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Smoothness and adaptivity in zero-th order nonparametric optimization

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We consider the problem of maximizing a function f with unknown regularity. We show that for the objective of cumulative regret minimization, there exists no optimal strategy that's adaptive to the unknown smoothness of f, even though such adaptive strategies exist in the optimization setting under the same assumptions. We also show sufficient conditions under which this impossibility result does not hold, and exhibit optimal adaptive procedures in these settings.

 

Dates: 
Thursday, May 3, 2018 - 11:00
Location: 
Inria, room A00
Speaker(s): 
Andrea Locatelli
Affiliation(s): 
Université de Magdeburg