Stochastic Gradient Discrete Langevin Dynamics
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Keywords: Stochastic Gradient, Langevin Dynamics, Discrete Langevin Dynamics, MCMC, Discrete Sampling
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TL;DR: We propose a stochastic gradient langevin dynamics to sample in discrete spaces.
Abstract: Sampling via Markov chain Monte Carlo can be inefficient when each evaluation of the gradient of energy function depends on a large dataset. In continuous spaces, this challenge has been addressed by extending Langevin samplers with stochastic gradient estimators. However, such an approach cannot be directly applied to discrete spaces, as a naive migration leads to biased estimation with large variance. To fill this gap, we propose a new sampling strategy, \emph{Stochastic Gradient Discrete Langevin Dynamics}, to provide the first practical method for stochastic distribution sampling in discrete spaces. Our approach mitigates the bias of naive ``gradient'' estimators via a novel caching scheme, and reduces the estimation variance by introducing a modified Polyak step size control for simulation time adaptation. We demonstrate significant efficiency improvements across various sampling problems in discrete spaces, including Bayesian learning, stochastic integer programming, and prompt tuning for text-image models.
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Submission Number: 4373
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