BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vincent Molin (Chalmers University of Technology & University of G othenburg) DTSTART:20250416T111500Z DTEND:20250416T120000Z DTSTAMP:20260422T161048Z UID:gbgstats/85 DESCRIPTION:Title: Controlled stochastic processes for simulated annealing\nby Vincent Molin (Chalmers University of Technology & University of Gothenburg) as pa rt of Gothenburg statistics seminar\n\nLecture held in MVL14.\n\nAbstract\ nSimulated annealing solves optimization problems by means of a random wal k in an energy landscape based on the objective function and a temperature parameter. By slowly decreasing the temperature\, the algorithm converges to the global optimal solution\, also for nonconvex functions. However\, if the temperature is decreased too quickly\, this procedure often gets st uck in local minima. To overcome this\, we here present a new perspective on simulated annealing. More precisely\, we consider the cooling landscape as a curve of probability measures and prove that there exists a minimal norm velocity field which solves the continuity equation. The latter is a differential equation which governs the evolution of the aforementioned cu rve. The solution is the weak gradient of an integrable function\, which i s in line with the interpretation of the velocity field as a derivative of optimal transport maps. We also show that controlling stochastic annealin g processes by superimposing this velocity field would allow them to follo w arbitrarily fast cooling schedules. Based on these findings\, we design novel interacting particle based optimization methods\, convergent optimal transport based approximations to this control\, that accelerate simulate d annealing processes. This acceleration behavior is also validated on a n umber of numerical experiments.\n LOCATION:https://researchseminars.org/talk/gbgstats/85/ END:VEVENT END:VCALENDAR