142. Convex Formulations For Training Two-Layer ReLU Neural Networks
Invited abstract in session MD-2: Optimization in machine Learning , stream Nonsmooth and nonconvex optimization.
Monday, 16:30-18:30Room: B100/7011
Authors (first author is the speaker)
| 1. | Karthik Prakhya
|
| Umeå University | |
| 2. | TOLGA BIRDAL
|
| Computing, Imperial College London | |
| 3. | Alp Yurtsever
|
| Umeå University |
Abstract
Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex formulations have been used for verifying neural network robustness, their application to training neural networks remains less explored. In response to this challenge, we reformulate the problem of training infinite-width two-layer ReLU networks as a convex completely positive program in a finite-dimensional (lifted) space. Despite the convexity, solving this problem remains NP-hard due to the complete positivity constraint. To overcome this challenge, we introduce a semidefinite relaxation that can be solved in polynomial time. We then experimentally evaluate the tightness of this relaxation, demonstrating its competitive performance in test accuracy across a range of classification tasks.
Keywords
- Conic and semidefinite optimization
- Optimization for learning and data analysis
- First-order optimization
Status: accepted
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