Experimental Improvements of Global Optimization Algorithms for Lipschitz Functions

Perceval Beja-Battais (1, 2) , Gaëtan Serré (1, 2) , Sophia Chirrane (3)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
2 CB - CB - Centre Borelli - UMR 9010
3 CentraleSupélec

In this paper, we define an experimental context in which we tested the performances of LIPO and AdaLIPO, two global optimization algorithms for Lipschitz functions, introduced in [10]. We provide experimental proofs of the efficiency of those algorithms, led numerical statistical analysis of our results, and suggested two intuitive improvements from the vanilla version of the algorithms, referred as LIPO-E and AdaLIPO-E. Within our test bench, these improvements allow the algorithms to converge significantly faster and whenever they struggle to find a better maximizer. Finally, we defined the scope of application of LIPO and AdaLIPO. We show that they are very prone to the curse of dimensionality and tend quickly to Pure Random Search when the dimension increases.

Mots clés: global optimization; Lipschitz applications; statistical analysis; convergence rate bounds; numerical analysis; global optimization Lipschitz applications statistical analysis convergence rate bounds numerical analysis

Domaines: Optimisation et contrôle [math.OC]; Calcul [stat.CO]

Perceval Beja-Battais, Gaëtan Serré, Sophia Chirrane. Experimental Improvements of Global Optimization Algorithms for Lipschitz Functions. Image Processing On Line, 2023, ⟨10.5201/ipol⟩. ⟨hal-04069150⟩