Global convergence of optimized adaptive importance samplers. (arXiv:2201.00409v1 [stat.CO])

We analyze the optimized adaptive importance sampler (OAIS) for performing
Monte Carlo integration with general proposals. We leverage a classical result
which shows that the bias and the mean-squared error (MSE) of the importance
sampling scales with the $\chi^2$-divergence between the target and the
proposal and develop a scheme which performs global optimization of
$\chi^2$-divergence. While it is known that this quantity is convex for
exponential family proposals, the case of the general proposals has been an
open problem. We …

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