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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:
- Convex programming Nonconvex programming Mathematical optimization
- Resource Type:
- Video
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e-book
Welcome to the exciting world of technical theatre. Studying this topic can lead to many different careers in several different sectors of the economy. The general skills needed for any of the careers or sectors have many things in common. Workers need to be dead-line oriented, as most productions have firm timelines that cannot be altered. Critical thinking and analysis are much needed skills. Almost every project in the field is unique and technicians and designers alike must discover the best way of reaching a project’s goal. Creative problem solving is trait successful practitioners have in common. With every project being unique, there are no guaranteed solutions to the problems that are presented. Technicians draw on their vast experience of what worked in the past that can be adapted to be a solution to the current problems. Clear communication and collaboration round out the necessary skills. No technical theatre project is ever handled by one person on their own. Collaboration with many people is the norm, and successful collaboration requires clear written and verbal communication skills.
- Subjects:
- Performing Arts
- Keywords:
- Theaters--Stage-setting scenery Stage management Theater -- Production direction Textbooks
- Resource Type:
- e-book
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e-book
An Introduction to Technical Theatre draws on the author’s experience in both the theatre and the classroom over the last 30 years. Intended as a resource for both secondary and post-secondary theatre courses, this text provides a comprehensive overview of technical theatre, including terminology and general practices. Introduction to Technical Theatre’s accessible format is ideal for students at all levels, including those studying technical theatre as an elective part of their education. The text’s modular format is also intended to assist teachers approach the subject at their own pace and structure, a necessity for those who may regularly rearrange their syllabi around productions and space scheduling.
- Subjects:
- Performing Arts
- Keywords:
- Theaters--Stage-setting scenery Stage management Theater -- Production direction Textbooks
- Resource Type:
- e-book
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e-book
'Institutional critique’ is best known through the critical practice that developed in the late 1960s and early 1970s by artists who presented radical challenges to the museum and gallery system. Since then it has been pushed in new directions by new generations of artists registering and responding to the global transformations of contemporary life. The essays collected in this volume explore this legacy and develop the models of institutional critique in ways that go well beyond the field of art. Interrogating the shifting relations between ‘institutions’ and ‘critique’, the contributors to this volume analyze the past and present of institutional critique and propose lines of future development. Engaging with the work of philosophers and political theorists such as Michel Foucault, Judith Butler, Gilles Deleuze, Antonio Negri, Paolo Virno and others, these essays reflect on the mutual enrichments between critical art practices and social movements and elaborate the conditions for politicized critical practice in the twenty-first century.
- Subjects:
- Visual Arts
- Keywords:
- Institutional Critique (Art movement)
- Resource Type:
- e-book
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MOOC
Understanding a city as a whole, its people, components, functions, scales and dynamics, is crucial for the appropriate design and management of the urban system. While the development of cities in different parts of the world is moving in diverse directions, all estimations show that cities worldwide will change and grow strongly in the coming years. Especially in the tropics over the next 3 decades, it is expected that the number of new urban residents will increase by 3 times the population of Europe today. Yet already now, there is an extreme shortage of designers and urban planners able to understand the functioning of a city as a system, and to plan a sustainable and resilient city. To answer questions like: Which methods can contribute to the sustainable performance of a city, and how can we teach this to the next generations, the ETH Future Cities Laboratory in Singapore has produced over the last 3 years many necessary research results. “Future Cities” aims to bring these latest results to the places where they are needed most. The only way to better understand the city is by going beyond the physical appearance and by focusing on different representations, properties and impact factors of the urban system. For that reason, in this course we will explore the city as the most complex human-made “organism” with a metabolism that can be modeled in terms of stocks and flows. We will open a holistic view on existing and new cities, with a focus on Asia. Data-driven approaches for the development of the future city will be studied, based on crowdsourcing and sensing. At first, we will give an overview of the components and dynamics of the future cities, and we will show the importance of information and information architecture for the cities of the future. The course will cover the origins, state-of-the-art and applications of information architecture and simulation. “Future Cities” will provide the basis to understand, shape, plan, design, build, manage and continually adapt a city. You will learn to see the consequences of citizen science and the merging of Architecture and information space. You will be up-to-date on the latest research and development on how to better understand, create and manage the future cities for a more resilient urban world.
- Subjects:
- Building Services Engineering and Building and Real Estate
- Keywords:
- Smart cities Cities towns -- Effect of technological innovations on City planning
- Resource Type:
- MOOC