Explore error bounds for mean-payoff Markov decision processes in this 29-minute conference talk from the "One World Optimization Seminar in Vienna" workshop at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the application of optimal transport techniques for deriving finite-time error bounds in reinforcement learning. Examine the talk's focus on stochastic Krasnoselski-Mann fixed point iterations for nonexpansive maps, uncovering sufficient conditions for almost sure convergence of iterates towards fixed points. Discover non-asymptotic error bounds and convergence rates, with particular emphasis on martingale difference noise with potentially unbounded variances. Investigate the analysis of uniformly bounded variances and their application to Stochastic Gradient Descent in convex optimization.