9 accepted papers
In $D$istributed optimization and $L$earning, and even more in the modern framework of federated learning, communication, which is slow and costly, is critical. We introduce LoCoDL, a communication-efficient algorithm that leverages the two popular and effective techniques of $Lo$cal training, which…
Proximal splitting algorithms are well suited to solving large-scale nonsmooth optimization problems, in particular those arising in machine learning. We propose a new primal–dual algorithm, in which the dual update is randomized; equivalently, the proximity operator of one of the function in the pr…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx = b, with an oracle providing evaluations of the gradient of F and multiplications by K and its transpo…
In distributed or federated optimization and learning, communication between the different computing units is often the bottleneck and gradient compression is widely used to reduce the number of bits sent within each communication round of iterative methods. There are two classes of compression oper…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an approximation thereof, in a distributed setting. Our work is moti…
In manufacturing, the monitoring of the fabrication process is crucial in order to be sure that objects are compliant. For nano-objects, most of this monitoring is done manually. In this paper, we propose a method to segment different materials in a manufactured object. The method uses design inform…
The nonlinear inverse problem of 2-D phase unwrapping consists in estimating an image, while its pixel values are observed modulo 2π. A variational formulation is considered, which consists in minimizing an energy, convex or not, under the nonconvex data fidelity constraints. We propose a new convex…
Splines are piecewise polynomials and widely used for interpolation and smoothing of observed data, due to their flexibility and optimality in the sense of certain variational problems for one-dimensional (1D) data. However, spline interpolation and smoothing are applicable only to the estimation of…
In this paper, we propose an adaptation of the PAM algorithm to the minimization of a nonconvex functional designed for joint image denoising and contour detection. This new functional is based on the Ambrosio-Tortorelli approximation of the well-known Mumford-Shah functional. We motivate the propos…