A ranking approach to global optimization

We consider the problem of maximizing an unknown function f over a compact and convex set X ⊂ R using as few observations f(x) as possible. We observe that the optimization of the function f essentially relies on learning the induced bipartite ranking rule of f . Based on this idea, we relate global optimization to bipartite ranking which allows to address problems with high dimensional input space, as well as cases of functions with weak regularity properties. The paper introduces novel meta-algorithms for global optimization which rely on the choice of any bipartite ranking method. Theoretical properties are provided as well as convergence guarantees and equivalences between various optimization methods are obtained as a by-product. Eventually, numerical evidence is given to show that the main algorithm of the paper which adapts empirically to the underlying ranking structure essentially outperforms existing state-of-the-art global optimization algorithms in typical benchmarks.