KOALA++: Efficient Kalman-Based Optimization with Gradient-Covariance Products

TL;DR

KOALA++ is a scalable, efficient optimization algorithm for neural networks that models structured gradient uncertainty using covariance products, outperforming or matching state-of-the-art methods without high computational costs.

Contribution

It introduces KOALA++, a novel Kalman-based optimizer that explicitly captures richer gradient uncertainty structures without full covariance matrices, improving efficiency and accuracy.

Findings

Achieves comparable or better accuracy than state-of-the-art optimizers.

Maintains efficiency similar to first-order methods.

Effectively models structured gradient uncertainty.

Abstract

We propose KOALA++, a scalable Kalman-based optimization algorithm that explicitly models structured gradient uncertainty in neural network training. Unlike second-order methods, which rely on expensive second order gradient calculation, our method directly estimates the parameter covariance matrix by recursively updating compact gradient covariance products. This design improves upon the original KOALA framework that assumed diagonal covariance by implicitly capturing richer uncertainty structure without storing the full covariance matrix and avoiding large matrix inversions. Across diverse tasks, including image classification and language modeling, KOALA++ achieves accuracy on par or better than state-of-the-art first- and second-order optimizers while maintaining the efficiency of first-order methods.