# Stochastic Trust Region Inexact Newton Method for Large-scale Machine Learning

## TL;DR

This paper introduces STRON, a stochastic trust region inexact Newton method that combines subsampling, variance reduction, and conjugate gradient techniques to efficiently solve large-scale machine learning problems.

## Contribution

The paper proposes a novel stochastic second-order optimization method, STRON, integrating subsampling and trust region strategies for large-scale learning.

## Key findings

- STRON outperforms existing methods on benchmark datasets.
- Variance reduction techniques did not improve large-scale learning.
- Preconditioned conjugate gradient was less effective in this context.

## Abstract

Nowadays stochastic approximation methods are one of the major research direction to deal with the large-scale machine learning problems. From stochastic first order methods, now the focus is shifting to stochastic second order methods due to their faster convergence and availability of computing resources. In this paper, we have proposed a novel Stochastic Trust RegiOn Inexact Newton method, called as STRON, to solve large-scale learning problems which uses conjugate gradient (CG) to inexactly solve trust region subproblem. The method uses progressive subsampling in the calculation of gradient and Hessian values to take the advantage of both, stochastic and full-batch regimes. We have extended STRON using existing variance reduction techniques to deal with the noisy gradients and using preconditioned conjugate gradient (PCG) as subproblem solver, and empirically proved that they do not work as expected, for the large-scale learning problems. Finally, our empirical results prove efficacy of the proposed method against existing methods with bench marked datasets.