Fast Monte-Carlo

Abstract

This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed eigenvalue-based methodology reduces the number of paths required for Monte Carlo from as many as 1,000,000 to as few as 10 (depending on the simulation time horizon $T$), and delivers comparable, distributionally robust results, as measured by the Wasserstein distance. The proposed methodology also produces a significant variance reduction in the steady-state distribution.

12 pages, originally published in the proceedings of the Winter Simulation Conference 2025

References in corpus (3)

• Optimal control as a graphical model inference problem
• In-memory eigenvector computation in time O(1)
• A Tutorial on the Spectral Theory of Markov Chains