S. Anthoine : Optimal Computational Trade-Off of Inexact Proximal Methods.
This is a joint work with Pierre Machart (LIF, Marseille).
Recent advances in machine learning and signal processing have led to
more involved optimisation problems, while abundance of data calls for
more efficient optimization algorithms. First-order methods are now
extensively employed to tackle these issues and, among them,
proximal-gradient algorithms are becoming increasingly popular. The
heart of these procedures is the proximity operator. In the favorable
cases, analytical forms exist. However, there are many problems where
the proximity operator can only be computed numerically, giving rise to
what can be referred to as inexact proximal-gradient algorithms. With
those algorithms, one needs to set: a) the number of iterations of the
precedure, b) the precision in the appoximation of the proximity
operator, at each iteration. These quantities, which can be seen as
hyper-parameters, are the object of study of this talk. Expressing the
computational cost of inexact proximal-gradient algorithms, we derive a
computationally optimal strategy to set those hyper-parameters.
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