The Sample Complexity of Parameter-Free Stochastic Convex Optimization

Fuente: arXiv
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Hauptverfasser: Lawrence, Jared, Kalinsky, Ari, Bradfield, Hannah, Carmon, Yair, Hinder, Oliver
Format: Preprint
Veröffentlicht: 2025
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author Lawrence, Jared
Kalinsky, Ari
Bradfield, Hannah
Carmon, Yair
Hinder, Oliver
author_facet Lawrence, Jared
Kalinsky, Ari
Bradfield, Hannah
Carmon, Yair
Hinder, Oliver
contents We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting the validation set. This method allows us to generically tune the learning rate of stochastic optimization methods to match the optimal known-parameter sample complexity up to $\log\log$ factors. Second, we develop a regularization-based method that is specialized to the case that only the distance to optimality is unknown. This method provides perfect adaptability to unknown distance to optimality, demonstrating a separation between the sample and computational complexity of parameter-free stochastic convex optimization. Combining these two methods allows us to simultaneously adapt to multiple problem structures. Experiments performing few-shot learning on CIFAR-10 by fine-tuning CLIP models and prompt engineering Gemini to count shapes indicate that our reliable model selection method can help mitigate overfitting to small validation sets.
format Preprint
id arxiv_https___arxiv_org_abs_2506_11336
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Sample Complexity of Parameter-Free Stochastic Convex Optimization
Lawrence, Jared
Kalinsky, Ari
Bradfield, Hannah
Carmon, Yair
Hinder, Oliver
Machine Learning
Optimization and Control
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting the validation set. This method allows us to generically tune the learning rate of stochastic optimization methods to match the optimal known-parameter sample complexity up to $\log\log$ factors. Second, we develop a regularization-based method that is specialized to the case that only the distance to optimality is unknown. This method provides perfect adaptability to unknown distance to optimality, demonstrating a separation between the sample and computational complexity of parameter-free stochastic convex optimization. Combining these two methods allows us to simultaneously adapt to multiple problem structures. Experiments performing few-shot learning on CIFAR-10 by fine-tuning CLIP models and prompt engineering Gemini to count shapes indicate that our reliable model selection method can help mitigate overfitting to small validation sets.
title The Sample Complexity of Parameter-Free Stochastic Convex Optimization
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2506.11336