Gradient-based Discrete Sampling with Automatic Cyclical Scheduling
This work addresses a bottleneck in sampling for high-dimensional deep models, offering an incremental improvement with automatic tuning for adaptability.
The paper tackles the problem of gradient-based discrete sampling getting trapped in local modes in multimodal distributions by proposing an automatic cyclical scheduling method, which demonstrates superiority in sampling complex multimodal discrete distributions through extensive experiments.
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.