NCCR Symposium - Complex Interconnected Systems and decision making in measure spaces

Chair: Saverio Bolognani, Florian Dörfler (Aula Auditorium)

The classic modeling and decision-making paradigm is that of a single monolithic system interconnected with a decision-making algorithm. However, this paradigm is inappropriate for many problems such as infrastructure networks, modeling of complex interactions amongst living beings, decision-making involving distributed computing, sensor networks, and many others. Rather these are characterized by a collection of individual subsystems and decision makers interconnected either physically, coordinated through their actions, or sharing information over a communication network. The speakers in this symposium will offer different perspectives on complex interconnected systems. 

12:00 - Lunch (Lichthof)

Afternoon Program (Aula Auditorium) 

13:30 - Intro

13:45 - Sonia Martinez "Distributionally Robust Coverage Control via Haar Wavelets"

14:45 - Naomi Leonard "Fast and Flexible Decision-Making in Complex Interconnected Systems"

15:45 - break

16:30 - Na Li "Scalable distributed control and learning of networked dynamical systems"

17:30 - Giancarlo Ferrari Trecate "Boosting the Performance of Nonlinear Systems with Neural-Network Control"

18:30 - Apéro (Lichthof)

09:00-12:00: Workshop on robust decision making in professional environments chaired by Elise Cahard and Silvia Mastellone (Aula Auditorium).

Interactive workshop: Employ your integrated analytical and social skills to address decision making problems from real life scenarios

Most of us think, that we act and decide very rationally. But we all have so-called unconscious biases. What are unconscious biases? What role do they play in our daily life as researchers? How do they influence us, when we work together, integrate new team members or in leadership situations? Gudrun Sander, Professor of Business Administration at the University of St. Gallen, will tackle these questions. By understanding how biases can impact our interactions with others, we become more equipped to make robust decisions and objective judgments. The following aspects form the foundation of the input session: the definition and impact of unconscious biases, different types of unconscious biases and how to avoid or mitigate them. After the input session, we will work on several cases and discuss, how to improve meetings, interview situations or appraisal talks.

12:00 - lunch (Lichthof)

Afternoon:

Decision making in probability spaces session chaired by Saverio Bolognani and Florian Dörfler (Aula Auditorium)

In large-scale systems it is often not practical to model individual subsystems and their discrete interactions for decision-making. Rather, it is more appropriate to consider the limit of infinitely many interacting subsystems resulting in dynamics described by their densities. Also probabilistic or data-driven modeling typically results in decision-making problems defined over measure spaces. Recently, a plethora of new analytic and computational methods have emerged for decision-making in such measure spaces, including control, games, optimization, inference, and so on. The speakers in this symposium will illuminate this emergent paradigm from many different angles.

13:30 - Intro

13:45 - Francis Bach "Information Theory with Kernel Methods"

14:45 - Marco Cuturi "On the optimization of Monge Maps: Structured Priors and Neural Networks"

15:45 - break

16:30 - Tryphon Georgiou "Measure Spaces of Thermodynamic States: Dissipation and Power in Physics and Biology"

17:30 - Daniel Kuhn - "Distributionally Robust Optimization: The Science of Underpromising and Overdelivering"

18:30 - end of scientific program and Apéro (Lichthof)

Abstract: Estimating and computing entropies of probability distributions are key computational tasks throughout data science. In many situations, the underlying distributions are only known through the expectation of some feature vectors, which has led to a series of works within kernel methods. In this talk, I will explore the particular situation where the feature vector is a rank-one positive definite matrix, and show how the associated expectations (a covariance matrix) can be used with information divergences from quantum information theory to draw direct links with the classical notions of Shannon entropies.

Bio: Francis Bach is a researcher at Inria, leading since 2011 the machine learning team which is part of the Computer Science department at Ecole Normale Supérieure. He graduated from Ecole Polytechnique in 1997 and completed his Ph.D. in Computer Science at U.C. Berkeley in 2005, working with Professor Michael Jordan. He spent two years in the Mathematical Morphology group at Ecole des Mines de Paris, then he joined the computer vision project-team at Inria/Ecole Normale Supérieure from 2007 to 2010. Francis Bach is primarily interested in machine learning, and especially in sparse methods, kernel-based learning, large-scale optimization, computer vision and signal processing. He obtained in 2009 a Starting Grant and in 2016 a Consolidator Grant from the European Research Council, and received the Inria young researcher prize in 2012, the ICML test-of-time award in 2014 and 2019, as well as the Lagrange prize in continuous optimization in 2018, and the Jean-Jacques Moreau prize in 2019. He was elected in 2020 at the French Academy of Sciences. In 2015, he was program co-chair of the International Conference in Machine learning (ICML), and general chair in 2018; he is now co-editor-in-chief of the Journal of Machine Learning Research.

