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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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Video
This mini lecture gives an overview on the principles underlying food spoilage and introduces different unit operations of food processing.
- Subjects:
- Food Science
- Keywords:
- Food industry trade Processed foods Food science
- Resource Type:
- Video
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Video
An online lecture on the topic of "Ultrasound: Application in Food Science and Technology". The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Food Science
- Keywords:
- Ultrasonic imaging Food science
- Resource Type:
- Video
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Video
An online lecture on the topic of "Chemical Reaction in Atmosphere".The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Environmental Sciences
- Keywords:
- Environmental chemistry Atmospheric chemistry
- Resource Type:
- Video
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Video
This mini-lecture discusses the science of global warming, impact of greenhouse gases (GHGs) emission to life on earth, and the mitigation strategies for climate change. The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Chemistry and Environmental Sciences
- Keywords:
- Greenhouse gases Global warming
- Resource Type:
- Video
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Video
This mini-lecture introduces the future battery. The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Physics and Chemistry
- Keywords:
- Storage batteries
- Resource Type:
- Video
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Video
This mini-lecture on the topic of "Tailoring The Smallest Machinery into Future Robotic Systems". The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Nanotechnology
- Keywords:
- Robotics Robots -- Design construction Nanotechnology
- Resource Type:
- Video
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Video
This mini-lecture introduces different types of microorganisms that are commonly found in food. The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Food Science
- Keywords:
- Bacteria Foodborne diseases -- Microbiology
- Resource Type:
- Video
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Video
This mini-lecture focuses on basic analytical chemistry and the science behind Crime Scene Investigation (CSI). The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Chemistry
- Keywords:
- Forensic sciences Analytical chemistry Crime laboratories
- Resource Type:
- Video
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Video
This mini-lecture gives an overview on how scientists have applied biotechnology techniques to develop medical treatment and food production through the manipulation of DNA. The Faculty of Applied Science and Textiles (FAST) and the Institute of Textiles & Clothing (ITC) organized the mini-lecture series for more than three years. The lectures aim to enrich students' knowledge in creative perspectives and arouse their interest in Sciences, Fashion and Textiles. In view of the unpredictable development of the COVID-19 pandemic, the upcoming mini-lecture Series will be switched from face-to-face mode to online mode.
- Subjects:
- Biology
- Keywords:
- Biotechnology Genetic engineering DNA
- Resource Type:
- Video