KOALA++: Efficient Kalman-Based Optimization with Gradient-Covariance Products
This work addresses the computational bottleneck of second-order optimization methods for neural network training, offering a more efficient alternative for practitioners in machine learning.
The authors tackled the problem of expensive second-order gradient calculations in neural network training by proposing KOALA++, a Kalman-based optimization algorithm that models structured gradient uncertainty through compact gradient covariance products. The method achieves accuracy comparable to or better than state-of-the-art optimizers while maintaining first-order efficiency across tasks like image classification and language modeling.
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.