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Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…
Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of the…
In many prediction problems, it is not uncommon that the number of variables used to construct a forecast is of the same order of magnitude as the sample size, if not larger. We then face the problem of constructing a prediction in the…
Consider the problem of choosing a set of actions to optimize an objective function that is a real-valued polymatroid function subject to matroid constraints. The greedy strategy provides an approximate solution to the optimization problem,…
We describe the Simple Greedy Matrix Completion Algorithm providing an efficient method for restoration of low-rank matrices from incomplete corrupted entries. We provide numerical evidences that, even in the simplest implementation, the…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
The usual approach to developing and analyzing first-order methods for smooth convex optimization assumes that the gradient of the objective function is uniformly smooth with some Lipschitz constant $L$. However, in many settings the…
The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information,…
The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic…
In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given $\vare>0$, so that the basis…