A prelimit coupling framework for analyzing nonsmooth stochastic approximation procedures is developed, which establishes Wasserstein convergence to a unique stationary distribution, characterize the limiting steady-state distribution as the step size vanishes, and shows that nonsmoothness can create a bias of order of...
It is derived that the asymptotic bias of nonsmooth contractive stochastic approximation (SA) with constant stepsize is proportional to the square root of the stepsize, which stands in sharp contrast to smooth SA.
For constant-stepsize stochastic approximation (SA), the iterates converge in distribution to a stationary law that depends on the stepsize $\alpha.$ Steady-state convergence (SSC) concerns the limit of the scaled stationary distribution as $\alpha \downarrow 0.$ Existing SSC theory requires i.i.d. or additive noise an...
We develop Gaussian approximation bounds in higher-order Wasserstein distance $W_p$, $p\geq2$, for sums of multivariate martingale differences generated by a uniformly ergodic Markov chain. Under an $L^{(2+\eta)p}$-moment condition with $\eta>0$, we establish the explicit bound $$ O\left( p^3 \|A\|_4^2 + pd^{1/4}\|A\|_...
Yi-Xuan Zhang, Qiao-Min Xie· 2 citations
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