SHIYUAN ZHANG
5 posts
Thrilled to announce our ICML 2026 paper: "Dimension-Independent Convergence of Underdamped Langevin Monte Carlo in KL Divergence" 🎉 We give the first dimension-free KL bounds for discretized underdamped Langevin — depending on tr(H), not the ambient dimension d.
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Two technical ingredients:
Refining strong/weak local errors with H-weighted norms (the standard Euclidean p alone forces d-dependence)
A change-of-measure lemma controlling 𝔼[‖∇V‖²] and 𝔼[‖p‖²_H] by tr(H) instead of d, via Taylor expansion rather than crude Gaussian moments.
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We close the gap: both standard ULMC and randomized midpoint enjoy dimension-free KL rates, in both the strongly convex and general convex settings. Via Talagrand's T₂, we also strictly improve the κ dependence in Wasserstein over Liu et al. 2023.
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