In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution with convexity and linear convergenc ...
This paper proposes a Control by Interconnection design, for a class of constrained Port-Hamiltonian systems, which is based on an associated Model Predictive Control optimization problem. This associated optimization problem allows to consider both state ...
Many robotics problems are formulated as optimization problems. However, most optimization solvers in robotics are locally optimal and the performance depends a lot on the initial guess. For challenging problems, the solver will often get stuck at poor loc ...
We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in orde ...
Strategic information is valuable either by remaining private (for instance if it is sensitive) or, on the other hand, by being used publicly to increase some utility. These two objectives are antagonistic and leaking this information by taking full advant ...
Sharpness-Aware Minimization (SAM) is a recent training method that relies on worst-case weight perturbations which significantly improves generalization in various settings. We argue that the existing justifications for the success of SAM which are based ...
In this thesis, we reveal that supervised learning and inverse problems share similar mathematical foundations. Consequently, we are able to present a unified variational view of these tasks that we formulate as optimization problems posed over infinite-di ...
Internet ranking algorithms play a crucial role in information technologies and numerical analysis due to their efficiency in high dimensions and wide range of possible applications, including scientometrics and systemic risk in finance (SinkRank, DebtRank ...
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth se ...
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 ...
