Related papers: Instance Optimal Geometric Algorithms
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
This paper considers stochastic first-order algorithms for convex-concave minimax problems of the form $\min_{\bf x}\max_{\bf y}f(\bf x, \bf y)$, where $f$ can be presented by the average of $n$ individual components which are $L$-average…
We study the Regularized A-optimal Design (RAOD) problem, which selects a subset of $k$ experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called $n$-fold integer programming. An $n$-fold integer program (IP) has a highly uniform…
Learning from temporally-correlated data is a core facet of modern machine learning. Yet our understanding of sequential learning remains incomplete, particularly in the multi-trajectory setting where data consists of many independent…
For the model of constrained multi-armed bandit, we show that by construction there exists an index-based deterministic asymptotically optimal algorithm. The optimality is achieved by the convergence of the probability of choosing an…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…
The adaptive moment estimation (Adam) optimizer proposed by Kingma & Ba (2014) is presumably the most popular stochastic gradient descent (SGD) optimization method for the training of deep neural networks (DNNs) in artificial intelligence…
We consider the problem of configuring general-purpose solvers to run efficiently on problem instances drawn from an unknown distribution. The goal of the configurator is to find a configuration that runs fast on average on most instances,…
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…
We study non-smooth stochastic decentralized optimization problems over time-varying networks, where objective functions are distributed across nodes and network connections may intermittently appear or break. Specifically, we consider two…
Given a nonconvex function that is an average of $n$ smooth functions, we design stochastic first-order methods to find its approximate stationary points. The convergence of our new methods depends on the smallest (negative) eigenvalue…
We reexamine fundamental problems from computational geometry in the word RAM model, where input coordinates are integers that fit in a machine word. We develop a new algorithm for offline point location, a two-dimensional analog of sorting…
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 studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from the existing robust SDP-based interior point method analysis due to [Huang, Jiang,…
We present two parallel optimization algorithms for a convex function $f$. The first algorithm optimizes over linear inequality constraints in a Hilbert space, $\mathbb H$, and the second over a non convex polyhedron in $\mathbb R^n$. The…