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Paper · 1703.02628 · 2017

Global optimization of Lipschitz functions

arXiv · PDF · Open in the Atlas

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We lifted 3 functions out of this paper's own repositories and ran 1 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
Sycor4x/lipo reimplementation 1 of 1
leonidk/physical_simulation pwc_unofficial 0 of 2
FunctionStatusWhere it lives
flatten_dict Ran Sycor4x/lipo/benchmarks.py
code served (permissive licence) · get_code("9bbabe0c6fef21bb")
get_prog_path_name Not yet run leonidk/physical_simulation/optimize.py
code served (permissive licence) · get_code("4dffa9d452e0ff9a")
run_prog_process Not yet run leonidk/physical_simulation/optimize.py
code served (permissive licence) · get_code("48e16180e52de1f4")

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Abstract

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO which assumes the Lipschitz constant to be known. Consistency, minimax rates for LIPO are proved, as well as fast rates under an additional Hölder like condition. An adaptive version of LIPO is also introduced for the more realistic setup where the Lipschitz constant is unknown and has to be estimated along with the optimization. Similar theoretical guarantees are shown to hold for the adaptive LIPO algorithm and a numerical assessment is provided at the end of the paper to illustrate the potential of this strategy with respect to state-of-the-art methods over typical benchmark problems for global optimization.

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