# Learning the Efficient Frontier

arXiv: https://arxiv.org/abs/2309.15775 · HTML: https://mlsanity.com/paper/2309.15775/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 47 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Quantifying the Carbon Emissions of Machine Learning](https://mlsanity.com/paper/1910.09700/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Axial Attention in Multidimensional Transformers](https://mlsanity.com/paper/1912.12180/) (2019)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer](https://mlsanity.com/paper/2110.02544/) (2021)
- [A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level](https://mlsanity.com/paper/2112.15594/) (2021)
- [GPU Acceleration of ADMM for Large-Scale Quadratic Programming](https://mlsanity.com/paper/1912.04263/) (2019)
- [Learning Convex Optimization Models](https://mlsanity.com/paper/2006.04248/) (2020)
- [Deep Learning the Efficient Frontier of Convex Vector Optimization Problems](https://mlsanity.com/paper/2205.07077/) (2022)
- [Two-Dimensional Batch Linear Programming on the GPU](https://mlsanity.com/paper/1902.04995/) (2019)
- [Exploiting GPU/SIMD Architectures for Solving Linear-Quadratic MPC Problems](https://mlsanity.com/paper/2209.13049/) (2022)

## Built on by (most cited first, 1 of 1)

- [GeMA: Learning Latent Manifold Frontiers for Benchmarking Complex Systems](https://mlsanity.com/paper/2603.16729/) (2026)

## Abstract (arXiv)

The efficient frontier (EF) is a fundamental resource allocation problem where one has to find an optimal portfolio maximizing a reward at a given level of risk. This optimal solution is traditionally found by solving a convex optimization problem. In this paper, we introduce NeuralEF: a fast neural approximation framework that robustly forecasts the result of the EF convex optimization problem with respect to heterogeneous linear constraints and variable number of optimization inputs. By reformulating an optimization problem as a sequence to sequence problem, we show that NeuralEF is a viable solution to accelerate large-scale simulation while handling discontinuous behavior.