# Global convergence of optimized adaptive importance samplers

arXiv: https://arxiv.org/abs/2201.00409 · HTML: https://mlsanity.com/paper/2201.00409/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 60 references that are in the map.
- First posted on arXiv 2 Jan 2022.

## Builds on (most cited first, 21 of 21)

- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Global Convergence of Langevin Dynamics Based Algorithms for Nonconvex Optimization](https://mlsanity.com/paper/1707.06618/) (2017)
- [The promises and pitfalls of Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1811.10072/) (2018)
- [Global Non-convex Optimization with Discretized Diffusions](https://mlsanity.com/paper/1810.12361/) (2018)
- [Variance reduction properties of the reparameterization trick](https://mlsanity.com/paper/1809.10330/) (2018)
- [Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization](https://mlsanity.com/paper/1910.02008/) (2019)
- [Faster Convergence of Stochastic Gradient Langevin Dynamics for Non-Log-Concave Sampling](https://mlsanity.com/paper/2010.09597/) (2020)
- [Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration](https://mlsanity.com/paper/1809.04618/) (2018)
- [Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.15980/) (2021)
- [Adaptive importance sampling for control and inference](https://mlsanity.com/paper/1505.01874/) (2015)
- [Layered Adaptive Importance Sampling](https://mlsanity.com/paper/1505.04732/) (2015)
- [Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization](https://mlsanity.com/paper/2002.05465/) (2020)
- [Convergence rates for optimised adaptive importance samplers](https://mlsanity.com/paper/1903.12044/) (2019)
- [Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks](https://mlsanity.com/paper/2105.13937/) (2021)
- [Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function](https://mlsanity.com/paper/2107.08649/) (2021)
- [Asymptotic optimality of adaptive importance sampling](https://mlsanity.com/paper/1806.00989/) (2018)
- [Langevin Incremental Mixture Importance Sampling](https://mlsanity.com/paper/1611.06874/) (2016)
- [Adaptive Importance Sampling via Stochastic Convex Programming](https://mlsanity.com/paper/1412.4845/) (2014)
- [MCMC-driven importance samplers](https://mlsanity.com/paper/2105.02579/) (2021)

## Built on by (most cited first, 2 of 2)

- [Cooperation in the Latent Space: The Benefits of Adding Mixture Components in Variational Autoencoders](https://mlsanity.com/paper/2209.15514/) (2022)
- [Adaptively Optimised Adaptive Importance Samplers](https://mlsanity.com/paper/2307.09341/) (2023)

## Abstract (arXiv)

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 chi2-divergence between the target and the proposal and develop a scheme which performs global optimization of chi2-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 close this gap by utilizing the nonasymptotic bounds for stochastic gradient Langevin dynamics (SGLD) for the global optimization of chi2-divergence and derive nonasymptotic bounds for the MSE by leveraging recent results from non-convex optimization literature. The resulting AIS schemes have explicit theoretical guarantees that are uniform-in-time.