A Brief Note on the Convergence of Langevin Monte Carlo in Chi-Square Divergence
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We study sampling from a target distribution ν_* ∝ e^-f using the unadjusted Langevin Monte Carlo (LMC) algorithm when the target ν_* satisfies the Poincaré inequality, and the potential f is first-order smooth and dissipative. Under an opaque uniform warmness condition on the LMC iterates, we establish that 𝒪(ϵ^-1) steps are sufficient for LMC to reach ϵ neighborhood of the target in Chi-square divergence. We hope that this note serves as a step towards establishing a complete convergence analysis of LMC under Chi-square divergence.
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