Sampling with Shielded Langevin Monte Carlo Using Navigation Potentials
This addresses a novel constrained sampling problem for applications like MIMO detection, though it appears incremental as an extension of LMC with navigation-inspired constraints.
The paper tackles the problem of sampling from unnormalized target distributions over non-convex spaces with convex holes, introducing shielded Langevin Monte Carlo that uses a spatially adaptive temperature and repulsive drift to keep samples feasible. Experiments on a 2D Gaussian mixture and MIMO symbol detection demonstrate its advantages over unconstrained methods.
We introduce shielded Langevin Monte Carlo (LMC), a constrained sampler inspired by navigation functions, capable of sampling from unnormalized target distributions defined over punctured supports. In other words, this approach samples from non-convex spaces defined as convex sets with convex holes. This defines a novel and challenging problem in constrained sampling. To do so, the sampler incorporates a combination of a spatially adaptive temperature and a repulsive drift to ensure that samples remain within the feasible region. Experiments on a 2D Gaussian mixture and multiple-input multiple-output (MIMO) symbol detection showcase the advantages of the proposed shielded LMC in contrast to unconstrained cases.