Abstract: After providing a short self-contained introduction on the Monge problem, its potential applications and its computational challenges, I will present in this talk two recent contributions that offer practical solutions. In the first part I will show how changing the so-called ground cost function of optimal transport problems directly influences the structure of such maps in theory, and how this can be turned into a practical tool. In the second part I present a simple approach to estimate  Monge maps using a simple regularizer (both works were presented at the ICML'23 conference, https://proceedings.mlr.press/v202/uscidda23a.html, https://proceedings.mlr.press/v202/cuturi23a.html ).

Abstract: The Wasserstein geometry of optimal mass transport in measure spaces has emerged as a powerful framework for modeling and regulation of stochastic systems. In the talk we will focus on the regulation of thermodynamic systems that obey Langevin dynamics for the purpose of harvesting energy from heat baths they are in contact with. Cyclic operation corresponds to tracing closed orbits on the measure space of thermodynamic states. We will present an embodiment of such a thermodynamic engine with interconnected electromechanical and thermal components and draw analogy to flagellar biological motors. For thermodynamic engines that are powered by thermal or chemical anisotropy, the minimal dissipation over a cycle is quantified by the Wasserstein length of the orbit while the work being extracted is quantified by an area integral. Thereby, the maximal attainable power can be quantified via an isoperimetric inequality in the underlying measure space.

Bio: Tryphon T. Georgiou was educated at the National Technical University of Athens, Greece (1979) and the University of Florida, Gainesville (PhD 1983).  He is currently a Distinguished Professor at the Department of Mechanical and Aerospace Engineering, University of California, Irvine. He is a Fellow of IEEE, SIAM, IFAC, AAAS and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA).

Title: Distributionally Robust Optimization: The Science of Underpromising and Overdelivering

Abstract: Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test samples are drawn from the same distribution—especially if the dimension of the uncertainty is large relative to the training sample size. Wasserstein distributionally robust optimization (DRO) seeks data-driven decisions that perform well under the most adverse distribution within a certain Wasserstein distance from a nominal distribution constructed from the training samples. It has a wide range of conceptual, statistical and computational benefits. Most prominently, the optimal decisions can often be computed efficiently, and they enjoy provable out-of-sample and asymptotic consistency guarantees. This talk will highlight two recent advances in Wasserstein DRO. First, we will develop a principled approach to leveraging samples from heterogeneous data sources for making better decisions. In addition, we will prove the optimality of linear policies in Wasserstein distributionally robust linear-quadratic control problems with imperfect state observations, and we will show that these policies can be computed efficiently using dynamic programming, Kalman filtering and automatic differentiation.

Bio: Daniel Kuhn is a Professor of Operations Research in the College of Management of Technology at EPFL, where he holds the Chair of Risk Analytics and Optimization. His research interests revolve around stochastic, robust and distributionally robust optimization, and his principal goal is to develop efficient algorithms as well as statistical guarantees for data-driven optimization problems. Before joining EPFL, Daniel Kuhn was a faculty member in the Department of Computing at Imperial College London and a postdoctoral researcher in the Department of Management Science and Engineering at Stanford University. He holds a PhD degree in Economics from the University of St. Gallen and an MSc degree in Theoretical Physics from ETH Zurich. He is an INFORMS fellow and the recipient of several research and teaching prizes including the Friedrich Wilhelm Bessel Research Award by the Alexander von Humboldt Foundation and the Frederick W. Lanchester Prize by INFORMS. He is the editor-in-chief of Mathematical Programming and the area editor for continuous optimization of Operations Research.
 

