Learning to Sample from Multimodal Distributions

Markov chain Monte Carlo (MCMC) is an established method for sampling from complex probability distributions by building Markov chains whose state transitions occur by a proposal-acceptance mechanism. MCMC however tends to fail on distributions whose modes are separated by wide low-probability regions. Neural networks have been integrated into MCMC to try and address this challenge, but existing approaches cannot guarantee that the resulting chain asymptotically produces samples from the target distribution, or even that they cover all modes. In this work, we use constrained optimization to put forward a new way of training neural MCMC that reduces samples correlation, ensures the coverage of all modes, and lower bounds the proposal acceptance rate. We prove that, under mild conditions, any solution of this constrained problem results in an ergodic Markov chain whose empirical measure converges to the target distribution. We then propose an effective algorithm to tackle this problem and illustrate its performance on a variety of applications from mixture models to physical systems, and reliability engineering showing that it matches or outperforms existing baselines.