Consensus-based optimization in the spirit of mirror descent
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In this talk, I will discuss a consensus-based optimization (CBO) (see Pinnau, Totzeck, Tse, and Martin 2017) scheme that is inspired by mirror descent. CBO has emerged as a powerful zero-order optimization algorithm with a well-posed mean field limit. Introducing the mirrored version (as in Bungert, Hoffmann, Kim, and Roith 2025) generalizes the scheme in the same way mirror descent generalizes standard gradient descent. Assuming bounds on the Bregman distance associated to the distance generating function, we provide asymptotic convergence results for MirrorCBO with explicit exponential rate. Furthermore, we show the flexibility and performance of the algorithm applied to sparsity-inducing and constrained optimization, in the gradient-free setting. This even allows us to easily integrate the mirrored version into the polarization setting of Bungert, Roith, and Wacker 2024. In particular, we will discuss an efficient implementation within the CBXPy (Bailo, Barbaro, Gomes, Riedl, Roith, Totzeck, and Vaes 2024) framework. Finally, we also discuss how CBO and its mirrored version can be used for closed-box adversarial attacks.