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SUMMARY:Non-convex Optimisation Using the Polyak-Łojasiewicz Inequality -
  Edoardo Calvello (Imperial College)
DTSTART:20200204T130000Z
DTEND:20200204T140000Z
UID:TALK135394@talks.cam.ac.uk
CONTACT:Mateja Jamnik
DESCRIPTION:We consider the idea of solving a non-convex optimisation prob
 lem by adding a large enough strongly-convex function to make the objectiv
 e function convex. This allows the use of simpler convex optimisers\, yet\
 , given the large strong-convexity constant required\, yields a value clos
 er to the minimum of the function added than that of the objective one. We
  try to fix this with the novel idea of instead adding a function that mak
 es the objective satisfy the Polyak-Łojasiewicz (PL) inequality\, a much 
 weaker condition than strong-convexity. Building on previous work\, we con
 struct an optimisation algorithm relying on this method. We find that a mu
 ch smaller multiplicative constant is needed for convergence to a minimum.
  We attempt to find and prove convergence rates and computational complexi
 ty and test which algorithm yields a more accurate minimum.
LOCATION:LT2\, Computer Laboratory\, William Gates Building
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