Abstract
In this work, we develop an implicit gradient-type (IG-AL) algorithm for bilevel optimization with strongly convex linear inequality constrained lower-level problems. Many learning problems of interest, including problems in distributed optimization, machine learning, economics, and transport research are captured by the above formulation. The key characteristics of the proposed algorithm are: (i) the use of a primal-dual augmented Lagrangian method for solving the lower-level problem, and (ii) construction of an implicit gradient (derived using the KKT conditions of the lower-level problem) for solving the upper-level problem. Importantly, the proposed algorithm avoids the (expensive) projection step to a half-space inherent to gradient descent-based alternatives. The performance of the proposed algorithm is evaluated on a set of numerical experiments.
| Original language | English (US) |
|---|---|
| Title of host publication | 2022 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 5438-5442 |
| Number of pages | 5 |
| ISBN (Electronic) | 9781665405409 |
| DOIs | |
| State | Published - 2022 |
| Event | 47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 - Virtual, Online, Singapore Duration: May 23 2022 → May 27 2022 |
Publication series
| Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
|---|---|
| Volume | 2022-May |
| ISSN (Print) | 1520-6149 |
Conference
| Conference | 47th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2022 |
|---|---|
| Country/Territory | Singapore |
| City | Virtual, Online |
| Period | 5/23/22 → 5/27/22 |
Bibliographical note
Publisher Copyright:© 2022 IEEE
Keywords
- constrained bilevel optimization
- implicit gradient