In this paper we study anisotropic consensus-based optimization (CBO), a multi-agent metaheuristic derivative-free optimization method capable of globally minimizing nonconvex and nonsmooth functions in high dimensions. CBO is based on stochastic swarm intelligence, and inspired by consensus dynamics and opinion formation. Compared to other metaheuristic algorithms like particle swarm optimization, CBO is of a simpler nature and therefore more amenable to theoretical analysis. By adapting a recently established proof technique, we show that anisotropic CBO converges globally with a dimension-independent rate for a rich class of objective functions under minimal assumptions on the initialization of the method. Moreover, the proof technique reveals that CBO performs a convexification of the optimization problem as the number of agents goes to infinity, thus providing an insight into the internal CBO mechanisms responsible for the success of the method. To motivate anisotropic CBO from a practical perspective, we further test the method on a complicated high-dimensional benchmark problem, which is well understood in the machine learning literature.

翻译：本文研究各向异性共识优化算法（CBO），这是一种基于多智能体的无导数元启发式优化方法，能够全局最小化高维非凸非光滑函数。CBO基于随机群体智能，受共识动力学和意见形成启发。与粒子群优化等其他元启发式算法相比，CBO特性更简单，因此更易于理论分析。通过采用近期建立的证明技术，我们证明各向异性CBO在初始化条件最小假设下，对一类丰富目标函数能以与维度无关的速率全局收敛。此外，该证明技术揭示：当智能体数量趋于无穷时，CBO实现了优化问题的凸化，从而揭示了该方法成功的内在CBO机制。为从实践角度验证各向异性CBO，我们进一步在机器学习领域公认的复杂高维基准问题上测试了该方法。