Computer Science > Machine Learning
[Submitted on 30 May 2023 (v1), last revised 2 Nov 2023 (this version, v2)]
Title:BiSLS/SPS: Auto-tune Step Sizes for Stable Bi-level Optimization
View PDFAbstract:The popularity of bi-level optimization (BO) in deep learning has spurred a growing interest in studying gradient-based BO algorithms. However, existing algorithms involve two coupled learning rates that can be affected by approximation errors when computing hypergradients, making careful fine-tuning necessary to ensure fast convergence. To alleviate this issue, we investigate the use of recently proposed adaptive step-size methods, namely stochastic line search (SLS) and stochastic Polyak step size (SPS), for computing both the upper and lower-level learning rates. First, we revisit the use of SLS and SPS in single-level optimization without the additional interpolation condition that is typically assumed in prior works. For such settings, we investigate new variants of SLS and SPS that improve upon existing suggestions in the literature and are simpler to implement. Importantly, these two variants can be seen as special instances of general family of methods with an envelope-type step-size. This unified envelope strategy allows for the extension of the algorithms and their convergence guarantees to BO settings. Finally, our extensive experiments demonstrate that the new algorithms, which are available in both SGD and Adam versions, can find large learning rates with minimal tuning and converge faster than corresponding vanilla SGD or Adam BO algorithms that require fine-tuning.
Submission history
From: Chen Fan [view email][v1] Tue, 30 May 2023 00:37:50 UTC (1,083 KB)
[v2] Thu, 2 Nov 2023 04:23:07 UTC (1,106 KB)
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