Postdoc Offer: 18 Months
Resilient Distributed Optimization using Scalable Algorithms
Advisor: Mohamed Maghenem
CNRS, GIPSA-Lab, Grenoble, France
Keywords: Control theory; networked systems; distributed optimization; Lyapunov methods; graph theory.
Context and Objectives
This project aims to propose control-theoretic frameworks to study resilience and scalability in consensus-based distributed-optimization problems. These problems are formulated in terms of a network of dynamical nodes seeking a consensual minimum of a global cost function. This function is usually decomposed into local cost functions assigned to the different nodes. The nodes dynamically exchange and adjust their minimizers to achieve a common minimum of the local cost functions.
Distributed optimization is a widely-studied subject [1], and it is driven by a wide range of applications including resource allocation [2], blockchains [3], and traffic management [4]. Of special interest are distributed learning and federated learning [5], which are foundational components of modern artificial intelligence (AI).
The latter applications bring new challenges including general forms of perturbations that go beyond computational errors and include Byzantine information, failures, and data loss. Existing theoretical guarantees usually assume perturbation-free scenarios [6], where predefined signals are sometimes used to mitigate the effect of small or vanishing perturbations [7]. To the best of our knowledge, appropriately handling general perturbations remains an open area of research. This subject calls for adaptive and fully distributed designs [8], which do not rely on global knowledge regarding the perturbation and the network's size or structure.
On the other hand, when the dimension of the minimizers is large, as in distributed-AI applications, the exchange process can be cumbersome in terms of both transmission channels and computation time, calling for scalable designs [9,10]. According to these approaches, the nodes exchange only a few components of the minimizers (or functions of the minimizers) at a given time. To the best of our knowledge, sparsity has been studied only in a stochastic setting. However, a deterministic framework could lead to stronger guarantees, avoiding probabilistic assumptions while ensuring stable convergence behaviors and precise triggering conditions.
Research Directions
These modern challenges call for a solid control-theoretical foundation in terms of formulating meaningful frameworks, proposing autonomous and scalable redesigns, and establishing rigorous guarantees.
In particular, we will seek adaptive and fully distributed redesigns of some algorithms in both continuous and discrete time. Exchange and optimization coefficients could be updated, and a minimum number of nodes can be required to be robust so as to induce the same property for the entire network. Our design is expected to allow changes in the size and structure of the network and to handle malicious nodes by a fine tuning of the robust ones.
Additionally, we aim to explore sparse exchanges by leveraging tools related to switched, persistently excited, and delayed systems, and investigate links with observability and controllability notions for time-varying systems.
Research Environment
The research will be conducted in GIPSA-Lab, a joint research laboratory of CNRS, Grenoble-INP and Grenoble Alpes University. At GIPSA-Lab, we develop theoretical and applied research on CONTROL, SIGNAL and IMAGE PROCESSING, SPEECH, COGNITION, ROBOTICS and ARTIFICIAL INTELLIGENCE.
Grenoble is an attractive city in the heart of the Alps, easily reachable from Paris, but also at a crossroads with Italy, Switzerland and Lyon, with a large student population and numerous cultural and sports facilities.
This postdoctoral grant is part of the IRGA project DROPS, funded by PERSYVAL-Lab and Grenoble Alpes University.
Expected Skills
A candidate holding a PhD degree with a solid background in control theory and mathematics. Experience or interest in networked systems and optimization is key.
Academic CV and references must be sent to:
References
[1] T. Yang et al. A Survey of Distributed Optimization. Annual Reviews in Control, 47:278–305, 2019.
[2] M. Doostmohammadian et al. Survey of Distributed Algorithms for Resource Allocation over Multi-Agent Systems. Annual Reviews in Control, 59:100983, 2025.
[3] E. Munsing, J. Mather, and S. Moura. Blockchains for Decentralized Optimization of Energy Resources in Microgrid Networks. In Proceedings of the IEEE Conference on Control Technology and Applications (CCTA), pp. 2164–2171, 2017.
[4] B. V. Philip, J. Alpcan, J. Tansu, and M. Palaniswami. Distributed Real-Time IoT for Autonomous Vehicles. IEEE Transactions on Industrial Informatics, 15(2):1131–1140, 2019.
[5] J. Verbraeken et al. A Survey on Distributed Machine Learning. ACM Computing Surveys, 2020.
[6] A. Nedic and A. Ozdaglar. Distributed Subgradient Methods for Multi-Agent Optimization. IEEE Transactions on Automatic Control, 2009.
[7] Y. Lou, Y. Hong, and S. Wang. Distributed Continuous-Time Approximate Projection Protocols for Shortest Distance Optimization Problems. Automatica, 2016.
[8] Y. Yan and Z. Chen. Adaptive Autonomous Synchronization of Heterogeneous Multi-Agent Systems. IEEE Transactions on Automatic Control, 2022.
[9] J. Wangni, J. Wang, J. Liu, and T. Zhang. Gradient Sparsification for Communication-Efficient Distributed Optimization. Advances in Neural Information Processing Systems, 31, 2018.
[10] L. Yujun, H. Song, M. Huizi, W. Yu, and J. D. William. Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training. In Proceedings of the International Conference on Learning Representations (ICLR), 2018.
