Simon Foucart
Texas A&M University-College Station, TX·Mathematics & Statistics
Many machine learning algorithms are built to work well most of the time, but in defense, medicine and transportation even rare failures are unacceptable. Optimal Recovery is a mathematical framework that gives worst-case guarantees: it says how well an unknown function can be learned or reconstructed from limited data under realistic assumptions, and which method does best.
- Fields
Mathematics & Statistics
Computer Science
- Topics
optimal recovery
approximation theory
function learning
- Grants
- 1 known grant, through Jul 2028
What they work on
- Extend Optimal Recovery theory, which guarantees worst-case accuracy for learning functions from data, from functions with single real-valued outputs to functions with more complex outputs, using optimization theory.
- Generalize Optimal Recovery beyond convexity assumptions on the target quantities and model sets, so guarantees can apply to non-convex models including neural networks.
- Develop Optimal Recovery methods for dynamical objects, especially time-changing graphs and data from destructive observations, and test them on application problems from Los Alamos National Laboratory.
More about the research
This project aims to widen what Optimal Recovery can handle.
Why it matters
Fields where an algorithm's occasional failure is unacceptable, such as defense, medicine and transportation, need learning methods with worst-case guarantees. Extending Optimal Recovery to complex outputs, neural network models and changing graphs could give these fields reliable mathematical guarantees for learning from data, with methods tested on Los Alamos National Laboratory problems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Somayeh Sojoudi
University of California-Berkeley, CA·Engineering·Early-career
Analyze when key non-convex machine-learning problems have spurious solutions (points that look locally best but are not globally best), and how the amount of data and problem structure remove them.
Yuxin Chen
University of Pennsylvania, PA·Mathematics & Statistics
Characterize the fundamental limits on sample and computational complexity of reinforcement learning, meaning how much data and computing an agent needs to learn good decisions in an unknown environment.
Alejandro Ribeiro
University of Pennsylvania, PA·Engineering
Develop optimization and statistical foundations for aligning generative models by exploiting that the problem is strongly concave in distribution space even though it is highly nonconvex in the parameters of deep networks and transformers.
The school
Texas A&M University-College Station: 23 labs on PI Pages, $1.4B a year on research, 768 research doctorates a year.
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