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[L2O-MOC]

Learning to optimise: from mathematical foundations to modeling and control

Project PCE

The research leading to these results has received funding from:

Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii (UEFISCDI)

Project title:

Learning to optimise: from mathematical foundations to modeling and control (L2O-MOC)

PN-III-P4-PCE-2021-0720, Contract No. 70/2022.

Institutul de Statistica Matematica si Matematica Aplicată „Gheorghe Mihoc- Caius Iacob” al Academiei Romane (ISMMA)

Abstract

Next generation of smart control systems (SCS) are expected to learn models from data and take optimal decisions in real-time, leading to increased performance, safety, energy efficiency, and ultimately value creation. Since, SCS produce large amounts of data, machine learning (ML) aims at extracting information from them. The key step in any ML technique is training, where an optimization problem is solved to tune the parameters of the ML model. In this project we reverse this paradigm, i.e. we use ML for devising efficient optimization algorithms. Our key observation is that the modelling and control approaches for SCS yield optimization problems that are extremely challenging due to their large dimension, stochasticity, nonconvexity, etc. Optimization algorithms addressing such problems usually involve many parameters that need to be hand-tuned after time-consuming experimentation and are prone to ill-conditioning and slow convergence. To address these challenges, L2O-MOC will develop learning-based techniques for devising efficient tuning-free optimization algorithms. A novel universal framework will be developed, which will serve as a solid theoretical ground for the design of new learning paradigms to train optimization methods with mathematical guarantees for convergence. Modelling and control problems for SCS, e.g. those arising in power networks, will provide the datasets for the training.

Project Team

Prof. Ion Necoara

Director

CSI Gabriela Marinoschi

Prof. Tudor C. Ionescu

Prof. Lucian Toma

Phd. student Daniela Lupu

Phd. student Nitesh Kumar Singh

Results

Publications and dissemination: Thanks to the expertise of the team and support from external collaborators, the proposed objectives have been achieved effectively and the results were published in top journals Q1/Q2 and conference proceedings (ieeexplore). The scientific breakthroughs have been disseminated by publications of 16 papers in high-impact journals (Q1/Q2) and 14 papers in conference proceedings indexed in ieeexplore, from various fields including optimization, machine learning and control (e.g., Siam Journal on Optimization, Journal of Machine Learning Research, IEEE Transactions on Automatic Control, Conference on Decision and Control, European Control Conference, etc). We have also produced open-source software available on Github. The members of L2O-MOC project have participate to specific international workshops and conferences: e.g., ECC 2023/2024, CDC 2023/2024, MED 2024, ISMP 2024, EUROPT 2023, NOPTA Workshop 2024, etc. Two PhD students have defended their thesis with grade “excellent” during this project: Daniela Lupu (October 2023) and Nitesh Kumar Singh (September 2024).
Impact: Our new optimization algorithms have created a good impact in the optimization community, our work being already cited in prestigious papers. Moreover, the modeling and control methods can have a big impact in the control community, especially on embedded control, where hard runtime constraints exist. More precisely, from extensive simulations we observed that our unfolded deep neural network-based MPC controllers can be applied on larger dynamical systems and their computation is much faster than with the existing approaches. Additionally, our modeling techniques can be used for solving privacy at consumer level and our MPC can be used for an economic management of the power grid.
Research activities: The main research activities for the years 2022, 2023 and 2024 are:
- 2022 – Efficient optimization algorithms (majorization-minimization type); Methods for modeling and control of smart systems. Expected results: 1 journal paper, 1 conference paper published. Achieved results: 3 ISI journal papers (Q1/Q2); 3 conference proceedings; 2 papers submitted to journals. Scientific Report 2022
- 2023 – Efficient optimization algorithms (using relaxation of convexity/smoothness); Methods for modeling and control of smart systems (model reduction methods); Learning to optimise (control-based approach). Expected results: 3 journal papers, 3 conference papers. Achieved results: 5 ISI journal papers (Q1/Q2); 8 conference proceedings. Scientific Report 2023
- 2024 – Efficient optimization algorithms (stochastic algorithms); Methods for modeling and control of smart systems (model predictive control); Learning to optimise (model predictive control for power systems). Expected results: 3 journal papers, 3 conference papers. Achieved results: 4 ISI journal papers (Q1/Q2); 2 other journal papers are either provisionally accepted or under revision; 4 conference papers were published in the proceedings or already/to be submitted to conferences. Scientific Report 2024

