6 papers · 1 filter
Stochastic Mirror Descent under Iterate-Dependent Markov Noise: Analysis in the Asymptotic and Finite Time Regimes
Anik Kumar Paul, Shalabh Bhatnagar
We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent…
Stochastic Recursive Inclusions under Biased Perturbations: An Input-to-State Stability Perspective
Anik Kumar Paul, Karthik Shenoy, Arun D. Mahindrakar
This paper investigates the asymptotic behavior of stochastic recursive inclusions in the presence of non-zero, non-diminishing bias, a setting that frequently arises in zeroth-ord…
Zeroth-Order Non-smooth Non-convex Optimization via Gaussian Smoothing
Anik Kumar Paul, Shalabh Bhatnagar
This paper addresses stochastic optimization of Lipschitz-continuous, nonsmooth and nonconvex objectives over compact convex sets, where only noisy function evaluations are availab…
Almost Sure Convergence and Non-asymptotic Concentration Bounds for Stochastic Mirror Descent Algorithm
Anik Kumar Paul, Arun D Mahindrakar, Rachel K Kalaimani
This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the al…
Convergence Analysis of Stochastic Saddle Point Mirror Descent Algorithm -- A Projected Dynamical View Point
Anik Kumar Paul, Arun D Mahindrakar, Rachel K Kalaimani
Saddle point problems, ubiquitous in optimization, extend beyond game theory to diverse domains like power networks and reinforcement learning. This paper presents novel approaches…
Robust Analysis of Almost Sure Convergence of Zeroth-Order Mirror Descent Algorithm
Anik Kumar Paul, Arun D Mahindrakar, Rachel K Kalaimani
This letter presents an almost sure convergence of the zeroth-order mirror descent algorithm. The algorithm admits non-smooth convex functions and a biased oracle which only provid…