Abstract: Fast and flexible decision-making is critical for complex interconnected systems to successfully manage the uncertainty, variability, and dynamic change encountered when operating in the real world. Decision-making is fast if it breaks indecision as quickly as indecision becomes costly. This requires fast divergence away from indecision in addition to fast convergence to a decision. Decision-making is flexible if it adapts to signals important to successful operation, even if they are weak or rare. This requires tunable sensitivity to input for modulating regimes in which the system is ultra-sensitive and in which it is robust. Nonlinearity and feedback in the decision-making process are necessary to meeting these requirements. I will present theory and application of decentralized nonlinear opinion dynamics that enable fast and flexible decision-making among multiple options for multi-agent systems interconnected by communication and belief system networks.  The result is a principled and systematic means for designing and analyzing decision-making in systems ranging from robot teams to social networks.

This is joint work with Alessio Franci and Anastasia Bizyaeva and based on the papers:

https://ieeexplore.ieee.org/document/9736598

https://arxiv.org/abs/2308.02755

https://epubs.siam.org/doi/10.1137/22M1507826

Bio: Naomi Ehrich Leonard is Chair and Edwin S. Wilsey Professor of Mechanical and Aerospace Engineering and associated faculty in Applied and Computational Mathematics and the Program in Biophysics at Princeton University.  She is also affiliated faculty at the Princeton Neuroscience Institute and Founding Editor of the Annual Review of Control, Robotics, and Autonomous Systems. She received her BSE in Mechanical Engineering from Princeton University and her PhD in Electrical Engineering from the University of Maryland.  She is a MacArthur Fellow, elected member of the American Academy of Arts and Sciences, and winner of the 2023 IEEE Control Systems Award and the 2017 IEEE CSS Henrik W. Bode Lecture Prize. She is Fellow of IEEE, IFAC, SIAM, and ASME.  Her current research focuses on dynamics, control, and learning for multi-agent systems on networks with application to multi-robot teams, collective animal behavior, social networks, and other multi-agent systems in technology, nature, and the visual and performing arts.

Abstract: Recent radical evolution in distributed sensing, computation, communication, and actuation has fostered the emergence of cyber-physical network systems. Regardless of the specific application, one central goal is to shape the network's collective behavior through the design of admissible local decision-making algorithms. This is nontrivial due to various challenges such as local connectivity, system complexity and uncertainty, limited information structure, and the complex intertwined physics and human interactions. 

 In this talk, I will present our recent progress in formally advancing the systematic design of distributed coordination in network systems via harnessing special properties of the underlying problems and systems. In particular, we will present three examples and discuss three types of properties, i) how to exploit network structure to ensure the performance of the local controllers; ii) how to use the information and communication to develop distributed learning rules; iii) how to use domain-specific properties to further improve the efficiency of the distributed control and learning algorithms. We will also discuss challenges and issues arising from these solutions. 

Bio: Na Li is a Winokur Family Professor of Electrical Engineering and Applied Mathematics at Harvard University.  She received her Bachelor's degree in Mathematics from Zhejiang University in 2007 and Ph.D. degree in Control and Dynamical systems from California Institute of Technology in 2013. She was a postdoctoral associate at the Massachusetts Institute of Technology 2013-2014.  She has held a variety of short-term visiting appointments including the Simons Institute for the Theory of Computing, MIT, and Google Brain. Her research lies in the control, learning, and optimization of networked systems, including theory development, algorithm design, and applications to real-world cyber-physical societal system.  She has been an associate editor for IEEE Transactions on Automatic Control, Systems & Control Letters, IEEE Control Systems Letters, and served on the organizing committee for a few conferences.  She received the NSF career award (2016), AFSOR Young Investigator Award (2017), ONR Young Investigator Award(2019),  Donald P. Eckman Award (2019), McDonald Mentoring Award (2020), the IFAC Manfred Thoma Medal (2023), along with some other awards.

