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This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…
The non-smooth finite-sum minimization is a fundamental problem in machine learning. This paper develops a distributed stochastic proximal-gradient algorithm with random reshuffling to solve the finite-sum minimization over time-varying…
In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
We study the performance of asymptotic and approximate consensus algorithms under harsh environmental conditions. The asymptotic consensus problem requires a set of agents to repeatedly set their outputs such that the outputs converge to a…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
This paper explores adaptive variance reduction methods for stochastic optimization based on the STORM technique. Existing adaptive extensions of STORM rely on strong assumptions like bounded gradients and bounded function values, or suffer…
The problem of least squares regression of a $d$-dimensional unknown parameter is considered. A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence…
Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
We consider a distributed multi-agent network system where the goal is to minimize a sum of convex objective functions of the agents subject to a common convex constraint set. Each agent maintains an iterate sequence and communicates the…
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the convergence properties…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than…
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…