Effectively Leveraging Momentum Terms in Stochastic Line Search Frameworks for Fast Optimization of Finite-Sum Problems

In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent line search approaches for stochastic optimization in the overparametrized regime and momentum directions. First, we point out that combining these two elements with computational benefits is not straightforward. To this aim, we propose a solution based on mini-batch persistency. We then introduce an algorithmic framework that exploits a mix of data persistency, conjugate-gradient type rules for the definition of the momentum parameter and stochastic line searches. The resulting algorithm is empirically shown to outperform other popular methods from the literature, obtaining state-of-the-art results in both convex and nonconvex large scale training problems.

Convergence Conditions for Stochastic Line Search Based Optimization of Over-parametrized Models

In this paper, we deal with algorithms to solve the finite-sum problems related to fitting over-parametrized models, that typically satisfy the interpolation condition. In particular, we focus on approaches based on stochastic line searches and employing general search directions. We define conditions on the sequence of search directions that guarantee finite termination and bounds for the backtracking procedure. Moreover, we shed light on the additional property of directions needed to prove fast (linear) convergence of the general class of algorithms when applied to PL functions in the interpolation regime. From the point of view of algorithms design, the proposed analysis identifies safeguarding conditions that could be employed in relevant algorithmic framework. In particular, it could be of interest to integrate stochastic line searches within momentum, conjugate gradient or adaptive preconditioning methods.