EigenGame Unloaded: When playing games is better than optimizing
Ian Gemp · Brian McWilliams · Claire Vernade · Thore Graepel
Keywords:
games
pca
principal components analysis
nash
eigendecomposition
svd
singular value decomposition
2022 Poster
Abstract
We build on the recently proposed EigenGame that views eigendecomposition as a competitive game. EigenGame's updates are biased if computed using minibatches of data, which hinders convergence and more sophisticated parallelism in the stochastic setting. In this work, we propose an unbiased stochastic update that is asymptotically equivalent to EigenGame, enjoys greater parallelism allowing computation on datasets of larger sample sizes, and outperforms EigenGame in experiments. We present applications to finding the principal components of massive datasets and performing spectral clustering of graphs. We analyze and discuss our proposed update in the context of EigenGame and the shift in perspective from optimization to games.
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