# Locally Convex Global Loss Network for Decision-Focused Learning

arXiv: https://arxiv.org/abs/2403.01875 · HTML: https://mlsanity.com/paper/2403.01875/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions](https://mlsanity.com/paper/2106.01798/) (2021)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [The Limited Multi-Label Projection Layer](https://mlsanity.com/paper/1906.08707/) (2019)
- [End-to-End Stochastic Optimization with Energy-Based Model](https://mlsanity.com/paper/2211.13837/) (2022)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [TaskMet: Task-Driven Metric Learning for Model Learning](https://mlsanity.com/paper/2312.05250/) (2023)

## Built on by (most cited first, 3 of 3)

- [Return Prediction for Mean-Variance Portfolio Selection: How Decision-Focused Learning Shapes Forecasting Models](https://mlsanity.com/paper/2409.09684/) (2024)
- [Diffusion-DFL: Decision-focused Diffusion Models for Stochastic Optimization](https://mlsanity.com/paper/2510.11590/) (2025)
- [Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study](https://mlsanity.com/paper/2502.17984/) (2025)

## Abstract (arXiv)

In decision-making problems under uncertainty, predicting unknown parameters is often considered independent of the optimization part. Decision-focused learning (DFL) is a task-oriented framework that integrates prediction and optimization by adapting the predictive model to give better decisions for the corresponding task. Here, an inevitable challenge arises when computing the gradients of the optimal decision with respect to the parameters. Existing research copes with this issue by smoothly reforming surrogate optimization or constructing surrogate loss functions that mimic task loss. However, they are applied to restricted optimization domains. In this paper, we propose Locally Convex Global Loss Network (LCGLN), a global surrogate loss model that can be implemented in a general DFL paradigm. LCGLN learns task loss via a partial input convex neural network which is guaranteed to be convex for chosen inputs while keeping the non-convex global structure for the other inputs. This enables LCGLN to admit general DFL through only a single surrogate loss without any sense for choosing appropriate parametric forms. We confirm the effectiveness and flexibility of LCGLN by evaluating our proposed model with three stochastic decision-making problems.