Rapid Overfitting of Multi-Pass Stochastic Gradient Descent in Stochastic Convex Optimization

• URL: http://arxiv.org/abs/2505.08306v1
• Date: Tue, 13 May 2025 07:32:48 GMT
• Title: Rapid Overfitting of Multi-Pass Stochastic Gradient Descent in Stochastic Convex Optimization
• Authors: Shira Vansover-Hager, Tomer Koren, Roi Livni,
• Abstract summary: We study the out-of-sample performance of multi-pass gradient descent (SGD) in the fundamental convex optimization (SCO) model.<n>We show that in the general non-smooth case of SCO, just a few epochs of SGD can already hurt its out-of-sample significantly and lead to overfitting.
• Score: 34.451177321785146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the out-of-sample performance of multi-pass stochastic gradient descent (SGD) in the fundamental stochastic convex optimization (SCO) model. While one-pass SGD is known to achieve an optimal $\Theta(1/\sqrt{n})$ excess population loss given a sample of size $n$, much less is understood about the multi-pass version of the algorithm which is widely used in practice. Somewhat surprisingly, we show that in the general non-smooth case of SCO, just a few epochs of SGD can already hurt its out-of-sample performance significantly and lead to overfitting. In particular, using a step size $\eta = \Theta(1/\sqrt{n})$, which gives the optimal rate after one pass, can lead to population loss as large as $\Omega(1)$ after just one additional pass. More generally, we show that the population loss from the second pass onward is of the order $\Theta(1/(\eta T) + \eta \sqrt{T})$, where $T$ is the total number of steps. These results reveal a certain phase-transition in the out-of-sample behavior of SGD after the first epoch, as well as a sharp separation between the rates of overfitting in the smooth and non-smooth cases of SCO. Additionally, we extend our results to with-replacement SGD, proving that the same asymptotic bounds hold after $O(n \log n)$ steps. Finally, we also prove a lower bound of $\Omega(\eta \sqrt{n})$ on the generalization gap of one-pass SGD in dimension $d = \smash{\widetilde O}(n)$, improving on recent results of Koren et al.(2022) and Schliserman et al.(2024).

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