An Approximate Monte Carlo Adaptive Importance Sampling Method

It is well known that zero-variance Monte Carlo solutions are possible if an exact importance function is available to bias the random walks. Geometric convergence with iteration has been demonstrated when the importance function estimated on the nʹth iteration is used to bias the random walks on the n + 1st iteration, i.e., adaptive importance sampling. Note that geometric convergence with iteration may be less efficient than a nonadaptive Monte Carlo calculation if the time per iteration grows too fast. This paper shows a general method for sampling the zero-variance kernels enabling a Monte Carlo solution that converges inversely with the computer time.