Yuhua Zhu
University of California-Los Angeles, CA·Mathematics & Statistics
Many problems in physics, chemistry and machine learning come down to finding the lowest point of a landscape that has many valleys. These are called nonconvex optimization problems.
- Fields
Mathematics & Statistics
Computer Science
- Topics
nonconvex optimization
global optimization
interacting particle systems
- Grants
- 1 known grant, through Jun 2027
What they work on
- Develop a consensus-based interacting particle method, where many searchers share information to agree on the best point, for nonconvex optimization problems with equality constraints.
- Extend the gradient-free consensus-based particle method to nonconvex optimization restricted to convex sets, and prove convergence for nonconvex and nonsmooth objective functions.
- Apply consensus-based interacting particle optimization to clustered federated learning, where groups of devices train shared machine learning models without pooling their data.
More about the research
Standard methods often get stuck in a nearby valley and miss the true global minimum. This project borrows the idea of collective intelligence, where groups of cells, animals or machines solve tasks better together than alone, to search such landscapes more effectively.
Why it matters
Better ways to find global minima could help with hard optimization problems in physics, chemistry and deep learning. Applied to clustered federated learning, the methods could help groups of devices train machine learning models together while keeping their data separate. Convergence proofs would tell users when these particle methods can be trusted.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Frank Curtis
Lehigh University, PA·Mathematics & Statistics
Revisit the basic properties that gradient sampling methods rely on to guarantee convergence, and strengthen them for nonconvex, nonsmooth, locally Lipschitz problems whose function values are corrupted by computational noise.
Stephen Becker
University of Colorado Boulder, CO·Mathematics & Statistics
Develop gradient-free optimization algorithms for objective functions whose matrix-valued gradients have low intrinsic dimensionality, such as sparsity, low rank, or sparsity-plus-low-rank, to break worst-case efficiency barriers.
Andrei Draganescu
University of Maryland-Baltimore County, MD·Mathematics & Statistics
Develop low-rank gradient flow (LRGF), a first-order optimization method that builds quadratic approximations with low-rank Hessians and computes their gradient flow exactly, ending each step with a Wolfe-condition line search.
The school
University of California-Los Angeles: 84 labs on PI Pages, $1.9B a year on research, 803 research doctorates a year.
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