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A particle consensus approach to solving nonconvex-nonconcave min-max problems
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We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims to solve the outer minimization problem. The dynamics are characterized by a consensus-type interaction with additional stochasticity to promote exploration of the objective landscape. Without relying on convexity or concavity assumptions, we establish theoretical convergence guarantees of the algorithm via a suitable mean-field approximation of the particle systems. Numerical experiments illustrate the validity of the proposed approach. In particular, the algorithm is able to identify a global min-max solution, in contrast to gradient-based methods, which typically converge to possibly suboptimal stationary points.
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Cited by 2 Pith papers
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Exploiting Structure with Anisotropic Consensus-Based Optimization
Anisotropic CBO's computational complexity depends exponentially only on the intrinsic dimension of an additively separable objective, not the ambient dimension, under aligned anisotropic noise.
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Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Consensus-based optimization matches or beats natural evolution strategies as a closed-box adversarial attack method in easier attack scenarios, and consensus hopping is shown to be a gradient-descent-like limit of CBO.
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