Gradient-based Discrete Sampling with Automatic Cyclical Scheduling
Patrick Pynadath Riddhiman Bhattacharya Arun Hariharan Ruqi Zhang
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.