论文标题
基于共识的优化：适当的和平均场限制
Consensus-Based Optimization on Hypersurfaces: Well-Posedness and Mean-Field Limit
论文作者
论文摘要
我们引入了一个新的随机差异模型，用于在紧凑型超曲面上全局优化非convex函数。该模型的灵感来自随机kuramoto-vicsek系统，属于基于共识的优化方法的类别。实际上，粒子在朝向瞬时共识点驱动的超浮雕上移动，该粒子根据拉普拉斯的原理计算为由成本函数加权的粒子位置的凸组合。共识点代表与全局最小化器的近似值。随机向量场进一步扰动动力学，以偏爱探索，其方差是粒子到共识点的距离的函数。特别是，一旦达成共识，随机组件就会消失。在本文中，我们研究了模型的适当性，并严格地得出了大粒子极限的平均场近似值。
We introduce a new stochastic differential model for global optimization of nonconvex functions on compact hypersurfaces. The model is inspired by the stochastic Kuramoto-Vicsek system and belongs to the class of Consensus-Based Optimization methods. In fact, particles move on the hypersurface driven by a drift towards an instantaneous consensus point, computed as a convex combination of the particle locations weighted by the cost function according to Laplace's principle. The consensus point represents an approximation to a global minimizer. The dynamics is further perturbed by a random vector field to favor exploration, whose variance is a function of the distance of the particles to the consensus point. In particular, as soon as the consensus is reached, then the stochastic component vanishes. In this paper, we study the well-posedness of the model and we derive rigorously its mean-field approximation for large particle limit.
