Designing alternative proposal chains with improved mixing

Develop alternative proposal Markov chains for Metropolis-adjusted constrained sampling that achieve similar or better mixing-time guarantees than MAPLA, and quantify their dependence on dimension and metric properties.

Background

MAPLA uses a natural-gradient-inspired proposal; the authors highlight the open question of whether other proposals might yield superior one-step overlap or acceptance properties and thus improved mixing times, especially under self-concordant or stronger metric assumptions.

Such designs could lead to new first-order samplers that are more efficient or robust across diverse constrained domains, complementing MAPLA and DikinWalk.