KOALA: A Kalman Optimization Algorithm with Loss Adaptivity

Authors

  • Aram Davtyan Computer Vision Group, University of Bern, Switzerland
  • Sepehr Sameni Computer Vision Group, University of Bern, Switzerland
  • Llukman Cerkezi Computer Vision Group, University of Bern, Switzerland
  • Givi Meishvili Computer Vision Group, University of Bern, Switzerland
  • Adam Bielski Computer Vision Group, University of Bern, Switzerland
  • Paolo Favaro Computer Vision Group, University of Bern, Switzerland

DOI:

https://doi.org/10.1609/aaai.v36i6.20599

Keywords:

Machine Learning (ML), Constraint Satisfaction And Optimization (CSO), Computer Vision (CV)

Abstract

Optimization is often cast as a deterministic problem, where the solution is found through some iterative procedure such as gradient descent. However, when training neural networks the loss function changes over (iteration) time due to the randomized selection of a subset of the samples. This randomization turns the optimization problem into a stochastic one. We propose to consider the loss as a noisy observation with respect to some reference optimum. This interpretation of the loss allows us to adopt Kalman filtering as an optimizer, as its recursive formulation is designed to estimate unknown parameters from noisy measurements. Moreover, we show that the Kalman Filter dynamical model for the evolution of the unknown parameters can be used to capture the gradient dynamics of advanced methods such as Momentum and Adam. We call this stochastic optimization method KOALA, which is short for Kalman Optimization Algorithm with Loss Adaptivity. KOALA is an easy to implement, scalable, and efficient method to train neural networks. We provide convergence analysis and show experimentally that it yields parameter estimates that are on par with or better than existing state of the art optimization algorithms across several neural network architectures and machine learning tasks, such as computer vision and language modeling. The project page with the code and the supplementary materials is available at https://araachie.github.io/koala/.

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Published

2022-06-28

How to Cite

Davtyan, A., Sameni, S., Cerkezi, L., Meishvili, G., Bielski, A., & Favaro, P. (2022). KOALA: A Kalman Optimization Algorithm with Loss Adaptivity. Proceedings of the AAAI Conference on Artificial Intelligence, 36(6), 6471-6479. https://doi.org/10.1609/aaai.v36i6.20599

Issue

Section

AAAI Technical Track on Machine Learning I