All Years Seminars
[INMA] 2023-12-05 (14h) : Two talks
At Euler building (room A.002)
Section 1:Exact convergence rate of the last iterate in subgradient methods
Speaker :
Zamani, Moslem
Abstract : Subgradient methods are widely employed for addressing non-differentiable optimization problems. In this talk, we study the convergence of the last iterate in subgradient methods applied to the minimization of a nonsmooth convex function with bounded subgradients. We propose a novel proof technique that expands upon the conventional analysis of subgradient methods. We then derive convergence rates for two variants of the subgradient method, with either fixed step size and fixed step length. We show that these rates are exact by constructing functions for which the subgradient method matches the proven rate. Finally, we introduce an optimized subgradient method, based on a new sequence of stepsizes, which achieves a last-iterate convergence rate matching the established lower bounds for non-differentiable convex optimization problems.
Section 2:Optimization without retraction on the random generalized Stiefel manifold for canonical correlation analysis
Speaker :
Vary, Simon
Abstract : Optimization over the set of matrices that satisfy X^T B X = I_p , referred to as the generalized Stiefel manifold, appears in many applications such as canonical correlation analysis (CCA) and the generalized eigenvalue problem (GEVP). Solving these problems for large-scale datasets is computationally expensive and is typically done by either computing the closed-form solution with subsampled data or by iterative methods such as Riemannian approaches. Building on the work of Ablin and Peyre (2022), we propose an inexpensive iterative method that does not enforce the constraint in every iteration exactly, but instead it produces iterations that converge to the generalized Stiefel manifold. We also tackle the random case, where the matrix B is an expectation. Our method requires only efficient matrix multiplications, and has the same sublinear convergence rate as its Riemannian counterpart. Experiments demonstrate its effectiveness in various machine learning applications involving generalized orthogonality constraints, including CCA for measuring model representation similarity.
[INMA] 2023-11-28 (14h) : A Formal Methods approach to the design of Cyber Physical Systems
At Euler building (room A.002)
Speaker :
Giordano Pola (University of L'Aquila)
Abstract :
A challenging paradigm in the design of modern engineered systems are Cyber–Physical Systems (CPS). CPS are complex, heterogeneous, spatially distributed systems where physical processes interact with distributed computing units through non-ideal communication networks. Key features of CPS are among many others, heterogeneity and complexity. Indeed, while physical processes are generally described by e.g. differential equations, computing units are generally described by finite state machines. To complicate things, communication infrastructures, conveying information in sub–systems of CPS, are characterized by a number of non–idealities that are needed to be considered towards a robust control design of such systems. The paradigm of symbolic models is promising of being appropriate in coping with the inherent heterogeneity of CPS. Symbolic models are abstract descriptions of control systems where any state corresponds to an aggregate of continuous states and any control label to an aggregate of control inputs. Since symbolic models are of the same nature as the mathematical models of the computing units, they offer a sound approach to solve control problems where software and hardware interact with the physical world, as in the case of CPS. Furthermore, by using symbolic models, one can address a wealth of logic specifications that are difficult to enforce by means of conventional control design methods. In this talk, I will give an overview of my research in this area and show an approach based on symbolic models for the control design of CPS. I will first show how a symbolic model can be constructed for approximating a nonlinear control system with any desired accuracy. I then will show how this symbolic model can be used to design digital and quantized controllers for enforcing complex logic specifications on the original nonlinear system. I will finally briefly discuss possible extensions to more realistic scenarios including disturbance inputs, time-delays in the state and control variables evolution, nonideal communication infrastructures, etc. Techniques to tame computational complexity of the approach taken will be also highlighted.
[INMA] 2023-11-27 (11h) : Benign nonconvexity in group synchronization and graph clustering
At Euler building (room A.002)
Speaker :
Andrew McRae (EPFL)
Abstract :
I consider an optimization problem arising in orthogonal group synchronization, in which we seek to estimate orthogonal matrices from (noisy) relative measurements. The least-squares estimator over orthogonal matrices is a nonconvex program that, in general, has many spurious local minima. We show that adding a small number of degrees of freedom (specifically, relaxing to optimization over slightly “wider” Stiefel manifold matrices) makes the nonconvexity benign and still yields an optimal solution to the original problem. The general matrix case is studied in our preprint. Time permitting, I will discuss how these results can be strengthened for $Z_2$ synchronization and can be extended to the graph clustering problem under the stochastic block model; our nonconvex approach yields exact recovery for these problems up to the information-theoretic SNR threshold.
[INMA] 2023-11-21 (14h) : Experimental and modeling approaches to tap into tactile feedback during manipulation
At Euler building (room A.002)
Speaker :
Delhaye, Benoit
Abstract :
The sense of touch originates from the skin, where the deformations caused by our interactions with objects and surfaces are transduced into neural signals by the mechanoreceptors. Those signals then travel the nerves and reach the central nervous system where they are processed to give rise to a sensation related to the touched surface, or a specific motor response to act on the object. My research aims to better understand the sense of touch by studying three aspects involved in tactile feedback: First, the characterization of skin biomechanics, second, computational modeling of neural activity in touch neurons, and third, quantifying sensory perception and motor behavior. In this talk, I will provide an example of those three important aspects in the context of the tactile mechanisms that signal friction during manipulation. Then, I will provide an overview of the recent developments made in our group to better understand the sense of touch
[INMA] 2023-11-14 (14h) : Online Riverflow Forecasting with Hydromax: Background and Last Developments
At Euler building (room A.002)
Speaker :
Monnoyer de Galland de Carnières, Charles
Abstract :
For almost 30 years, the « Hydromax » application has been used for online river flow forecasting in Wallonia with the aim of warning of extreme hydrological events (such as floods and low waters). In this talk, we first provide a general description of Hydromax, and in particular of the mathematical models used to perform both short-term and long-term forecasting, respectively based on past rainfall and river flow measurements and on meteorological forecasts. We then overview the last developments recently brought to Hydromax, focusing on the one hand on new statistical corrections added to the forecasts to better deal with low-water episodes for small stations, and on the other hand on the addition of a model to forecast the level of water in the lake at the Eupen dam, with an alternative modelling able to handle temporary lacks of river flow data (such as observed during the flood of July 2021).
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