相关论文: Quantitative results on the multi-parameters Proxi…
In this work, a convergence lemma for function $f$ being finite compositions of analytic mappings and the maximum operator is proved. The lemma shows that the set of $\delta$-stationary points near an isolated local minimum point $x^*$ is…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
We propose an extended forward-backward algorithm for approximating a zero of a maximal monotone operator which can be split as the extended sum of two maximal monotone operators. We establish the weak convergence in average of the sequence…
Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
We study the convergence of $Q$-learning with linear function approximation. Our key contribution is the introduction of a novel multi-Bellman operator that extends the traditional Bellman operator. By exploring the properties of this…
We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…
This paper introduces the concept of quasi $\alpha$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $\alpha$-firmly nonexpansive mappings satisfying a…
Two distributed algorithms are described that enable all users connected over a network to cooperatively solve the problem of minimizing the sum of all users' objective functions over the intersection of all users' constraint sets, where…
Wu, Lou, Lai and Chang proposed a multi-exponentiation algorithm using binary complements and the non-adjacent form. The purpose of this paper is to show that neither the analysis of the algorithm given by its original proposers nor that by…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
We consider the post-training quantization problem, which discretizes the weights of pre-trained deep neural networks without re-training the model. We propose multipoint quantization, a quantization method that approximates a…
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
We consider the following stochastic optimization problem first introduced by Chen et al. in \cite{chen}. We are given a vertex set of a random graph where each possible edge is present with probability p_e. We do not know which edges are…
We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of $\mathcal…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
We revisit the Chen-Teboulle algorithm using recent insights and show that this allows a better bound on the step-size parameter.
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…