Complex Momentum for Optimization in Games

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 upda...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Lorraine, Jonathan, Acuna, David, Vicol, Paul, Duvenaud, David
Format: Article
Language:English
Subjects:
Convergence
Learning
Momentum
Zero sum games
Online Access:Get full text
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Summary: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 generalization to a complex-valued Adam variant, which we use to train BigGAN to better inception scores on CIFAR-10.
ISSN:2331-8422