Distributed Quasi Monte-Carlo Methods in a Heterogeneous Environment

We present an asynchronous Quasi-Monte Carlo (QMC) algorithm for numerical integration tailored for heterogeneous environments. QMC techniques are better suited for high dimensions than adaptive methods and have generally better convergence properties than classical Monte Carlo methods. The algorithm focuses on the asynchronous computation of randomized lattice (Korobov) rules. Whereas the individual rules disallow realistic error estimates, randomization provides a tool for giving confidence intervals for the magnitude of the error. The algorithm generates a sequence of stochastic families, using an increasing number of points, for the purpose of automatic termination. In the algorithm, each each randomized rule constitutes a single unit of work; a work assignment consists of a set of work units. Static and dynamic load balancing strategies are explored to keep the processors busy performing useful work while gradually calculating higher-level families needed to reach the desired accuracy. We present results in the context of a performance model for parallel programs executing in a heterogeneous environment.