Related papers: An Instance-optimal Algorithm for Bichromatic Rect…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
It is a well known fact that sequential algorithms which exhibit a strong "local" nature can be adapted to the distributed setting given a legal graph coloring. The running time of the distributed algorithm will then be at least the number…
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
We propose a new and, arguably, a very simple reduction of instance segmentation to semantic segmentation. This reduction allows to train feed-forward non-recurrent deep instance segmentation systems in an end-to-end fashion using…
Often multiple instances of an object occur in the same scene, for example in a warehouse. Unsupervised multi-instance object discovery algorithms are able to detect and identify such objects. We use such an algorithm to provide object…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
This paper shows that the optimal subgradient algorithm, OSGA, proposed in \cite{NeuO} can be used for solving structured large-scale convex constrained optimization problems. Only first-order information is required, and the optimal…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
The performance of the Quantum Approximate Optimisation Algorithm (QAOA) relies on the setting of optimal parameters in each layer of the circuit. This is no trivial task, and much literature has focused on the challenge of finding optimal…
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…
Optimal search strategies where targets are observed at several different angles are found. Targets are assumed to exhibit rectangular symmetry and have a uniformly-distributed orientation. By rectangular symmetry, it is meant that one side…
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples. The time complexity of our…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
Visual object localization is the key step in a series of object detection tasks. In the literature, high localization accuracy is achieved with the mainstream strongly supervised frameworks. However, such methods require object-level…