Particle gradient descent is widely used to optimize functions of probability measures. Mean-field analyses tend the number of particles to infinity, thereby providing insights on the density of particles. In a mean-field regime, the particles globally optimize displacement convex functions. We investigate the consequence of this convergence for a finite number of particles. To achieve an ϵ-optimal solution, we prove that O(1/ϵ^2) particles and O(d/ϵ^4) time are sufficient for Lipschitz displace…