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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260804T120000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/optimization
 -seminar-david-torregrosa-belen-convergence
SUMMARY:Optimization seminar-David Torregrosa Belén-Convergence of a proxi
 mal\nstochastic subgradient method under the Kurdyka-Lojasiewicz condition
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n David Torregrosa Belén\n\nAFFILIATION:\n University
  of Alicante\n\nLOCATION:\n MC 5501\n\nABSTRACT:This talk presents a proxi
 mal stochastic subgradient\nmethod for minimizing the sum of an expected 
 cost and a lower\nsemicontinuous\, prox-bounded function. We target a bro
 ad class of\nnonconvex integrands obeying a nonsmooth\, localized variant
  of the\ndescent lemma in the decision variable\, which in particular cov
 ers\nsmooth losses with Lipschitz gradient. At each iteration\, the\nexpe
 cted cost is replaced by a sample average that is progressively\nrefined\
 , and the proximal stepsize is selected by an Armijo-type line\nsearch en
 forcing a\nsufficient decrease property up to stochastic errors induced by
 \nthe sample-based approximation. This framework accommodates more\ngener
 al problem formulations than existing methods and our analysis\nyields c
 onvergence guarantees that\, to the best of our knowledge\,\nare new even
  in the smooth setting. Specifically\, we establish almost\nsure converg
 ence of the sequence of function values and stationarity\nof every accumu
 lation point of the trajectories under the relaxed\nrequirement that the 
 sample-size sequence be merely nondecreasing and\nunbounded. Leveraging t
 he Kurdyka-Lojasiewicz property\, we further\nproof convergence of the wh
 ole trajectory to a single stationary\npoint. Finally\, for exponential-t
 ype desingularizing functions and\npolynomially growing sample sizes\, we
  derive explicit polynomial\nconvergence rates\, up to logarithmic factor
 \, for both the function\nvalues and the iterates. This is a joint work w
 ith Felipe Atenas\,\nPedro Pérez-Aros and Alejandro\nJofré\, from the Un
 iversity of Chile.
DTSTAMP:20260803T040645Z
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