Publications

Papers accepted/submitted in ISI journals:

[J1] I. Necoara, N.K. Singh, Stochastic subgradient projection methods for composite optimization with functional constraints, Journal of Machine Learning Research (Q1), 23(265), 1-35, 2022 (https://www.jmlr.org/papers/volume23/21-1062/21-1062.pdf).
[J2] I. Necoara, D. Lupu, General higher-order majorization-minimization algorithms for (non)convex optimization, provisionally accepted in Siam Journal on Optimization, 2022.
[J3] L. El Bourkhissi, I. Necoara, Complexity of linearized augmented Lagrangian for optimization with nonlinear equality constraints, Journal of Global Optimization, doi: 10.1007/s10898-024-01456-3, 2024.
[J4] D. Lupu, I. Necoara, Convergence analysis of stochastic higher-order majorization-minimization algorithms, Optimization Methods and Software (Q2), doi: 10.1080/10556788.2023.2256447, 2023.
[J5] F. Chorobura, I. Necoara, Random coordinate descent methods for nonseparable composite optimization, Siam Journal on Optimization (Q1), 33(3), doi: 10.1137/22M148700X, 2023.
[J6] N.K. Singh, I. Necoara, V. Kungurtsev, Mini-batch stochastic subgradient for functional constrained optimization, Optimization (Q2), doi: 10.1080/02331934.2023.2189015, 2023.
[J7] Y. Nabou, I. Necoara, Efficiency of higher-order algorithms for minimizing general composite optimization, Computational Optimization and Applications (Q1), doi: 10.1007/s10589-023-00533-9, 2023.
[J8] F. Chorobura, I. Necoara, Coordinate descent methods beyond smoothness and separability, Computational Optimization and Applications (Q1), 88, 107–149, doi: 10.1007/s10589-024-00556-w, 2024.
[J9] I. Necoara, F. Chorobura, Efficiency of stochastic coordinate proximal gradient methods on nonseparable composite optimization, Mathematics of Operations Research (Q1), doi: 10.1287/moor.2023.0044, 2024.
[J10] N. K. Singh, I. Necoara, A stochastic moving ball approximations method for smooth convex constrained minimization, Computational Optimization and Applications (Q1), 89, 659–689, doi: 10.1007/s10589-024-00612-5, 2024.
[J11] L. Tondji, I. Necoara, D. A. Lorenz, Acceleration and restart for the randomized Bregman-Kaczmarz method, Linear Algebra and Its Applications (Q2), 699, 508–538, doi: 10.1016/j.laa.2024.07.009, 2024.
[J12] N. K. Singh, I. Necoara, Stochastic halfspace approximation method for convex optimization with nonsmooth functional constraints, IEEE Transactions on Automatic Control (Q1), 70(1), doi: 10.1109/TAC.2024.3426888, 2025.
[J13] D. Lupu, I. Necoara, Exact representation and efficient approximations of linear model predictive control laws via HardTanh type deep neural networks, Systems and Control Letters (Q1), 186, doi: 10.1016/j.sysconle.2024.105742, 2024.
[J14] L. El Bourkhissi and I. Necoara, Convergence rates for an inexact linearized ADMM for nonsmooth optimization with nonlinear equality constraints, provisionally accepted in Computational Optimization and Applications (Q1), 2024.
[J15] T. C. Ionescu, O. V. Iftime and R. Stefan, “Loewner matrices-based data-driven loopshaping design with closed-loop pole placement”, submitted to IEEE Transactions on Automatic Control (Q1), 2024.
[J16] D. Lupu, J. Garrett, T. A. Johansen, M. Orlandic, I. Necoara, Quick unsupervised hyperspectral dimensionality reduction for earth observation: a comparison, submitted to IEEE Transactions on Computational Imaging (Q2), 20 June 2024.

