All Years Seminars
[INMA] 2022-11-08 (14h) : Learning to Optimize Network Systems via Online Optimization and Control Theory with Applications to Traffic Control
At Euler building (room a.002)
Speaker :
Bianchin, Gianluca
Abstract : Operating networked dynamical systems at an optimal setpoint in the presence of humansin-
the loop constitutes one of the most central and impactful problems ahead of systems and control
theory. Motivated by this, in this talk I will first present my work on the development of feedback-based
optimization algorithms as one of the most fundamental tools that enable to simultaneously control and
optimize modern cyber-physical-human systems. I will begin by reviewing some of the classical techniques
in numerical optimization and by showing how these can be translated to solve complex control problems.
I will then demonstrate how these algorithms can be adapted to control dynamical systems whose model
is unknown, and how data-driven control techniques can be combined with online optimization methods.
In the second part of the talk and motivated by the first, I will focus on applications in traffic control and
demonstrate how strategic decisions made by humans negatively impact the stability of modern traffic
networks. I will show how control-theoretic tools can be used to prevent oscillatory congestion in traffic
systems via proper design of the information that is made available to humans. While specific focus
will be given to traffic management problems, these results are relevant for a wide range of applications
ranging from energy management to the control of epidemic outbreaks.
[INMA] 2022-10-25 (14h) : Repulsive particles and random matrix eigenvalues
At Euler building (room a.002)
Speaker :
Tom Claeys (IRMP,UCLouvain)
Abstract : Determinantal point processes are a class of models for repulsive particles with a specific structure. This structure allows one to effectively study relevant probabilistic quantities. I will discuss some examples of them, including random matrix eigenvalues, and show a glimpse of their rich mathematical structure.
[INMA] 2022-10-18 (14h) : Unsupervised Learning to Solve Linear Inverse Problems
At Euler building (room a.002)
Speaker :
Tachella, Julián
Abstract : In recent years, deep neural networks have obtained state-of-the-art performance in multiple imaging inverse problems ranging from medical imaging to computational photography. Networks are generally trained with supervised pairs of signals and associated measurements. However, in various imaging problems, we often only have access to incomplete measurements of the underlying signals, thus hindering this learning-based approach. In this talk, I will present a new unsupervised learning framework which overcomes this limitation by exploiting the invariance to transformations (translations, rotations, etc.) present in natural signals. I will also present necessary and sufficient conditions for learning without ground truth. Our proposed learning strategy performs as well as fully supervised methods and can handle noisy data. I will show results on various inverse problems, including sparse-view X-ray computed tomography, accelerated magnetic resonance imaging and image inpainting.
[INMA] 2022-10-11 (14h) : Geometry of the symmetric eigenvalue problem
At Euler building (room a.002)
Speaker :
Foivos Alimisis (Université de Genève)
Abstract : Eigenvalue problems are some of the most characteristic linear algebra applications of optimization techniques over Riemannian manifolds. These techniques are usually well benefited by the presence of a convexity structure. We study the geodesic convexity structure of the standard problem of computing some of the eigenvectors of a symmetric matrix (Rayleigh quotient) on the sphere and on the Grassmann manifold. We prove that, while the problem is only very locally convex, it satisfies in general weaker convexity properties (weak-quasi-convexity, quadratic growth) that are enough to provide convergence guarantees for many important algorithms. Namely, we prove that gradient descent for the Rayleigh quotient on the Grassmann manifold enjoys a linear convergence rate, while if its step-size is chosen via an exact line search, it empirically outperforms the more popular subspace iteration (power method). We also apply our results in the case of accelerated gradient descent (Nesterov's momentum), which turns out to be particularly beneficial when the gaps between the eigenvalues of the original matrix are small.
[INMA] 2022-10-04 (14h) : Distributed Coordination and Optimization with Privacy Guarantees and Quantized Communication
At Euler building (room a.002)
Speaker :
Apostolos Rikos (Division of Decision and Control Systems, KTH Royal Institute of Technology, Sweden)
Abstract : A distributed system (or network) can be viewed as a set of subsystems that can share information via interconnection links, which form a generally directed communication topology. Distributed systems prove to be of vital importance for the effectiveness of performing various tasks in the areas of cooperative control, distributed coordination, and control of multicomponent systems. This presentation concerns novel distributed algorithms for (i) distributed averaging, (ii) resource allocation, and (iii) privacy preservation. During the operation of the proposed algorithms, each node operates over a directed communication topologies, processes and transmits quantized information and converges in finite time.In the first part of this presentation, we focus on the distributed quantized average consensus problem. In this problem, each node is associated with some initial quantized value. The goal is for the nodes to obtain the average of these initial values (or some value close to the average). We present and analyze a novel distributed averaging algorithm which operates exclusively with quantized values (the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and rely on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage).In the second part of this presentation, we focus on the resource allocation problem. In this problem, each node is associated with a convex local cost function. The goal is for the nodes is to cooperatively minimize a common additive cost function. More specifically, nodes aim to to calculate a set of parameters that minimize the global cost function which is the summation of the local cost functions. We present and analyze a novel distributed resource allocation algorithm which operates exclusively with quantized values and rely on event-driven updates.In the third part of this presentation, we focus on privacy preservation strategies for the algorithms presented in the previous two parts. A node is said to preserve the privacy of its initial state if its value cannot be inferred by any curious node in the network and also curious nodes are not able to determine a finite range in which this value belongs. We propose privacy preservation strategies which operate in an event-driven fashion, and are adjusted to the quantized nature of the proposed algorithms in the first two parts of this presentation.
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