All Years Seminars
[INMA] 2023-10-03 (14h) : Systematic Analysis of Iterative Black-Box Optimization Algorithms using Control
At Euler building (room A.002)
Speaker :
Bryan Van Scoy (Miami University, Ohio)
Abstract :
Iterative algorithms are used to solve optimization problems throughout control, robotics, statistics and estimation, signal processing, communication, networks, machine learning, and data science. Recent work from both optimization and control communities has developed a systematic methodology to analyze the worst-case performance of a black-box algorithm over a class of problems. In this talk, we first describe this systematic methodology from a controls perspective and then show how it can be used to analyze and design algorithms in various contexts, such as trading off convergence rate and robustness to gradient noise with noisy first-order oracles, consensus optimization for a multi-agent system, and primal-dual algorithms.
[INMA] 2023-09-26 (14h) : Reinforcement Models via Pólya Urns
At Euler building (room A.002)
Speaker :
Somya Singh (UCLouvain)
Abstract :
Classical Pólya urns have been widely used in the field of applied mathematics to model social and contagion networks. In this talk, I will illustrate three distinct random reinforcement models constructed via modified Pólya urns, through which an epidemic spread model, a consensus-achieving network of agents and a randomly growing preferential attachment graph is developed. The former two models are devised via interacting two-color finite memory Pólya urns, where the underlying draw process is Markovian in nature, while the latter is constructed via an expanding color Pólya urn.
[INMA] 2023-09-19 (14h) : Global optimization using random embeddings
At Euler building (room A.002)
Speaker :
Massart, Estelle
Abstract :
We address global high-dimensional optimization problems in which the objective is mostly varying along a low-dimensional subspace of the search space. These problems appear, e.g., in complex engineering and physical simulation/inverse problems. We propose a random-subspace algorithmic framework (referred to as X-REGO) that randomly projects, in a sequential or simultaneous manner, the high-dimensional original problem into low-dimensional subproblems that can then be solved with any global, or even local, optimization solver. For Lipschitz-continuous objectives, we analyse its convergence using novel tools from probability theory as well as conic integral geometry; our analysis relies on an estimation of the probability that the randomly-embedded subproblem shares (approximately) the same global optimum as the original problem. This success probability is then used to show almost sure convergence of X-REGO to an approximate global solution of the original problem, under weak assumptions on the problem (having a strictly feasible global solution) and on the solver (guaranteed to find an approximate global solution of the reduced problem with sufficiently high probability).
This is joint work with C. Cartis (University of Oxford) and A. Otemissov (Nazarbayev University).
[INMA] 2023-05-16 (14h) : Emergence of dissipative structures in chemical systems
At Auditorium BARB 11
Speaker :
Yannick De Decker (Université Libre de Bruxelles)
Abstract :
Reactive systems maintained far from equilibrium are known to generate various types of spatiotemporal organizations. These structures are often macroscopic and involve time scales that are much longer than the typical reaction times. The connection between the microscopic and macroscopic scales is commonly explained by the propagation of local correlations over large distances, which would be induced by non-reactive transport processes. In this talk, we will explore examples of real-life chemical systems to evaluate the plausibility of this mechanism. Data from atom microscope experiments and models of spatial coupling in living systems both suggest that nature often relies on more intricate ways to propagate chemical information.
[INMA] 2023-05-09 (14h) : Convex Analysis and Synthesis of Accelerated Gradient Algorithms
At Euler building (room A.002)
Speaker :
Carsten Sherer (University of Stuttgart, Department of Mathematics)
Abstract :
Gradient descent is a well-established technique for solving optimization problems in the current era of big data and machine learning. Recent years have witnessed a strong interest in so-called accelerated gradient algorithms which have superior convergence properties if compared to standard gradient descent applied to convex optimization problems. It has been known for a long time that such algorithms can be viewed as a linear time-invariant discrete-time system in feedback with the gradient of the to-be-minimized function as a nonlinearity. This point-of-view provides an immediate link to the so-called absolute stability problem for Lur’e systems in control. It opens up the possibility to apply advanced tools from robust control in order to compute the convergence rate of a given accelerated gradient algorithm by semi-definite programming.
A much more challenging task is the direct computational design of algorithms in order to achieve optimal convergence rates. This questions falls into the area of robust feed- back controller synthesis. In this talk we survey how to analyze and synthesize algorithms by robust control techniques. A particular emphasis will be laid on highlighting the key structural aspects that enable the construction of suitable small-sized semi-definite pro- grams to determine optimal algorithms. As a distinguishing feature, we reveal that our techniques seamlessly extend to extremum control, with the goal to design controllers that drive the output of a general linear system to the minimum of a convex function with an optimal rate of convergence.
Seminars
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Mon – Fri 9:00A.M. – 5:00P.M.
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