Improving Stochastic Cubic Newton with Momentum

• URL: http://arxiv.org/abs/2410.19644v1
• Date: Fri, 25 Oct 2024 15:49:16 GMT
• Title: Improving Stochastic Cubic Newton with Momentum
• Authors: El Mahdi Chayti, Nikita Doikov, Martin Jaggi,
• Abstract summary: We show that momentum provably stabilizes the variance of estimates. Using our globalization technique, we prove a convergence point. We also show convex Newtonized methods with momentum.
• Score: 37.1630298053787
• License:
• Abstract: We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that momentum provably improves the variance of stochastic estimates and allows the method to converge for any noise level. Using the cubic regularization technique, we prove a global convergence rate for our method on general non-convex problems to a second-order stationary point, even when using only a single stochastic data sample per iteration. This starkly contrasts with all existing stochastic second-order methods for non-convex problems, which typically require large batches. Therefore, we are the first to demonstrate global convergence for batches of arbitrary size in the non-convex case for the Stochastic Cubic Newton. Additionally, we show improved speed on convex stochastic problems for our regularized Newton methods with momentum.

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