  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.
