BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andreas Bärmann/Kevin Aigner (FAU Erlangen-Nürnberg) DTSTART:20210706T101500Z DTEND:20210706T114500Z DTSTAMP:20260423T022602Z UID:MathDeep/12 DESCRIPTION:Title: Online Learning for Optimization Problems with Unknown or Uncertain Cost Functions\nby Andreas Bärmann/Kevin Aigner (FAU Erlangen-Nürnberg) as part of Mathematics of Deep Learning\n\n\nAbstract\nThe first part of t he talk begins by recapitulating several basic algorithms and results in o nline learning\, in particular the multiplicative weights method and onlin e gradient descent. Based on these algorithms\, we demonstrate how to lear n the objective function of a decision-maker while only observing the prob lem input data and the decision-maker’s corresponding decisions over mul tiple rounds. Our approach works for linear objectives over arbitrary feas ible sets for which we have a linear optimization oracle. The two exact al gorithms we present – based on multiplicative weights updates and online gradient descent respectively – converge at a rate of $O(1/\\sqrt T)$ a nd thus allow taking decisions which are essentially as good as those of t he observed decision-maker already after relatively few observations. We s how the effectiveness and possible applications of our methods in a broad computational study. This is joint work with Alexander Martin\, Sebastian Pokutta and Oskar Schneider.\n\nIn the second part of the talk\, we consid er the robust treatment of stochastic optimization problems involving rand om vectors with unknown discrete probability distributions. With this prob lem class\, we demonstrate the basic concepts of data-driven optimization under uncertainty. Furthermore\, we introduce a new iterative approach tha t uses scenario observations to learn more about the uncertainty over time . This means our solutions become less and less conservative\, interpolati ng between distributionally robust and stochastic optimization. We achieve this by solving the distributionally robust optimization problem over tim e via an online-learning approach while iteratively updating the ambiguity sets. We provide a regret bound for the quality of the obtained solutions that converges at a rate of $O(\\log T/T)$ and illustrate the effectivene ss of our procedure by numerical experiments. Our proposed algorithm is ab le to solve the online learning problem significantly faster than equivale nt reformulations. This is joint work with Kristin Braun\, Frauke Liers\, Sebastian Pokutta\, Oskar Schneider\, Kartikey Sharma and Sebastian Tschup pik.\n LOCATION:https://researchseminars.org/talk/MathDeep/12/ END:VEVENT END:VCALENDAR