Work-Package 1: Accelerated MM approaches
Modern signal and image recovery problems require powerful optimization frameworks to handle high dimensionality while providing reliable numerical solutions in a reasonable time. In this perspective, asynchronous parallel optimization algorithms have received an increasing attention by overcoming memory limitation issues and communication bottlenecks.
Our main results around these aspects are (1) proposition of block alternating, and block distributed MM algorithms, with convergence guarantees, to tackle efficiently large scale non-convex differentiable optimization problems, (2) design of deep unrolled MM algorithms with GPU implementation, and supervised data-driven strategy to learn optimal hyper-parameters, (3) application of the methodological developments to the resolution of inverse problems of image and signal processing, and to sparse graph inference problems.
Work-Package 2: Robust MM approaches
In WP2, we analyzed the impact of numerical errors arising at the practical level on the convergence of the method with the aim to propose MM algorithms robust to inaccurately implemented steps. Our main results are (1) new fundamental results of the stability properties of MM and proximal algorithms under the situation of adjoint mismatch, frequently encountered in tomographic image reconstruction, (2) new convergence results of MM algorithms facing stochastic errors in the gradient computation, beyond the convex case, (3) application to the resolution of inverse problems of imaging, and to machine learning scenarios.
Work-Package 3 – Flexible MM approaches
MM algorithms are powerful tools for optimization at a large scale. Nonetheless, for several classes of problems, open questions regarding their convergence guarantees and even their applicability remained open, that we proposed to investigate in this work-package. Our main results are (1) proposition of new MM method for solving large scale constrained differentiable optimization problems based on local search and trust-region mechanism, (2) implementation of MM strategies to boost sampling exploration in the context of Monte-Carlo algorithms, (3) development of MM algorithms going beyond Euclidian metrics, to deal with Bregman divergence minimization problems, arising from various situations in variational inference, proposition law adaptation, Poisson image reconstruction.
The results have been disseminated in multiple journal and conference publications. An updated list can be found in the project's website
https://opis-inria.eu/majoris/(odnośnik otworzy się w nowym oknie).
