Develop computationally controlled warm starts for heavy-tailed projection samplers

Construct an initialization procedure with controlled computational cost and establish quantitative warm-start guarantees for stereographic and Sub-Cauchy projection samplers targeting heavy-tailed distributions.

Background

The main mixing-time theorems assume warm initial distributions: polynomially warm starts in the moderately heavy-tailed regime and uniformly bounded warmness in the heavier-tailed regime. These assumptions provide the initial-distribution control needed by the conductance argument but do not themselves specify an efficiently computable initialization.

The paper notes that constructing such an initialization is challenging and refers to algorithmic warm-start results for MALA and HMC as related developments. An analogous guarantee for projection samplers targeting heavy-tailed distributions is explicitly left open.