Practical and Provably Optimal Methods for Large-Scale Convex-Composite Optimization
Abstract
This research aims to develop new algorithms and fundamental theory for a broad and increasingly common family of convex-composite optimization problems. These problems balance the optimization of many component objectives being weighed with sophisticated nonlinear tradeoffs. The overall computational optimization model captures a wide range of applications relevant to problems confronting the U.S. Air Force and Space Force. As a sample of the applications addressed by this proposal’s methodology, (i) in modern image recognition-processing, performance on each batch of training images is used as one component of measuring overall performance, (ii) in adversarial-robust optimization, one seeks resiliency via a strategy that performs well across a suite of diverse possible scenarios which must all be weighed, (iii) limits on resource allotment produce constrained optimization problems balancing feasibility against objective performance, and (iv) in multiobjective optimization, tasks often arise from balancing an operation’s expected effectiveness with its variance and other risk measures whose tradeoffs follow diminishing returns. Such problems are particularly challenging for existing methods when objectives are nonsmooth and-or nonconvex and when the number of distinct objective components grows to modern scales. The proposed new optimization methods will overcome these limitations by extending the reach of successful stochastic optimization techniques (variance-reduction) to encompass these hard, often nonsmooth, composite optimization problems. Practical concerns of adapting to problem data (without manual tuning) and allowing heterogeneous objective components and foundational concerns on the optimality of the proposed methods will be addressed. Recent advances in computer-aided design will be used to optimize resulting methods.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310531
Entities
People
- Benjamin Grimmer
Organizations
- Air Force Office of Scientific Research
- Johns Hopkins University
- United States Air Force