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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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MOOC
This course is about resonating with your experience and meaningfully engaging patients to make good decisions and to address the significance of interprofessional collaborations in health care. Service users’ experience and views across all points on health promotion, management and support services are crucial to developing optimal health care practice. Join Prof Elwynis a leader committed in Shared Decision Making (SDM) practice and research to promote high quality decision making. Taking into account the best scientific evidence available, he will explain to you how this collaborative process and the use of decision-aids help eliciting patients’ beliefs and integrating patient preferences and priorities to treatment options after thorough considerations of the trade-offs. Together, we are oriented to the interprofessional collaborative initiative that synergizes the strengths among health care allies toachieve optimal clinical practice and health outcomes. Renowned experts in various health care fields share their first hand experiences, eliciting profound insights and wisdoms about interprofessional collaborations. This is aspirational in learning to reflect, decipher, interpret and construct ways in enhancing effective coordination of care to meet health needs. Making sense of the SDM and IPC concepts and recognizing the available evidences and resources is crucial to enabling good team dynamics. Using a docu-drama, it takes you through a patient’s journey having a stroke due to his hidden assumptions in receiving treatment to atrial fibrillation (an abnormal heart rhythm). His attitude and struggles point to a challenging recovery process. Contemplate on how SDM and IPC could step in at different stages to improve health outcomes. Identifying gaps in the existing scientific evidence and services will help you to pursue influential strategies and design innovative programs or products to attain better outcomes. Your understanding and participation in this course will create positive impact over time in advancing the present health system to deliver the best possible outcomes to various stakeholders. We are excited to see your passion in affecting health decisions and determination in accomplishing excellent care delivery. Get connected with a global community of learners and simply enjoy gaining new ideas about making a difference in health care.
- Subjects:
- Health Sciences
- Keywords:
- Patient participation Clinical medicine -- Decision making Medical care -- Decision making
- Resource Type:
- MOOC