasar-convexity

Qiang Fu, Dongchu Xu, Ashia Camage Wilson
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:10431-10460, 2023.

Abstract

Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is quasar-convexity, a non-convex generalization of convexity that subsumes convex functions. Existing algorithms for minimizing quasar-convex functions in the stochastic setting have either high complexity or slow convergence, which prompts us to derive a new class of stochastic methods for optimizing smooth quasar-convex functions. We demonstrate that our algorithms have fast convergence and outperform existing algorithms on several examples, including the classical problem of learning linear dynamical systems. We also present a unified analysis of our newly proposed algorithms and a previously studied deterministic algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-fu23e, title = {Accelerated Stochastic Optimization Methods under Quasar-convexity}, author = {Fu, Qiang and Xu, Dongchu and Wilson, Ashia Camage}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {10431--10460}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/fu23e/fu23e.pdf}, url = {https://proceedings.mlr.press/v202/fu23e.html}, abstract = {Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is quasar-convexity, a non-convex generalization of convexity that subsumes convex functions. Existing algorithms for minimizing quasar-convex functions in the stochastic setting have either high complexity or slow convergence, which prompts us to derive a new class of stochastic methods for optimizing smooth quasar-convex functions. We demonstrate that our algorithms have fast convergence and outperform existing algorithms on several examples, including the classical problem of learning linear dynamical systems. We also present a unified analysis of our newly proposed algorithms and a previously studied deterministic algorithm.} }
Endnote
%0 Conference Paper %T Accelerated Stochastic Optimization Methods under Quasar-convexity %A Qiang Fu %A Dongchu Xu %A Ashia Camage Wilson %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-fu23e %I PMLR %P 10431--10460 %U https://proceedings.mlr.press/v202/fu23e.html %V 202 %X Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is quasar-convexity, a non-convex generalization of convexity that subsumes convex functions. Existing algorithms for minimizing quasar-convex functions in the stochastic setting have either high complexity or slow convergence, which prompts us to derive a new class of stochastic methods for optimizing smooth quasar-convex functions. We demonstrate that our algorithms have fast convergence and outperform existing algorithms on several examples, including the classical problem of learning linear dynamical systems. We also present a unified analysis of our newly proposed algorithms and a previously studied deterministic algorithm.
APA
Fu, Q., Xu, D. & Wilson, A.C.. (2023). Accelerated Stochastic Optimization Methods under Quasar-convexity. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:10431-10460 Available from https://proceedings.mlr.press/v202/fu23e.html.

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