# Deep Learning the Efficient Frontier of Convex Vector Optimization Problems

arXiv: https://arxiv.org/abs/2205.07077 · HTML: https://mlsanity.com/paper/2205.07077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2022.

## Built on by (most cited first, 2 of 2)

- [Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms](https://mlsanity.com/paper/2302.10183/) (2023)
- [Learning the Efficient Frontier](https://mlsanity.com/paper/2309.15775/) (2023)

## Abstract (arXiv)

In this paper, we design a neural network architecture to approximate the weakly efficient frontier of convex vector optimization problems (CVOP) satisfying Slater's condition. The proposed machine learning methodology provides both an inner and outer approximation of the weakly efficient frontier, as well as an upper bound to the error at each approximated efficient point. In numerical case studies we demonstrate that the proposed algorithm is effectively able to approximate the true weakly efficient frontier of CVOPs. This remains true even for large problems (i.e., many objectives, variables, and constraints) and thus overcoming the curse of dimensionality.