We show that the herding procedure of Welling (2009) takes exactly the form
of a standard convex optimization algorithm--namely a conditional gradient
algorithm minimizing a quadratic moment discrepancy. This link enables us to
invoke convergence results from convex optimization and to consider faster
alternatives for the task of approximating integrals in a reproducing kernel
Hilbert space. We study the behavior of the different variants through
numerical simulations. The experiments indicate that while we can improve over
herding on the task of approximating integrals, the original herding algorithm
tends to approach more often the maximum entropy distribution, shedding more
light on the learning bias behind herding.

本文研究了 Welling（2009）的聚集过程，发现其采用标准的凸优化算法，即条件渐近算法，通过最小化二次矩差异。通过数值模拟研究了不同变体的行为。结果表明，虽然我们可以在近似积分的任务上对 herding 进行改进，但原始的 herding 算法更倾向于接近最大熵分布，揭示了 herding 背后的学习偏差。