We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with Lipschitz gradient and $g$ is convex and globally Lipschitz. Under an explicit parameter-dependent step-size co...
This work studies prediction parameterization for stochastic generative dynamics in diffusion models. Existing velocity-based generative models provide the simplicity of learning a single transport field, but their standard formulation is deterministic, whereas stochastic extensions generally require additional score i...
Yun-Hong Zhang, Chang-Jie Cao, Zhi-Hua Zhang et al.· 0 citations
We study the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA) for $\pi(\,\mathrm{d} x)\propto e^{-f(x)-g(x)}\,\mathrm{d} x$, where $f\in C^2(\mathbb{R}^d)$ is $m$-strongly convex with $L_f$-Lipschitz gradient and $g:\mathbb{R}^d\to\mathbb{R}$ is convex and globally $G$-Lipschitz. For the Moreau-smoothed t...
A Lyapunov function is constructed for the gap process between the estimated cumulative loss of the optimal arm and that of the best competing arm, and establishes a lower bound on the exponent of $\operatorname{Err}_t$ for any $\rho>0$, showing that the exponent $2$ is essentially tight.
Jingxin Zhan, Yuze Han, Zhihua Zhang· 0 citations
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