Abstract:A wide range of optimization problems can often be written in terms of generalized convex functions (GCFs). When this structure is present, it can convert certain nested bilevel objectives into single-level problems amenable to standard first-order optimization methods. We provide a new differentiable layer with a convex parameter space and show (Theorems 5.1 and 5.2) that it and its gradient are universal approximators for GCFs and their gradients. We demonstrate how this parameterization can be leveraged in practice by (i) learning optimal transport maps with general cost functions and (ii) learning optimal auctions of multiple goods. In both these cases, we show how our layer can be used to convert the existing bilevel or min-max formulations into single-level problems that can be solved efficiently with first-order methods.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG) |
| MSC classes: | 91-08, 91-10, 91B68, 62P20, 90C26, 90C30, 65D40, 65K10, 49J52, 41A30 |
| ACM classes: | G.1.2; G.1.6; G.1.10; I.5.1 |
| Cite as: | arXiv:2509.04477 [math.OC] |
| (or arXiv:2509.04477v3 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2509.04477 arXiv-issued DOI via DataCite |
From: Moeen Nehzati [view email]
[v1]
Sat, 30 Aug 2025 15:21:33 UTC (182 KB)
[v2]
Mon, 8 Dec 2025 23:54:44 UTC (2,811 KB)
[v3]
Tue, 12 May 2026 18:14:58 UTC (2,717 KB)
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