In addition to solving (1), we also wish topreserve privacyfor the people who contributed to the dataset Z.

Numerical experiments are conducted tosupport our theoretical results.

Recently, diffusion models havebeen used to solvevarious inverse problems in anunsupervised manner withappropriate modifications tothesampling process.

Smooth convex optimization problems over polytopes are an important class of problems that appear in many settings, such as low-rank matrix completion [1],structured supervised learning [2,3],electrical flowsovergraphs [4],video co-localization in computer vision [5], traffic assignment problems [6], and submodular function minimization [7].