BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Kuhn (EPFL) DTSTART:20210531T133000Z DTEND:20210531T143000Z DTSTAMP:20260423T021009Z UID:OWOS/54 DESCRIPTION:Title: A General Framework for Optimal Data-Driven Optimization\nby Daniel Kuhn (EPFL) as part of One World Optimization seminar\n\n\nAbstract\nWe propos e a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally\, a data-driven decision i s simply a function that maps the available training data to a feasible ac tion. It can always be expressed as the minimizer of a surrogate optimizat ion model constructed from the data. The quality of a data-driven decision is measured by its out-of-sample risk. An additional quality measure is i ts out-of-sample disappointment\, which we define as the probability that the out-of-sample risk exceeds the optimal value of the surrogate optimiza tion model. The crux of data-driven optimization is that the data-generati ng probability measure is unknown. An ideal data-driven decision should th erefore minimize the out-of-sample risk simultaneously with respect to eve ry conceivable probability measure (and thus in particular with respect to the unknown true measure). Unfortunately\, such ideal data-driven decisio ns are generally unavailable. This prompts us to seek data-driven decision s that minimize the out-of-sample risk subject to an upper bound on the ou t-of-sample disappointment - again simultaneously with respect to every co nceivable probability measure. We prove that such Pareto-dominant data-dri ven decisions exist under conditions that allow for interesting applicatio ns: the unknown data-generating probability measure must belong to a param etric ambiguity set\, and the corresponding parameters must admit a suffic ient statistic that satisfies a large deviation principle. If these condit ions hold\, we can further prove that the surrogate optimization model gen erating the optimal data-driven decision must be a distributionally robust optimization problem constructed from the sufficient statistic and the ra te function of its large deviation principle. This shows that the optimal method for mapping data to decisions is\, in a rigorous statistical sense\ , to solve a distributionally robust optimization model. Maybe surprisingl y\, this result holds irrespective of whether the original stochastic opti mization problem is convex or not and holds even when the training data is non-i.i.d. As a byproduct\, our analysis reveals how the structural prope rties of the data-generating stochastic process impact the shape of the am biguity set underlying the optimal distributionally robust optimization mo del.\n\nThis is joint work with Tobias Sutter and Bart Van Parys.\n\nThe a ddress and password of the zoom room of the seminar are sent by e-mail on the mailinglist of the seminar one day before each talk\n LOCATION:https://researchseminars.org/talk/OWOS/54/ END:VEVENT END:VCALENDAR