Stochastic Polyak Stepsize with a Moving Target

Abstract

We propose a new stochastic gradient method called MOTAPS (Moving Targetted Polyak Stepsize) that uses recorded past loss values to compute adaptive stepsizes. MOTAPS can be seen as a variant of the Stochastic Polyak (SP) which is also a method that also uses loss values to adjust the stepsize. The downside to the SP method is that it only converges when the interpolation condition holds. MOTAPS is an extension of SP that does not rely on the interpolation condition. The MOTAPS method uses $n$ auxiliary variables, one for each data point, that track the loss value for each data point. We provide a global convergence theory for SP, an intermediary method TAPS, and MOTAPS by showing that they all can be interpreted as a special variant of online SGD. We also perform several numerical experiments on convex learning problems, and deep learning models for image classification and language translation. In all of our tasks we show that MOTAPS is competitive with the relevant baseline method.

arXiv comment49 pages, 13 figures, 1 table

References in corpus (10)

• Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivity
• Better Theory for SGD in the Nonconvex World
• Unified Optimal Analysis of the (Stochastic) Gradient Method
• Stochastic Polyak Step-size for SGD: An Adaptive Learning Rate for Fast Convergence
• Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates
• Fast and Faster Convergence of SGD for Over-Parameterized Models and an Accelerated Perceptron
• Variance Reduced Stochastic Gradient Descent with Neighbors
• Sketch and Project: Randomized Iterative Methods for Linear Systems and Inverting Matrices
• Statistical Adaptive Stochastic Gradient Methods
• Stochastic Gradient Descent with Polyak's Learning Rate