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This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games played in class and to examples drawn from economics, politics, the movies, and elsewhere.
- Subjects:
- Mathematics and Statistics and Economics
- Keywords:
- Game theory
- Resource Type:
- Video
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Video
Before the advent of computers around 1950, optimization centered either on small-dimensional problems solved by looking at zeroes of first derivatives and signs of second derivatives, or on infinite-dimensional problems about curves and surfaces. In both cases, "variations" were employed to understand how a local solution might be characterized. Computers changed the picture by opening the possibility of solving large-scale problems involving inequalities, instead of only equations. Inequalities had to be recognized as important because the decisions to be optimized were constrained by the need to respect many upper or lower bounds on their feasibility. A new kind of mathematical analysis, beyond traditional calculus, had to be developed to address these needs. It built first on appealing to the convexity of sets and functions, but went on to amazingly broad and successful concepts of variational geometry, subgradients, subderivatives, and variational convergence beyond just that. This talk will explain these revolutionary developments and why there were essential.
Event date: 1/11/2022
Speaker: Prof. Terry Rockafellar (University of Washington)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computer science -- Mathematics Mathematical optimization Convex sets Convex functions
- Resource Type:
- Video
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Video
Adaptive computation is of great importance in numerical simulations. The ideas for adaptive computations can be dated back to adaptive finite element methods in 1970s. In this talk, we shall first review some recent development for adaptive methods with some application. Then, we will propose a deep adaptive sampling method for solving PDEs where deep neural networks are utilized to approximate the solutions. In particular, we propose the failure informed PINNs (FI-PINNs), which can adaptively refine the training set with the goal of reducing the failure probability. Compared with the neural network approximation obtained with uniformly distributed collocation points, the proposed algorithms can significantly improve the accuracy, especially for low regularity and high-dimensional problems.
Event date: 18/10/2022
Speaker: Prof. Tao Tang (Beijing Normal University-Hong Kong Baptist University United International College)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical models Differential equations Partial -- Numerical solutions Adaptive computing systems Sampling (Statistics)
- Resource Type:
- Video
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Video
Convex Matrix Optimization (MOP) arises in a wide variety of applications. The last three decades have seen dramatic advances in the theory and practice of matrix optimization because of its extremely powerful modeling capability. In particular, semidefinite programming (SP) and its generalizations have been widely used to model problems in applications such as combinatorial and polynomial optimization, covariance matrix estimation, matrix completion and sensor network localization. The first part of the talk will describe the primal-dual interior-point methods (IPMs) implemented in SDPT3 for solving medium scale SP, followed by inexact IPMs (with linear systems solved by iterative solvers) for large scale SDP and discussions on their inherent limitations. The second part will present algorithmic advances for solving large scale SDP based on the proximal-point or augmented Lagrangian framework In particular, we describe the design and implementation of an augmented Lagrangian based method (called SDPNAL+) for solving SDP problems with large number of linear constraints. The last part of the talk will focus on recent advances on using a combination of local search methods and convex lifting to solve low-rank factorization models of SP problems.
Event date: 11/10/2022
Speaker: Prof. Kim-Chuan Toh (National University of Singapore)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Semidefinite programming Convex programming
- Resource Type:
- Video
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Video
We introduce a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while using only Hessian-vector products in two directions. Moreover; the computational overhead remains comparable to the first-order such as the gradient descent method. We show that the method has a local super-linear convergence and a global convergence rate of 0(∈-3/2) to satisfy the first-order and second-order conditions under a commonly used approximated Hessian assumption. We further show that this assumption can be removed if we perform one step of the Krylov subspace method at the end of the algorithm, which makes DRSOM the first first-order-type algorithm to achieve this complexity bound. The applicability and performance of DRSOM are exhibited by various computational experiments in logistic regression, L2-Lp minimization, sensor network localization, neural network training, and policy optimization in reinforcement learning. For neural networks, our preliminary implementation seems to gain computational advantages in terms of training accuracy and iteration complexity over state-of-the-art first-order methods including SGD and ADAM. For policy optimization, our experiments show that DRSOM compares favorably with popular policy gradient methods in terms of the effectiveness and robustness.
Event date: 19/09/2022
Speaker: Prof. Yinyu Ye (Stanford University)
Hosted by: Department of Applied Mathematics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Nonconvex programming Mathematical optimization Convex programming
- Resource Type:
- Video
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Video
Machine learning can deliver unprecedented performance. Its application domain has expanded into safety-critical cyber-physical systems such as UAVs and self-driver cars. However, the safety assurance of vehicular control has two conditions: 1) an analytical model of system behaviors such as provable stability, and 2) the software safety certification process (e.g., DO 178C) requires that the software be simple enough so that software safety can be validated by a combination of model checking and near exhaustive testing. Although ML software, as is, does not meet these two safety requirements, the real-time physics model supervised ML architecture holds the promise to 1) meet the two safety requirements and 2) enable ML software to safely improve control performance and safely learn from its experience in real-time. This talk will review the structure of the proposed architecture and some methods to embed physics into ML-enabled CPS control.
Event Date: 12/05/2022
Speaker: Prof. Lui Sha (University of Illinois Urbana-Champaign)
Hosted by: Graduate School
- Subjects:
- Computing, Data Science and Artificial Intelligence and Aeronautical and Aviation Engineering
- Keywords:
- Machine learning Computer software -- Reliability Drone aircraft Vehicles Remotely piloted
- Resource Type:
- Video
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Video
An online lecture on the topic of "Computer Software Challenges for Aerospace Missions".This lecture of “Science World: Exploring Space to Benefit Mankind” Education Programme in the 2021/22 school year for secondary students, which aims to cultivate the interest of local youth in space science and elevate their enthusiasm for participating in the development of space technology.
- Subjects:
- Computing, Data Science and Artificial Intelligence and Aeronautical and Aviation Engineering
- Keywords:
- Computer programming Aeronautics -- Data processing
- Resource Type:
- Video
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Video
At TEDIndia, Pranav Mistry demos several tools that help the physical world interact with the world of data -- including a deep look at his SixthSense device and a new, paradigm-shifting paper "laptop." In an onstage Q&A, Mistry says he'll open-source the software behind SixthSense, to open its possibilities to all.
- Subjects:
- Electronic and Information Engineering and Computing, Data Science and Artificial Intelligence
- Keywords:
- Augmented reality Human-computer interaction
- Resource Type:
- Video
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Video
Months after he was born, in 1948, Ron McCallum became blind. In this charming, moving talk, he shows how he reads -- and celebrates the progression of clever tools and adaptive computer technologies that make it possible. With their help, and the help of volunteers, he's become a lawyer, an academic, and, most of all, a voracious reader. Welcome to the blind reading revolution.
- Subjects:
- Computing, Data Science and Artificial Intelligence, Technology, and Electronic and Information Engineering
- Keywords:
- Blind -- Books reading Assistive computer technology Reading -- Aids devices
- Resource Type:
- Video
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Video
How can technology help improve our quality of life? How can we navigate the world without using the sense of vision? Inventor and IBM Fellow Chieko Asakawa, who's been blind since the age of fourteen, is working on answering these questions. In a charming demo, she shows off some new technology that's helping blind people explore the world ever more independently ... because, she suggests, when we design for greater accessibility, everyone benefits.
- Subjects:
- Computing, Data Science and Artificial Intelligence, Technology, and Communication Design
- Keywords:
- Assistive computer technology Self-help devices for people with disabilities
- Resource Type:
- Video