Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization (1809.05504v2)

Abstract: Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is first trained via a measure of predictive accuracy, and then its predictions are used as input into an optimization algorithm which produces a decision. However, the loss function used to train the model may easily be misaligned with the end goal, which is to make the best decisions possible. Hand-tuning the loss function to align with optimization is a difficult and error-prone process (which is often skipped entirely). We focus on combinatorial optimization problems and introduce a general framework for decision-focused learning, where the machine learning model is directly trained in conjunction with the optimization algorithm to produce high-quality decisions. Technically, our contribution is a means of integrating common classes of discrete optimization problems into deep learning or other predictive models, which are typically trained via gradient descent. The main idea is to use a continuous relaxation of the discrete problem to propagate gradients through the optimization procedure. We instantiate this framework for two broad classes of combinatorial problems: linear programs and submodular maximization. Experimental results across a variety of domains show that decision-focused learning often leads to improved optimization performance compared to traditional methods. We find that standard measures of accuracy are not a reliable proxy for a predictive model's utility in optimization, and our method's ability to specify the true goal as the model's training objective yields substantial dividends across a range of decision problems.

• The paper presents a novel decision-focused learning framework that integrates optimization objectives directly into machine learning training.
• It employs continuous relaxation and gradient-based methods to tackle both linear programming and submodular maximization challenges.
• Experimental results reveal superior decision outcomes in areas like budget allocation and recommendation despite lower standard predictive metrics.

Decision-Focused Learning for Combinatorial Optimization: A Framework for Integrated Data-Decisions Pipelines

In the research paper "Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization" by Bryan Wilder, Bistra Dilkina, and Milind Tambe, the authors address the decoupling often observed in the traditional data-decisions pipeline in AI. The paper proposes a decision-focused learning methodology, which seamlessly integrates machine learning models with combinatorial optimization algorithms. This integration is posited to enhance decision-making quality compared to the conventional two-stage processes that separate prediction from optimization.

The traditional pipeline typically involves training a predictive model using generic accuracy metrics. These metrics are not necessarily aligned with the ultimate objective of optimization – making the best decision possible. This misalignment can lead to suboptimal decisions when the predictive model's errors are managed independently of the decision-making context. By contrast, decision-focused learning adjusts the predictive model's training to prioritize decision quality.

Methodological Contributions

The primary methodological contribution of the paper is a framework designed to integrate combinatorial optimization directly into the training process of machine learning models. The approach involves a continuous relaxation of discrete optimization problems, allowing for gradient descent approaches to be applied. The authors demonstrate this framework's application to two major categories of combinatorial problems: linear programs and submodular maximization problems.

1. Continuous Relaxation: The framework utilizes continuous relaxation techniques, converting discrete optimization problems into a form suitable for gradient-based training. This strategy involves differentiating through the optimization process by considering the continuous relaxation of the combinatorial problem.
2. Application to Linear Programs and Submodular Maximization: For linear programs, a regularization method transforms the problem into a quadratic program, ensuring differentiability. In submodular maximization, projected stochastic gradient ascent is employed to find local optima in the continuous problem space, facilitating backpropagation for neural network training.

Results and Implications

The experimental results provided in the paper highlight the efficacy of the decision-focused learning framework across various domains, including budget allocation, bipartite matching, and diverse recommendation. Notably, decision-focused models frequently outperform traditional two-stage models in decision quality despite potentially having worse predictive accuracy according to conventional metrics like mean squared error and cross-entropy.

The outcomes have significant implications. They suggest that aligning predictive model training objectives with optimization goals can yield superior decision outcomes. This alignment encourages models to focus on aspects of predictions that directly impact decision quality, even at the expense of generic accuracy.

Future Directions

The framework opens several avenues for further research. Future work could explore extending this methodology to other classes of combinatorial problems and deploying it in real-world settings where the decision-making impact is critical, such as logistics, resource allocation, and recommendation systems. Additionally, investigating the trade-offs between model complexity and the alignment of training objectives with decision tasks would provide deeper insights into optimizing both predictive accuracy and decision quality.

Overall, this paper contributes to a more cohesive and purpose-driven approach to AI system design, ensuring that each component in the pipeline is tuned for optimal decision end results. It sets a foundation for future explorations in AI where the decision quality is prioritized through a unified and integrated data-decisions learning pipeline.