Variance reduction for generalized likelihood ratio method by conditional Monte Carlo and randomized Quasi-Monte Carlo methods

Abstract

The generalized likelihood ratio (GLR) method is a recently introduced gradient estimation method for handling discontinuities in a wide range of sample performances. We put the GLR methods from previous work into a single framework, simplify regularity conditions to justify the unbiasedness of GLR, and relax some of those conditions that are difficult to verify in practice. Moreover, we combine GLR with conditional Monte Carlo methods and randomized quasi-Monte Carlo methods to reduce the variance. Numerical experiments show that variance reduction could be significant in various applications.

Keywords

• Simulation
• Stochastic gradient estimation
• Conditional Monte Carlo
• Randomized quasi-Monte Carlo