Composite Self-Concordant Minimization

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In this paper we study the problem of social learning under multiple true hypotheses and self-interested agents. In this setup, each agent receives data that might be generated from a different hypothesis (or state) than the data other agents receive. In c ...

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

We consider the problem of finding a saddle point for the convex-concave objective

\min_x \max_y f(x) + \langle Ax, y\rangle - g^*(y)

, where

f

is a convex function with locally Lipschitz gradient and

g

is convex and possibly non-smooth. We propose an ...

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed ...

We study convex optimization problems that feature low-rank matrix solutions. In such scenarios, non-convex methods offer significant advantages over convex methods due to their lower space complexity as well as faster convergence speed. Moreover, many of ...

The self-concordant-like property of a smooth convex func- tion is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self- concordant-like property, this concept has heretofor ...

The self-concordant-like property of a smooth convex function is a new analytical structure that generalizes the self-concordant notion. While a wide variety of important applications feature the self- concordant-like property, this concept has heretofore ...

A new decomposition optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this algorithm does not require ...

This paper proposes a smoothing technique for nonsmooth convex minimization using self-concordant barriers. To illustrate the main ideas, we compare our technique and the proximity smoothing approach (Nesterov2005) via the classical gradient method on both ...

The convex

\ell_1

-regularized

\log\det

divergence criterion has been shown to produce theoretically consistent graph learning. However, this objective function is challenging since the

\ell_1

-regularization is nonsmooth, the

\log\det

objective is n ...

The convex l(1)-regularized log det divergence criterion has been shown to produce theoretically consistent graph learning. However, this objective function is challenging since the l(1)-regularization is nonsmooth, the log det objective is not globally Li ...

We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadra ...

Over the past few decades we have been experiencing a data explosion; massive amounts of data are increasingly collected and multimedia databases, such as YouTube and Flickr, are rapidly expanding. At the same time rapid technological advancements in mobil ...

Composite Self-Concordant Minimization

Chattez avec Graph Search

Social Learning with Disparate Hypotheses

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

A first-order primal-dual method with adaptivity to local smoothness

Adaptation in Stochastic Algorithms: From Nonsmooth Optimization to Min-Max Problems and Beyond

A Newton Frank-Wolfe method for constrained self-concordant minimization

Data-Driven Chance Constrained Programs over Wasserstein Balls

A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

Composite convex minimization involving self-concordant-like cost functions

Composite convex minimization involving self-concordant-like cost functions

Path-following gradient-based decomposition algorithms for separable convex optimization

Barrier Smoothing for Nonsmooth Convex Minimization

Fast Proximal algorithms for Self-concordant function minimization with application to sparse graph selection

Fast Proximal Algorithms For Self-Concordant Function Minimization With Application To Sparse Graph Selection

A proximal Newton framework for composite minimization: Graph learning without Cholesky decompositions and matrix inversions

Geometry-aware analysis of high-dimensional visual information sets