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DTSTAMP:20261020T022408Z
SUMMARY:Junior Analysis Seminar – Alexandra Borkowski (KCL)
DESCRIPTION:Title\nA game interpretation of accelerated gradient flows: fro
 m convex optimisation to log-concave sampling\nAbstract\n\nI will discuss 
 two results on stable finite-time blow-up for semilinear wave equations wi
 th quadratic derivative nonlinearities. In one dimension\, both the time-d
 erivative and spatial-derivative nonlinearities admit “generalised self-
 similar” blow-up solutions. I will begin by briefly reviewing a result o
 n the construction and asymptotic stability of such solutions in the time-
 derivative case.\nFollowing the work of Wang\, Abernethy\, and Levy (2023)
 \, a two-player online game can be used to describe accelerated convex opt
 imisation algorithms. We will begin by developing this viewpoint in contin
 uous time\, i.e. by discussing what this game interpretation tells us abou
 t accelerated gradient flows. We then ask if a similar framework can be de
 veloped for sampling\, and construct an analogous two-player game for samp
 ling from probability measures with a log-concave density. In particular\,
  suitable choices of strategies for the two players recover the Underdampe
 d Langevin dynamics. This overall perspective provides a unified way of bo
 th understanding the Underdamped Langevin dynamics and obtaining explicit 
 accelerated convergence rates in KL divergence.\n\nPlease note that the se
 minar will take place in person in room 140 of Huxley Building.\n\nClick h
 ere to get to the Junior Analysis Seminar webpage.
URL:https://www.imperial.ac.uk/events/215209/junior-analysis-seminar-alexan
 dra-borkowski-kcl/
DTSTART;TZID=Europe/London:20261007T140000
DTEND;TZID=Europe/London:20261007T150000
LOCATION:140\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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