Click here to flash read.
In this work, we study the Uncertainty Quantification (UQ) of an algorithmic
estimator of the saddle point of a strongly-convex strongly-concave objective.
Specifically, we show that the averaged iterates of a Stochastic Extra-Gradient
(SEG) method for a Saddle Point Problem (SPP) converges almost surely to the
saddle point and follows a Central Limit Theorem (CLT) with optimal covariance
under two different noise settings, namely the martingale-difference noise and
the state-dependent Markov noise. To ensure the stability of the algorithm
dynamics under the state-dependent Markov noise, we propose a variant of SEG
with truncated varying sets. Our work opens the door for online inference of
SPP with numerous potential applications in GAN, robust optimization, and
reinforcement learning to name a few. We illustrate our results through
numerical experiments.
No creative common's license