PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming (2206.14234v2)

Abstract: In deterministic optimization, it is typically assumed that all problem parameters are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from historical data. A typical predict-then-optimize approach separates predictions and optimization into two stages. Recently, end-to-end predict-then-optimize has become an attractive alternative. In this work, we present the PyEPO package, a PyTorchbased end-to-end predict-then-optimize library in Python. To the best of our knowledge, PyEPO (pronounced like pineapple with a silent "n") is the first such generic tool for linear and integer programming with predicted objective function coefficients. It provides four base algorithms: a convex surrogate loss function from the seminal work of Elmachtoub and Grigas [16], a differentiable black-box solver approach of Pogancic et al. [35], and two differentiable perturbation-based methods from Berthet et al. [6]. PyEPO provides a simple interface for the definition of new optimization problems, the implementation of state-of-the-art predict-then-optimize training algorithms, the use of custom neural network architectures, and the comparison of end-to-end approaches with the two-stage approach. PyEPO enables us to conduct a comprehensive set of experiments comparing a number of end-to-end and two-stage approaches along axes such as prediction accuracy, decision quality, and running time on problems such as Shortest Path, Multiple Knapsack, and the Traveling Salesperson Problem. We discuss some empirical insights from these experiments, which could guide future research. PyEPO and its documentation are available at https://github.com/khalil-research/PyEPO.

• The paper introduces PyEPO, a library that integrates predictive modeling with optimization using end-to-end PyTorch training.
• It employs methods like SPO+ loss, differentiable solvers, and linear relaxations to enhance decision quality over traditional two-stage models.
• Empirical results demonstrate superior performance in problems such as shortest path, knapsack, and TSP, leveraging parallel processing for efficiency.

Analysis of PyEPO: A PyTorch-based Predict-then-Optimize Library

The paper introduces PyEPO, a Python library developed to facilitate end-to-end predict-then-optimize processes using PyTorch. This library addresses the need for tools to integrate predictive modeling with optimization, particularly in contexts where linear and integer programming are employed.

Key Contributions

PyEPO aims to solve the challenge of integrating prediction with optimization by providing a seamless PyTorch-based interface. This tool supports several central algorithms: the Smart Predict-then-Optimize (SPO+) loss, differentiable black-box solver, and differentiable perturbation-based methods. These cater to scenarios involving predicted objective function coefficients in linear and integer programming problems. The library offers a platform for integrating state-of-the-art predict-then-optimize training algorithms with custom neural network architectures. It allows users to define optimization problems easily and employs parallel computing to enhance training efficiency.

One of PyEPO's significant features is its compatibility with popular optimization and machine learning frameworks, such as GurobiPy and Pyomo, and its ability to build models that can be easily customized to fit different constraints and costs. The library also emphasizes improving computational efficiency, offering options to use linear relaxation in problems that naturally involve integer programming.

Empirical Insights

The paper provides empirical benchmarks across several datasets and optimization problems, including the Shortest Path, Multi-Dimensional Knapsack, and Traveling Salesperson Problems. The experiments reveal that end-to-end models often outperform traditional two-stage models in terms of decision quality. The library's ability to handle images as input is demonstrated using the Warcraft terrain dataset, showcasing PyEPO's versatility when applied to problems with rich contextual features.

PyEPO also allows experimenting with model relaxations, such as using linear relaxation instead of integer programming to speed up training, and prediction regularizations to balance the trade-off between prediction accuracy and decision quality. This flexibility underscores PyEPO's potential as a research tool, facilitating future explorations in predict-then-optimize methodologies.

Theoretical and Practical Implications

The introduction of PyEPO has theoretical implications for the field of data-driven optimization, providing a practical tool that bridges the divide between predictive modeling and optimization. Practically, its implementation in PyTorch positions PyEPO as a resource for leveraging deep learning architectures to tackle complex optimization problems effectively.

The discussion on empirical results further fuels potential innovations, suggesting that the end-to-end predict-then-optimize framework could revolutionize how cost predictions and decision-making are integrated. The tool’s use of parallel processing further enhances its applicability to large-scale problem-solving, a practical necessity in real-world applications.

Future Directions

The future trajectory for PyEPO involves its expansion to accommodate mixed-integer and non-linear constraints and the inclusion of warm starting techniques and other improvements. There's also potential for integrating additional training methods and developing newer variations based on PyEPO’s existing framework.

Final Thoughts

PyEPO represents a significant stride in the predict-then-optimize landscape, offering a robust and flexible solution for integrating predictive modeling with optimization processes in linear and integer programming contexts. Its practical implications align well with current trends in artificial intelligence and optimization, highlighting the need for tools that can effectively handle complex decision-making tasks in uncertain environments.