Two Losses Are Better Than One: Faster Optimization Using a Cheaper Proxy

Blake Woodworth, Konstantin Mishchenko, Francis Bach
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:37273-37292, 2023.

Abstract

We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal-point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is $\delta$-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a $\delta$-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-woodworth23a, title = {Two Losses Are Better Than One: Faster Optimization Using a Cheaper Proxy}, author = {Woodworth, Blake and Mishchenko, Konstantin and Bach, Francis}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {37273--37292}, 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/woodworth23a/woodworth23a.pdf}, url = {https://proceedings.mlr.press/v202/woodworth23a.html}, abstract = {We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal-point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is $\delta$-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a $\delta$-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.} }
Endnote
%0 Conference Paper %T Two Losses Are Better Than One: Faster Optimization Using a Cheaper Proxy %A Blake Woodworth %A Konstantin Mishchenko %A Francis Bach %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-woodworth23a %I PMLR %P 37273--37292 %U https://proceedings.mlr.press/v202/woodworth23a.html %V 202 %X We present an algorithm for minimizing an objective with hard-to-compute gradients by using a related, easier-to-access function as a proxy. Our algorithm is based on approximate proximal-point iterations on the proxy combined with relatively few stochastic gradients from the objective. When the difference between the objective and the proxy is $\delta$-smooth, our algorithm guarantees convergence at a rate matching stochastic gradient descent on a $\delta$-smooth objective, which can lead to substantially better sample efficiency. Our algorithm has many potential applications in machine learning, and provides a principled means of leveraging synthetic data, physics simulators, mixed public and private data, and more.
APA
Woodworth, B., Mishchenko, K. & Bach, F.. (2023). Two Losses Are Better Than One: Faster Optimization Using a Cheaper Proxy. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:37273-37292 Available from https://proceedings.mlr.press/v202/woodworth23a.html.

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