asymptotic normality

Gradient Tracking Methods for Distributed Stochastic Optimization Problems with Decision-dependent Distributions

  • Licheng Deng
  • Yongchao Liu
    • Categories Stochastic Programming Tags , , , ,

    This paper aims to seek the performative stable solution and the optimal solution of the distributed stochastic optimization problem with decision-dependent distributions, which is a finite-sum stochastic optimization problem over a network and the distribution depends on the decision variables. For the performative stable solution, we provide an algorithm, DSGTD-GD, which combines the distributed stochastic … Read more

    An Analysis of Constant Step Size SGD in the Non-convex Regime: Asymptotic Normality and Bias

  • Krishnakumar Balasubramanian
  • Stanislav Volgushev
  • Murat A. Erdogdu
  • Lu Yu
    • Categories Statistics, Stochastic Approaches, Stochastic Programming Tags , ,

    Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for such problems. However, quantifying the uncertainty associated with the underlying training algorithm is not well-studied in the non-convex setting. In order to address this short-coming, in this work, … Read more

    Epi-convergence of Sample Averages of a Random Lower Semi-continuous Functional Generated by a Markov Chain and Application to Stochastic Optimization

  • John Birge
  • Arnab Sur
    • Categories Stochastic Programming Tags , , , , , ,

    The purpose of this article is to establish epigraphical convergence of the sample averages of a random lower semi-continuous functional associated with a Harris recurrent Markov chain with stationary distribution $\pi$. Sample averages associated with an ergodic Markov chain with stationary probability distribution will epigraphically converge from $\pi$-almost all starting points. The property of Harris … Read more