The paper revises Mertikopoulos et al.'s MD/OMD convergence theorems: for coherent problems monotone decrease is only eventual, and stochastic guarantees are high-probability rather than almost sure.
With such choice of n0, we will prove that D(x∗, Xn+1) ≤ ǫ for all n ≥ n0
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On the modes of convergence of Stochastic Optimistic Mirror Descent (OMD) for saddle point problems
The paper revises Mertikopoulos et al.'s MD/OMD convergence theorems: for coherent problems monotone decrease is only eventual, and stochastic guarantees are high-probability rather than almost sure.