Exploring Non-Convex Discrete Energy Landscapes: A Langevin-Like Sampler with Replica Exchange
Keywords: discrete sampling, Langevin dynamics, replica exchange, energy-based model, Metropolis-Hastings, Markov Chain Monte Carlo, locally-balanced proposal
TL;DR: We propose a discrete Langevin-like sampler with replica exchange to efficiently explore non-convex discrete energy landscapes.
Abstract: Gradient-based Discrete Samplers (GDSs) are effective for sampling discrete energy landscapes. However, they often stagnate in complex, non-convex settings. To improve exploration, we introduce the Discrete Replica EXchangE Langevin (DREXEL) sampler and its variant with Adjusted Metropolis (DREAM). These samplers use two GDSs at different temperatures and step sizes: one focuses on local exploitation, while the other explores broader energy landscapes. When energy differences are significant, sample swaps occur, which are determined by a mechanism tailored for discrete sampling to ensure detailed balance. Theoretically, we prove both DREXEL and DREAM converge asymptotically to the target energy and exhibit faster mixing than a single GDS. Experiments further confirm their efficiency in exploring non-convex discrete energy landscapes.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 1657
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