In this paper we study consensus-based optimization (CBO), which is a  metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on an experimentally supported intuition that CBO  performs a gradient descent on the convex envelope of a given objective , we derive a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions. Our results unveil internal mechanisms of CBO that are responsible for the success of the method.  Furthermore, we improve prior analyses by requiring minimal assumptions about the initialization of the method and by covering objectives that are merely locally Lipschitz continuous. As a by-product of our analysis, we establish a quantitative nonasymptotic Laplace principle, which may be of independent interest.
In this paper we study consensus-based optimization (CBO), which is a multi-agent metaheuristic derivative-free optimization method that can globally minimize nonconvex nonsmooth functions and is amenable to theoretical analysis. Based on an experimentally supported intuition that CBO always performs a gradient descent of the squared Euclidean distance to the global minimizer , we derive a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions. The result unveils internal mechanisms of CBO that are responsible for the success of the method. In particular, we prove that CBO performs a convexification of a very large class of optimization problems as the number of optimizing agents goes to infinity. Furthermore, we improve prior analyses by requiring minimal assumptions about the initialization of the method and by covering objectives that are merely locally Lipschitz continuous. As a by-product of the analysis, we establish a quantitative nonasymptotic Laplace principle, which may be of independent interest.
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multi-agent
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always
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on the convex envelope of a given objective
of the squared Euclidean distance to the global minimizer
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Our results unveil
The result unveils
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In particular, we prove that CBO performs a convexification of a very large class of optimization problems as the number of optimizing agents goes to infinity.
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our
the