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We consider the consensus problem in a decentralized network, focusing on a compact submanifold that acts as a nonconvex constraint set. By leveraging the proximal smoothness of the compact submanifold, which encompasses the local singleton…
In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…
We study the problem of finding the global Riemannian center of mass of a set of data points on a Riemannian manifold. Specifically, we investigate the convergence of constant step-size gradient descent algorithms for solving this problem.…
We estimate $n$ phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which…
In the context of statistical supervised learning, the noiseless linear model assumes that there exists a deterministic linear relation $Y = \langle \theta_*, X \rangle$ between the random output $Y$ and the random feature vector $\Phi(U)$,…
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…
Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…
Recently, several studies (Zhou et al., 2021a; Zhang et al., 2021b; Kim et al., 2021; Zhou and Gu, 2022) have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often…
Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…
In this letter, we study the deterministic sampling patterns for the completion of low rank matrix, when corrupted with a sparse noise, also known as robust matrix completion. We extend the recent results on the deterministic sampling…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in…
We address the problem of finding reliable dense correspondences between a pair of images. This is a challenging task due to strong appearance differences between the corresponding scene elements and ambiguities generated by repetitive…
We propose a novel multi-layer neural network architecture that gives a promising neural network empowered optimization approach to the image restoration problem. The proposed architecture is motivated by the recent study of monotone…
There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…