A Mean Field Approach for Optimization in Particle Systems and Applications

This paper investigates the limit behavior of Markov decision processes made of independent particles evolving in a common environment, when the number of particles goes to infnity. In the fnite horizon case or with a discounted cost and an infnite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges to the optimal cost of a deterministic system. Convergence also holds for optimal policies. We further provide insights on the speed of convergence by proving several central limits theorems for the cost and the state of the Markov decision process with explicit formulas for the limit. Then, our framework is applied to a brokering problem in grid computing. Several simulations with growing numbers of processors are reported. They compare the performance of the optimal policy of the limit system used in the fnite case with classical policies by measuring its asymptotic gain.