# An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making

arXiv: https://arxiv.org/abs/2311.06972 · HTML: https://mlsanity.com/paper/2311.06972/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 77 references that are in the map.
- First posted on arXiv 12 Nov 2023.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Attention-Based Models for Speech Recognition](https://mlsanity.com/paper/1506.07503/) (2015)
- [Recurrent Models of Visual Attention](https://mlsanity.com/paper/1406.6247/) (2014)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [Neural Machine Translation: A Review and Survey](https://mlsanity.com/paper/1912.02047/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Online Mixed-Integer Optimization in Milliseconds](https://mlsanity.com/paper/1907.02206/) (2019)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [Dynamic Knapsack Optimization Towards Efficient Multi-Channel Sequential Advertising](https://mlsanity.com/paper/2006.16312/) (2020)
- [Guidelines for the Computational Testing of Machine Learning approaches to Vehicle Routing Problems](https://mlsanity.com/paper/2109.13983/) (2021)
- [Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information](https://mlsanity.com/paper/1807.11876/) (2018)
- [Facility Location in Evolving Metrics](https://mlsanity.com/paper/1403.6758/) (2014)
- [Learning Optimal Solutions via an LSTM-Optimization Framework](https://mlsanity.com/paper/2207.02937/) (2022)
- [A language processing algorithm for predicting tactical solutions to an operational planning problem under uncertainty](https://mlsanity.com/paper/1910.08216/) (2019)
- [Generative deep learning for decision making in gas networks](https://mlsanity.com/paper/2102.02125/) (2021)
- [Multistage Knapsack](https://mlsanity.com/paper/1901.11260/) (2019)
- [LP-based algorithms for multistage minimization problems](https://mlsanity.com/paper/1909.10354/) (2019)

## Built on by (most cited first, 4 of 4)

- [Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling](https://mlsanity.com/paper/2510.24013/) (2025)
- [Toward TransfORmers: Revolutionizing the Solution of Mixed Integer Programs with Transformers](https://mlsanity.com/paper/2402.13380/) (2024)
- [Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers](https://mlsanity.com/paper/2604.11507/) (2026)
- [Learning to Optimize at Scale: A Benders Decomposition-TransfORmers Framework for Stochastic Combinatorial Optimization](https://mlsanity.com/paper/2607.22550/) (2026)

## Abstract (arXiv)

We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of sequential dependence, infeasibility, and generalization in machine learning (ML) to make predictions for optimal solutions to combinatorial problems. The sequential nature of the combinatorial optimization problems considered is captured with recurrent neural networks and a sliding-attention window. We integrate an attention-based encoder-decoder neural network architecture with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions to time-dependent optimization problems. In this framework, the required level of predictions is optimized to eliminate the infeasibility of the ML predictions. These predictions are then fixed in mixed-integer programming (MIP) problems to solve them quickly with the aid of a commercial solver. We demonstrate our approach to tackling the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and multi-dimensional knapsack (MSMK). Our results show that models trained on shorter and smaller-dimensional instances can be successfully used to predict longer and larger-dimensional problems. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. We compare PredOpt with various specially designed heuristics and show that our framework outperforms them. PredOpt can be advantageous for solving dynamic MIP problems that need to be solved instantly and repetitively.