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About this paper
Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili, Marcelo Pereyra
HRLMC adapts Langevin Monte Carlo sampling to a mirror geometry by combining gradient steps with Hessian-dependent Gaussian noise. It maps states into mirror coordinates and back, and reduces to mirror descent when noise is removed. Under stated relative curvature and regularity assumptions, its Wasserstein error contracts; with vanishing step-sizes, it approaches a target-centered ball, not generally the target.
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