The paper "Train faster, generalize better: Stability of stochastic gradient descent" by Moritz Hardt, Benjamin Recht, and Yoram Singer explores the stability of stochastic gradient descent (SGD) and its implications for generalization. The authors prove that SGD, when used with a reasonable number of iterations, achieves small generalization error. They achieve this by demonstrating that SGD is algorithmically stable in the sense of Bousquet and Elisseeff. The analysis relies on elementary tools from convex and continuous optimization. The paper provides new insights into why multiple epochs of SGD generalize well in practice, especially for convex optimization problems. For non-convex optimization, the authors show that popular techniques like dropout and $\ell_2$-regularization improve stability and help achieve good generalization. The findings highlight the importance of reducing training time not only for computational efficiency but also for improving generalization. Key contributions include: - Proving that SGD is uniformly stable under standard Lipschitz and smoothness assumptions. - Deriving stability bounds for both convex and non-convex optimization. - Showcasing how various heuristics, such as dropout and $\ell_2$-regularization, enhance the stability of SGD. - Demonstrating that fast training time alone is sufficient to prevent overfitting, even for complex models with no explicit regularization. The paper also discusses the theoretical underpinnings of these results, including the connection between stability and generalization, and provides practical implications for machine learning practitioners.The paper "Train faster, generalize better: Stability of stochastic gradient descent" by Moritz Hardt, Benjamin Recht, and Yoram Singer explores the stability of stochastic gradient descent (SGD) and its implications for generalization. The authors prove that SGD, when used with a reasonable number of iterations, achieves small generalization error. They achieve this by demonstrating that SGD is algorithmically stable in the sense of Bousquet and Elisseeff. The analysis relies on elementary tools from convex and continuous optimization. The paper provides new insights into why multiple epochs of SGD generalize well in practice, especially for convex optimization problems. For non-convex optimization, the authors show that popular techniques like dropout and $\ell_2$-regularization improve stability and help achieve good generalization. The findings highlight the importance of reducing training time not only for computational efficiency but also for improving generalization. Key contributions include: - Proving that SGD is uniformly stable under standard Lipschitz and smoothness assumptions. - Deriving stability bounds for both convex and non-convex optimization. - Showcasing how various heuristics, such as dropout and $\ell_2$-regularization, enhance the stability of SGD. - Demonstrating that fast training time alone is sufficient to prevent overfitting, even for complex models with no explicit regularization. The paper also discusses the theoretical underpinnings of these results, including the connection between stability and generalization, and provides practical implications for machine learning practitioners.