EigenGame Unloaded: When playing games is better than optimizing

Ian Gemp, Brian McWilliams, Claire Vernade, Thore Graepel

Keywords: pca, principal components analysis, nash, games, eigendecomposition, svd, singular value decomposition

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.

One-sentence Summary: We improve the EigenGame algorithm by removing update bias, enabling further parallelism and better performance.