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Colloquium
Variational Characterizations of First-Order Algorithms via Self-Duality
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Speaker: Lorenzo Orecchia (Chicago) Assistant Professor of Computer Science University of Chicago Wednesday, October 29, 2025 11:30AM - 1:00PM Lunch in 1307 from 11:30-12:00pm
Talk in 1327 from 12:00-1:00pm Location: Yale Institute for Foundations of Data Science, Kline Tower 13th Floor, Room 1327, New Haven, CT 06511 and via Webcast: https://yale.hosted.panopto.com/Panopto/Pages/Viewer.aspx?id=2bb244d2-f4ff-435f-a430-b35a01119d81 |
Talk summary: First-order methods for convex optimization play an important role in the efficient deployment of machine learning algorithms. While a large number of such methods exist, each tuned to the specific properties of the problem under consideration, it is not always clear how to generalize their approach to a new setting or to a different set of assumptions.
At the same time, certain phenomena, such acceleration, remain unintuitive.
An interest approach to systematize the design of first-order method is based on interpreting each method as the discretization of a continuous dynamics, which can be characterized variationally. This allows us to bring in a large set of tools from the calculus of variation and geometric integration to bear. However, current interpretations only yield characterizations as stationary points and focus on acceleration, without explaining other methods such as metric gradient descent or mirror descent. We present improved characterization that yield characterizations of first-order methods as global minima of natural, duality-gap based, variational problems. The key idea in our approach is self-duality, which allows us to move beyond Euler-Lagrange equations as a way to introduce variational defined dynamics. We also connect our work with the study of variational formulations for more general dissipative systems.
Speaker bio: Lorenzo Orecchia is an assistant professor in the Department of Computer Science at the University of Chicago. Lorenzo’s research focuses on the design of efficient algorithms for fundamental computational challenges in machine learning and combinatorial optimization. His approach is based on combining ideas from continuous and discrete optimization into a single framework for algorithm design. Lorenzo obtained his PhD in computer science at UC Berkeley under the supervision of Satish Rao in 2011, and was an applied mathematics instructor at MIT under the supervision of Jon Kelner until 2014. He was a recipient of the 2014 SODA Best Paper award and a co-organizer of the Simons semester “Bridging Continuous and Discrete Optimization” in Fall 2017.
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