Pengxiang Xu

Normalized stochastic proximal approximation methods for nonsmooth composite optimization under heavy-tailed noise

  • Chunhao Han
  • Xiao Wang
  • Pengxiang Xu
  • Jin Zhang
    • Categories Nonlinear Optimization, Nonsmooth Optimization

    In this paper, we study nonsmooth composite optimization problems under heavy-tailed noise, with the objective being a summation of a nested function and a nonsmooth convex regularizer. We propose stochastic proximal approximation methods incorporating a normalization technique to handle the potential challenges caused by the nonsmooth regularizer and heavy-tailed noise. For the case where the … Read more

    Non-convex stochastic compositional optimization under heavy-tailed noise

  • Chunhao Han
  • Xiao Wang
  • Pengxiang Xu
  • Jin Zhang
    • Categories Nonlinear Optimization

    This paper investigates non-convex stochastic compositional optimization under heavy-tailed noise, where the stochastic noise exhibits bounded $p$th moment with $p\in(1,2]$. The main challenges arise from biased gradient estimates of the objective and the violation of the standard bounded-variance assumption. To address these issues, we propose a generic algorithm framework of Normalized Stochastic Compositional Gradient methods … Read more