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[00995] Convergence of a Normal Map-Based Prox-SGD Method for Stochastic Composite Optimization

  • Session Time & Room : 1E (Aug.21, 17:40-19:20) @F309
  • Type : Contributed Talk
  • Abstract : In this talk, we present a novel stochastic normal map-based algorithm (nor-SGD) for nonconvex composite-type optimization problems and discuss its asymptotic convergence properties. We first analyze the global convergence behavior of nor-SGD and show that every accumulation point of the generated sequence of iterates is a stationary point almost surely and in an expectation sense. The obtained results hold under standard assumptions and extend the more limited convergence guarantees of nonconvex prox-SGD. In addition, based on the Kurdyka-Lojasiewicz (KL) framework and utilizing an adaptive time window mechanism, we establish almost sure convergence of the iterates and derive convergence rates that depend on the KL exponent and the step size dynamics. The techniques studied in this work can be potentially applied to other families of stochastic and simulation-based algorithms.
  • Classification : 90C06, 90C15, 90C26
  • Format : Talk at Waseda University
  • Author(s) :
    • Andre Milzarek (The Chinese University of Hong Kong, Shenzhen)
    • Junwen Qiu (The Chinese University of Hong Kong, Shenzhen)