PhD Talk/Colloquia

The Ph.D. colloquium has added a new, shorter format: the Ph.D. Talk! Ph.D. Talks are scheduled throughout the fall. The talks are 20 minutes and informal, with the purpose of letting students discuss their research, get feedback and ideas, and share resources.

The spring colloquium is a one-hour format, designed for practicing longer conference presentations or job talks. Participants in the spring colloquium will be candidates for the Best PhD Colloquium award.

Please sign up here.

Seminars and Talks will be held in Towne 337 on Wednesdays at 12:00 PM unless otherwise specified.

Santiago Paternain

OCT 11

"A Second Order Method for Nonconvex Optimization"

Machine learning problems such as neural network training, tensor decomposition, and matrix factorization, require local minimization of a nonconvex function. This local minimization is challenged by the presence of saddle points, of which there can be many and from which descent methods may take an inordinately large number of iterations to escape. In this talk, we present a second-order method that modifies the update of Newton's method by replacing the negative eigenvalues of the Hessian by their absolute values and uses a truncated version of the resulting matrix to account for the objective function's curvature. The method is shown to escape saddles exponentially with base 1.5 regardless of the condition number of the problem. Adding classical properties of Newton's method, the paper proves convergence to a local minimum with high probability after a number of iterations that is logarithmic in the target accuracy.

Santiago Paternain received the B.Sc. degree in electrical engineering from Universidad de la Rep\'ublica Oriental del Uruguay, Montevideo, Uruguay in 2012. Since August 2013, he has been working toward the Ph.D. degree in the Department of Electrical and Systems Engineering, University of Pennsylvania. His research interests include optimization and control of dynamical systems.

Mark Eisen

OCT 18

"A Decentralized Primal-Dual Quasi-Newton Method for Consensus Optimization"

This work considers consensus optimization problems where each node of a network has access to a different summand of an aggregate cost function. Nodes try to maximize the aggregate cost function, while they exchange information only with their neighbors. We modify the augmented Lagrangian method to incorporate a curvature correction inspired by the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method. The resulting primal-dual BFGS method is a fully decentralized algorithm in which nodes approximate curvature information of themselves and neighbors for both the primal and dual variables of the augmented Lagrangian through the satisfaction of a secant condition. The developed algorithm is of interest in consensus problems that are not well conditioned, making first order decentralized methods ineffective, and in which second order information is not readily available, making decentralized second order methods infeasible. We establish a linear convergence rate to the exact solution of the consensus problem and performance advantages relative to alternative decentralized algorithms are shown numerically.

Mark Eisen received the B.Sc. degree in electrical engineering from the University of Pennsylvania, Philadelphia, PA, USA, in 2014. He is currently working toward the Ph.D. in the Department of Electrical and Systems Engineering, University of Pennsylvania. His research interests include distributed optimization and machine learning. In the summer of 2013, he was a research intern in the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN, USA. He received the Outstanding Student Presentation at the 2014 Joint Mathematics Meeting, as well as the 2016 Penn Outstanding Undergraduate Research Mentor Award.

Andreea Alexandru

OCT 18

"Privacy Preserving Cloud-Based Quadratic Optimization"

In the Internet of Things setup, cloud-outsourced computations are ubiquitous, because of the low computation, battery and storage requirements of the participating devices. Due to the increasing number of cyberattacks, privacy infringements and financial interests arising from owning private data, it is unrealistic to assume that the cloud does not try to take advantage of the users' data. The most common framework in which multi-party computation is performed is the semi-honest model, which, intuitively, describes rival parties that collaborate to achieve a common goal. Under this setup, we wish to develop protocols that satisfy cryptographic security, i.e., no party can infer anything about the private data of other parties. More specifically, we address optimization problems, which lie at the core of control applications, such as state estimation, model predictive control etc. In this talk, we propose a protocol for privately solving constrained quadratic optimization problems with sensitive data. The problem encompasses the private data of multiple agents and is outsourced to an untrusted server. We present an interactive protocol that achieves the solution by making use of partially homomorphic cryptosystems to securely effectuate computations.

Andreea Alexandru received the B.Sc. degree in Automatic Control and Systems Engineering from “Politehnica” University of Bucharest, Romania, in 2015. She is currently in her third year of Ph.D. program in the Department of Electrical and Systems Engineering, University of Pennsylvania, working with prof. George Pappas and prof. Ali Jadbabaie. Her research interests lie in the security of control systems, involving both cryptographic and information-theory tools.

David Hopper

OCT 25

"Amplified Sensitivity of Nitrogen-Vacancy Center Sensors with All-Optical Charge Readout"

The nitrogen-vacancy (NV) center in diamond is a solid-state qubit and nanoscale sensor for applications including single-molecule nuclear magnetic resonance and dynamic electrochemical potential sensing with nanoscale resolution. These demonstrations are possible due to the NV’s photoluminescence dependence on changes in the spin or charge state of the qubit, which provides an optical indicator of the external environment. Despite these impressive demonstrations, ideal sensing platforms such as nanodiamonds exhibit poor signal-to-noise ratios for spin and charge measurements, which prevent the wide adoption of these sensing capabilities. In this talk, I will discuss recent work from our group on circumventing these technological hurdles by leveraging full control over the NV’s spin, orbital, and charge dynamics in nanodiamonds. Critical to our method is the development of a high signal-to-noise ratio, all-optical charge readout protocol along with a means for efficiently correlating a spin state with a charge distribution. I will conclude by discussing how these methods can improve current state-of-the-art NV sensors.

David Hopper earned his bachelor’s degree in Physics with Honors from The Pennsylvania State University in 2014. He is currently pursuing his PhD in Physics at the University of Pennsylvania with Professor Lee Bassett as part of the physics graduate group. He is broadly interested in semiconductor quantum dynamics and quantum information science, with a current focus on improving the readout capabilities of the nitrogen-vacancy center in diamond.

Mahyar Fazlyab

OCT 25

"Analysis of optimization algorithms via Integral Quadratic Constraints: Non-strongly convex problems"

In this work, we develop a unified framework, based on robust control theory and semidefinite programming, to analyze the performance of iterative first-order optimization algorithms, as well as their continuous-time counterparts. Our starting point is to represent these algorithms as linear dynamical systems interconnected with a nonlinear component. We then propose a family of time-dependent nonquadratic Lyapunov functions that are particularly useful for establishing arbitrary (exponential or subexponential) convergence rates. Using Integral Quadratic Constraints (IQCs) from robust control theory to describe the class of nonlinearities in the interconnection, we derive sufficient conditions for the Lyapunov stability of these algorithms in terms of Linear Matrix Inequalities (LMIs), whose size is independent of the problem dimension. We show how the developed LMI-based framework unifies the convergence analysis by studying several algorithms, namely, the gradient method, the Nesterov's accelerated method, proximal algorithms, and their accelerated variants. We perform the analysis for both strongly-convex and convex settings, where we expect exponential and subexponential convergence rates, respectively.

Mahyar received the B.Sc. and M.Sc. degree in Mechanical engineering from Sharif University of Technology, Tehran, Iran. Since 2013, he has been working towards the Ph.D. degree in Electrical and Systems Engineering at University of Pennsylvania. His research interests include the analysis, optimization, and control of dynamical systems.

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