226. Constrained sampling with Primal-Dual Langevin Monte Carlo
Invited abstract in session TC-1: First-Order Methods for Structured Optimization and Sampling, stream Zeroth and first-order optimization methods.
Tuesday, 14:00-16:00Room: B100/1001
Authors (first author is the speaker)
| 1. | Luiz Chamon
|
| Department of Applied Mathematics, École polytechnique |
Abstract
We consider the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of requirements. In contrast to traditional problem that considers only support constraints, however, our requirements are specified by the expected values of general nonlinear functions. Hence, methods based on mirror maps, barriers, and penalties, are not suited for this task. In this talk, we introduce a discrete-time primal-dual Langevin Monte Carlo algorithm (PD-LMC) that simultaneously constrains the target distribution and samples from it. By extending classical optimization arguments for saddle-point algorithms to the geometry of Wasserstein space, we derive convergence guarantees for target distributions satisfying (strong) convexity and log-Sobolev inequalities. We showcase the relevance and effectiveness of PD-LMC in fair and counterfactual Bayesian inference.
Keywords
- First-order optimization
Status: accepted
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