mlsanityData to 7 Oct 2026

Universal Representation of Generalized Convex Functions and their Gradients

arXiv 2509.04477 ↗First posted 30 Aug 2025math.OC cs.LGcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 32 of its 61 references that are in the map. First posted on arXiv 30 Aug 2025.

Builds on

32 of 61 references.

References · 32

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  3. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  4. 2019Differentiable Convex Optimization Layerscited by 458
  5. 2016Input Convex Neural Networkscited by 407
  6. 2019Optimal transport mapping via input convex neural networkscited by 202
  7. 2018Differentiable MPC for End-to-end Planning and Controlcited by 178
  8. 2020Deep Network Approximation for Smooth Functionscited by 163
  9. 2018Universal approximations of invariant maps by neural networkscited by 127
  10. 2022Neural Optimal Transportcited by 123
  11. 2016Why Deep Neural Networks for Function Approximation?cited by 82
  12. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 82
20 more
  1. 2021Generative Modeling with Optimal Transport Mapscited by 80
  2. 2019Deep Declarative Networks: A New Hopecited by 77
  3. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
  4. 2020Scalable Computations of Wasserstein Barycenter via Input Convex Neural Networkscited by 49
  5. 2018Automated Mechanism Design via Neural Networkscited by 31
  6. 2022Kernel Neural Optimal Transportcited by 31
  7. 2020Auction learning as a two-player gamecited by 29
  8. 2022Optimal-er Auctions through Attentioncited by 26
  9. 2023A Scalable Neural Network for DSIC Affine Maximizer Auction Designcited by 23
  10. 2022Differentiable Economics for Randomized Affine Maximizer Auctionscited by 21
  11. 2019On approximating nabla f with neural networkscited by 18
  12. 2021Input Convex Gradient Networkscited by 17
  13. 2021Learning Revenue-Maximizing Auctions With Differentiable Matchingcited by 14
  14. 2014Duality and Optimality of Auctions for Uniform Distributionscited by 12
  15. 2017Reinforcement Mechanism Design, with Applications to Dynamic Pricing in Sponsored Search Auctionscited by 11
  16. 2024JacNet: Learning Functions with Structured Jacobianscited by 7
  17. 2022The GroupMax neural network approximation of convex functionscited by 5
  18. 2019Adversarial learning for revenue-maximizing auctionscited by 4
  19. 2022Parameterized Convex Universal Approximators for Decision-Making Problemscited by 4
  20. 2021Generalized permutahedra and optimal auctionscited by 1

Built on by

Not cited yet.