Some Guidelines and Guarantees for Common Random Numbers

Abstract

Common random numbers (CRN) is a widely-used technique for reducing variance in comparing stochastic systems through simulation. Its popularity derives from its intuitive appeal and ease of implementation. However, though CRN has been observed to work well with a broad range of models, the class of systems for which it is provably advantageous has remained rather limited. This paper has two purposes: We first discuss the effectiveness and optimality of CRN in a general setting, stressing the roles played by monotonicity and continuity properties. We then present specific, new classes of systems and comparisons for which CRN is beneficial and even optimal. Our conclusions for these systems are largely consistent with simulation practice and lend further theoretical support to folklore. Our results differ from those of previous analyses primarily because we put conditions on the timing of events, rather than the sequence of states, in a discrete-event simulation. We formulate our results in three settings corresponding to three applications of CRN: distributional comparisons, structural comparisons, and sensitivity analysis. In each case, we make use of conditions that simultaneously ensure monotonicity and continuity in the timing of events. These properties are established through explicit recursions for event epochs in terms of increasing, continuous functions.simulation, variance reduction techniques, stochastic ordering, common random numbers

Universal parameter optimisation in games based on SPSA

“…In fact, if this method is employed, the convergence rate is improved to O(t −1/2 ). This was shown for FDSA by Glasserman and Yao (1992) and L'Ecuyer and Yin (1998) and later extended to SPSA by Kleinman, Spall and Neiman (1999).…”

“…When the objective function is evaluated by means of running some computer simulation then it has been observed that the method of Common Random Numbers (CRN) can be used to decrease the variance of the gradient's estimate (Glasserman & Yao, 1992;L'Ecuyer & Yin, 1998;Kleinman, Spall & Neiman, 1999). In fact, if this method is employed, the convergence rate is improved to O(t −1/2 ).…”

Investigating the Effectiveness of Variance Reduction Techniques in Manufacturing, Call Center and Cross-Docking Discrete Event Simulation Models

“…They conclude that the application of CRN on discrete event simulation models is guaranteed to yield a variance reduction (Glasserman and Yao 1992 In comparison to CRN, the AV technique reduces variance by artificially inducing a correlation between replications of the simulation model. Unlike CRN, the AV technique applies when seeking to improve the performance of a single system's performance.…”

Intractability results in discrete-event simulation

“…Our results then imply that it is unlikely to algorithmically détermine whether satisfactory synchronization is achieved in such runs. As an easy instance, common random numbers together with inversion have been shown to minimize estimator variance provided that the monotonicity condition holds (Glasserman and Yao, 1992b). One should recall, however, that the vérification of the commuting condition is a hard problem.…”