# From Sequential to Recursive: Enhancing Decision-Focused Learning with Bidirectional Feedback

arXiv: https://arxiv.org/abs/2511.08035 · HTML: https://mlsanity.com/paper/2511.08035/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [MIPaaL: Mixed Integer Program as a Layer](https://mlsanity.com/paper/1907.05912/) (2019)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Reviving and Improving Recurrent Back-Propagation](https://mlsanity.com/paper/1803.06396/) (2018)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [End-to-End Learning and Intervention in Games](https://mlsanity.com/paper/2010.13834/) (2020)
- [End-to-end Learning for Fair Ranking Systems](https://mlsanity.com/paper/2111.10723/) (2021)
- [An online learning approach to dynamic pricing for demand response](https://mlsanity.com/paper/1404.1325/) (2014)
- [Equilibrated Recurrent Neural Network: Neuronal Time-Delayed Self-Feedback Improves Accuracy and Stability](https://mlsanity.com/paper/1903.00755/) (2019)

## Abstract (arXiv)

Decision-focused learning (DFL) has emerged as a powerful end-to-end alternative to conventional predict-then-optimize (PTO) pipelines by directly optimizing predictive models through downstream decision losses. Existing DFL frameworks are limited by their strictly sequential structure, referred to as sequential DFL (S-DFL). However, S-DFL fails to capture the bidirectional feedback between prediction and optimization in complex interaction scenarios. In view of this, we first time propose recursive decision-focused learning (R-DFL), a novel framework that introduces bidirectional feedback between downstream optimization and upstream prediction. We further extend two distinct differentiation methods: explicit unrolling via automatic differentiation and implicit differentiation based on fixed-point methods, to facilitate efficient gradient propagation in R-DFL. We rigorously prove that both methods achieve comparable gradient accuracy, with the implicit method offering superior computational efficiency. Extensive experiments on both synthetic and real-world datasets, including the newsvendor problem and the bipartite matching problem, demonstrate that R-DFL not only substantially enhances the final decision quality over sequential baselines but also exhibits robust adaptability across diverse scenarios in closed-loop decision-making problems.