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In this article, we study the convergence of Mirror Descent (MD) andOptimistic Mirror Descent (OMD) for saddle point problems satisfying the notionof coherence as proposed in Mertikopoulos et al. We prove convergence of OMDwith exact gradients for coherent saddle point problems, and show that monotoneconvergence only occurs after some sufficiently large number of iterations.This is in contrast to the claim in Mertikopoulos et al. of monotoneconvergence of OMD with exact gradients for coherent saddle point problems.Besides highlighting this important subtlety, we note that the almost sureconvergence guarantees of MD and OMD with stochastic gradients for strictlycoherent saddle point problems that are claimed in Mertikopoulos et al. are notfully justified by their proof. As such, we fill out the missing details in theproof and as a result have only been able to prove convergence with highprobability.  We would like to note that our analysis relies heavily on the core ideas andproof techniques introduced in Zhou et al. and Mertikopoulos et al., and weonly aim to re-state and correct the results in light of what we were able toprove rigorously while filling in the much needed missing details in theirproofs.

On the modes of convergence of Stochastic Optimistic Mirror Descent (OMD) for saddle point problems