Gradient-based Discrete Sampling with Automatic Cyclical Scheduling

TL;DR

This paper introduces an automatic cyclical scheduling method for gradient-based discrete sampling that effectively explores multimodal distributions, ensuring better convergence and sampling accuracy in high-dimensional discrete models.

Contribution

We propose a novel automatic cyclical scheduling approach with adaptive hyperparameter tuning for improved sampling in multimodal discrete distributions, with proven convergence guarantees.

Findings

Outperforms existing methods in sampling complex multimodal distributions

Achieves better exploration of multiple modes with cyclical schedules

Demonstrates robustness across diverse datasets

Abstract

Discrete distributions, particularly in high-dimensional deep models, are often highly multimodal due to inherent discontinuities. While gradient-based discrete sampling has proven effective, it is susceptible to becoming trapped in local modes due to the gradient information. To tackle this challenge, we propose an automatic cyclical scheduling, designed for efficient and accurate sampling in multimodal discrete distributions. Our method contains three key components: (1) a cyclical step size schedule where large steps discover new modes and small steps exploit each mode; (2) a cyclical balancing schedule, ensuring "balanced" proposals for given step sizes and high efficiency of the Markov chain; and (3) an automatic tuning scheme for adjusting the hyperparameters in the cyclical schedules, allowing adaptability across diverse datasets with minimal tuning. We prove the non-asymptotic convergence and inference guarantee for our method in general discrete distributions. Extensive experiments demonstrate the superiority of our method in sampling complex multimodal discrete distributions.