Complex Momentum for Optimization in Games
Jonathan P. Lorraine, David Acuna, Paul Vicol, David Duvenaud
Abstract
We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and alternating updates. Our method gives real-valued parameter updates, making it a drop-in replacement for standard optimizers. We empirically demonstrate that complex-valued momentum can improve convergence in realistic adversarial games–like generative adversarial networks– by showing we can find better solutions with an almost identical computational cost. We also show a practical complex-valued Adam variant, which we use to train BigGAN to improve inception scores on CIFAR-10.
BibTeX
@InProceedings{pmlr-v151-lorraine22a,
title = { Complex Momentum for Optimization in Games },
author = {Lorraine, Jonathan P. and Acuna, David and Vicol, Paul and Duvenaud, David},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {7742--7765},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/lorraine22a/lorraine22a.pdf},
url = {https://proceedings.mlr.press/v151/lorraine22a.html},
abstract = { We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and alternating updates. Our method gives real-valued parameter updates, making it a drop-in replacement for standard optimizers. We empirically demonstrate that complex-valued momentum can improve convergence in realistic adversarial games–like generative adversarial networks– by showing we can find better solutions with an almost identical computational cost. We also show a practical complex-valued Adam variant, which we use to train BigGAN to improve inception scores on CIFAR-10. }
}