arXiv Machine Learning By Yuchen Xin, Zhihua Zhang

Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling

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arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.

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arXiv Machine Learning
Jul 13

Solving Stochastic Fixed-Point Equations with High Probability

arXiv:2607. 09097v1 Announce Type: cross Abstract: We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment.

By Jelena Diakonikolas
arXiv Machine Learning
Jul 21

Scaling Limits of Constant-Stepsize SGD at Flat Minima

arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.

By Jingyi Zhang, Cheng Mao, Debankur Mukherjee
arXiv Machine Learning
Aug 10

Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples

arXiv:2608. 06687v1 Announce Type: cross Abstract: We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations $\mathfrak L_\beta u=f$ using linearized ReLU$^k$ neural networks on the sphere, where $\mathfrak L_\beta$ is a positive elliptic spectral multiplier of order $\beta$.

By Xinliang Liu, Tong Mao, Jinchao Xu
arXiv Machine Learning
Jun 3

Decentralized Stochastic Nonconvex Optimization under the $(L_0,L_1)$-Smoothness

arXiv:2509. 08726v3 Announce Type: replace-cross Abstract: This paper focuses on the decentralized stochastic optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$ over a connected network of $n$ agents, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};{\boldsymbol \xi}_i)\right]$ which satisfies the $(L_0,L_1)$-smooth condition but possibly nonconvex and each random variable ${\boldsymbol \xi}_i$ follows distribution ${\mathcal D}_i$.

By Luo Luo, Xue Cui, Tingkai Jia, Cheng Chen