Abstract: Multi-robot coverage control, by which a group of agents aims to optimally deploy over a spatial region of interest, has received wide attention in the robotics and controls literature. A main body of work relies on the k-means clustering formulation and Lloyd's algorithm. However, this formulation is non-robust when the environment's random events are generated by unknown distributions.  In this talk, we present a data-driven approach that addresses this issue via a distributionally robust optimization. In a first step, we introduce a parameterization of ambiguity sets that makes use of Haar wavelet functions. Haar wavelets, which build data-driven histograms with probabilistic guarantees, allows us to reduce this infinite-dimensional problem to a more tractable finite-dimensional counterpart, and, at the same time, include valuable prior information on the uncertainty.  Yet, the resulting coverage control objective function is non-smooth. This last hurdle is addressed via a generalized gradient sampling algorithm, which approximates the function's Clarke generalized gradient to find appropriate algorithm descent directions. In analogy with the Lloyd's algorithm for differentiable costs, our solution is shown to converge to a stationary multi-robot location. The talk concludes with a discussion of the results in simulation.

Bio: Sonia Martínez is a Full Professor at the Department of Mechanical and Aerospace Engineering at the University of California, San Diego and a Jacobs Faculty Scholar. Prof. Martínez received her B.S. degree from the Universidad de Zaragoza, Spain in 1997, and her Ph.D. degree in Engineering Mathematics from the Universidad Carlos III de Madrid, Spain, in May 2002. Following a year as a Visiting Assistant Professor of Applied Mathematics at the Technical University of Catalonia, Spain, she obtained a Postdoctoral Fulbright Fellowship and held appointments at the Coordinated Science Laboratory of the University of Illinois, Urbana-Champaign during 2004, and at the Center for Control, Dynamical systems and Computation (CCDC) of the University of California, Santa Barbara during 2005. From January 2006 to June 2010, she was an Assistant Professor with the department of Mechanical and Aerospace Engineering at the University of California, San Diego. From July 2010 to June 2014, she was an Associate Professor with the department of Mechanical and Aerospace Engineering at the University of California, San Diego.

Dr Martínez' research interests include networked control systems, multi-agent systems, and nonlinear control theory with applications to robotics, cyber-physical systems, and natural/social networks. In particular, she has focused on the modeling and control of robotic sensor networks, the development of distributed coordination algorithms for groups of autonomous vehicles, and the geometric control of mechanical systems. For her work on the control of underactuated mechanical systems she received the Best Student Paper award at the 2002 IEEE Conference on Decision and Control. She was the recipient of a NSF CAREER Award in 2007. For the co-authored papers "Motion coordination with Distributed Information," and "Tutorial on dynamic average consensus: The problem, its applications, and the algorithms", she received respectively the 2008 and 2021 Control Systems Magazine Outstanding Paper Award. She is a Senior Editor of Automatica and an IEEE Fellow. Recently, she was named the inaugural Editor in Chief of a new Control System Society publication, the IEEE Open Journal of Control Systems (IEEE OJCS).

Abstract: Most of us think, that we act and decide very rationally. But we all have so-called unconscious biases. What are unconscious biases? What role do they play in our daily life as researchers? How do they influence us, when we work together, integrate new team members or in leadership situations? Gudrun Sander, Professor of Business Administration at the University of St. Gallen, will tackle these questions. By understanding how biases can impact our interactions with others, we become more equipped to make robust decisions and objective judgments. The following aspects form the foundation of the input session: the definition and impact of unconscious biases, different types of unconscious biases and how to avoid or mitigate them. After the input session, we will work on several cases and discuss, how to improve meetings, interview situations or appraisal talks.

Bio: Gudrun Sander is a Professor of Business Administration with a special emphasis on Diversity Management and a Senior Lecturer. She completed her PhD (Dr. oec. HSG) at the University of St. Gallen in 1997. For her dissertation she received the recognition award of the Swiss Society for Organisation and Management (SGO) in 1998. Gudrun Sander is Director of the Competence Centre for Diversity and Inclusion (CCDI) and Director of the Research Institute for International Management (FIM) at the University of St. Gallen. For three decades, she has been committed to diversity, equity and inclusion in research, practice, teaching and further education. Among other things, she initiated the St. Gallen Diversity Benchmarking and the Gender Intelligence Report, launched the management training „Women Back to Business“, is an expert in salary analysis and sees her strength at the interface between research and practice. She is a sought-after speaker in executive education and especially for company-specific workshops and trainings on topics such as Unconscious Bias, Diversity & Inclusion, Strategic Management and Leadership.

She is a member of the Women’s Empowerment Principles Leadership Group (WEPs LG) of UN Women and UN Global Compact as well as of the Principles for Responsible Management Education (PRME) Working Group for Gender Equality.