In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. is hybrid between two classical methods, coordinate descent (“S”-inkhorn) and proximal gradient (“ISTA”). It alternates phase of exact minimization over potentials parameters cost. We prove that method converges linearly, illustrate on simulated examples it significant...

We study the problem of online linear optimization with sparsity constraints in the 1 semi-bandit setting. It can be seen as a marriage between two well-known problems: 2 the online linear optimization problem and the combinatorial bandit problem. For 3 this problem, we provide two algorithms which are efficient and achieve sublinear 4 regret bounds. Moreover, we extend our results to two gener...

We introduce a new constraint system for sparse variable selection in statistical learning. Such a system arises when there are logical conditions on the sparsity of certain unknown model parameters that need to be incorporated into their selection process. Formally, extending a cardinality constraint, an affine sparsity constraint (ASC) is defined by a linear inequality with two sets of variab...

Structured sparsity approaches have recently received much attention in the statistics, machine learning, and signal processing communities. A common strategy is to exploit or assume prior information about structural dependencies inherent in the data; the solution is encouraged to behave as such by the inclusion of an appropriate regularization term which enforces structured sparsity constrain...

Multitask learning addresses the problem of learning related tasks whose information on parameters is assumed to be shared with each other. Previous approaches usually deal with homogeneous tasks such as a set of regression tasks only or a set of classification tasks only. In this paper, we consider the problem of learning multiple related tasks, where tasks consist of predicting both continuou...

Discussion of “Minimax Estimation of Large Covariance Matrices under L1-Norm” by Tony Cai and Harrison Zhou. To appear in Statistica Sinica. Introduction. Estimation of covariance matrices in various norms is a critical issue that finds applications in a wide range of statistical problems, and especially in principal component analysis. It is well known that, without further assumptions, the em...

We show that designing sparse H∞ controllers, in a discrete (LTI) setting, is easy when the controller is assumed to be an FIR filter. In this case, the problem reduces to a static output feedback problem with equality constraints. We show how to obtain an initial guess, for the controller, and then provide a simple algorithm that alternates between two (convex) feasibility programs until conve...