Papers in conferences proceedings:

[C1]. Y. Nabou, L. Toma, I. Necoara, Modified projected Gauss-Newton method for constrained nonlinear least-squares: application to power flow analysis, Proceedings of IEEE European Control Conference, doi: 10.23919/ECC57647.2023.10178179, 2023.
[C2]. T.C. Ionescu, L. El Bourkhissi, I. Necoara, Least-squares moment matching-based model reduction using convex optimization, Proceedings of IEEE International Conference on System Theory, Control and Computing, doi: 10.1109/ICSTCC55426.2022.9931837, 2022.
[C3]. F. Chorobura, D. Lupu, I. Necoara, Coordinate projected gradient descent minimization and its application to orthogonal nonnegative matrix factorization, Proceedings of IEEE Conference on Decision and Control, doi: 10.1109/CDC51059.2022.9992996, 2022.
[C4] D. Lupu, I. Necoara, Deep unfolding projected first order methods-based architectures: application to linear model predictive control, , Proceedings of IEEE European Control Conference, doi: 10.23919/ECC57647.2023.10178167, 2023.
[C5] L. El Bourkhissi, I. Necoara, P. Patrinos, Linearized ADMM for nonsmooth nonconvex optimization with nonlinear equality constraints, Proceedings of IEEE Conference on Decision and Control, doi: 10.1109/CDC49753.2023.10384166, 2023.
[C6] L.N. Tondji, D. Lorenz, I. Necoara, An accelerated randomized Bregman-Kaczmarz method for strongly convex linearly constraint optimization, Proceedings of IEEE European Control Conference, doi: 10.23919/ECC57647.2023.10178390, 2023.
[C7] F. Chorobura, F. Glineur, I. Necoara, Can random proximal coordinate descent be accelerated on nonseparable convex composite minimization problems?, Proceedings of IEEE European Control Conference, doi: 10.23919/ECC57647.2023.10178217, 2023.
[C8] T. C. Ionescu, O. V. Iftime and R. Stefan, A moment matching-based loop shaping design with closed-loop pole placement, Proceedings of IEEE European Control Conference, doi: 10.23919/ECC57647.2023.10178150, 2023.
[C9] Y. Kawano, T. C. Ionescu and O. V. Iftime, Gramian Preserving Moment Matching for Linear Systems, Proceedings of IEEE European Control Conference, doi: 10.23919/ECC57647.2023.10178382, 2023.
[C10] X. Cheng, T.C. Ionescu, O.V. Iftime and I. Necoara, Moment matching for second order systems with pole-zero placement, Proceedings of IEEE Conference on Decision and Control, December 2024.
[C11] N.K. Singh, I. Necoara, Unified analysis of stochastic gradient projection methods for convex optimization with functional constraints, Proceedings of IEEE European Control Conference, doi: 10.23919/ECC64448.2024.10591311, 2024.
[C12] D. Lupu, I. Necoara, L. Toma, Deep unfolding primal-dual architectures: application to linear model predictive control, submitted to European Control Conference, Greece, 2025.
[C13] T.C. Ionescu, O. Iftime and I. Necoara, Data-driven Loewner matrices-based modeling and model predictive control of a single machine infinite bus model, Proceedings of IEEE Meditaranean Control Conference, doi: 10.1109/MED61351.2024.10566187, 2024.
[C14] N. K. Singh, I. Necoara, Model predictive control problem with ellipsoidal state constraints and its application to a multi-machine power system, to be submitted to Meditaranean Control Conference, 2024.

Software package

Unfolded DeepNN MPC: open-source, Python code, on Github. It contains an interface, where the user can introduce easily the data for the dynamical system and the associated finite horizon optimal control problem. Once the control problem has been introduced, it solves it either with optimization algorithms or it generates a set of training data, trains a deep neural network inspired from these optimization methods and thus learning the MPC law. For testing, we consider a power system test case widely used in the literature, called CIGRE.

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