End to end learning and optimization on graphs (1905.13732v3)

Abstract: Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes are often only partially observed, introducing learning problems such as link prediction which must be solved prior to optimization. Standard approaches treat learning and optimization entirely separately, while recent machine learning work aims to predict the optimal solution directly from the inputs. Here, we propose an alternative decision-focused learning approach that integrates a differentiable proxy for common graph optimization problems as a layer in learned systems. The main idea is to learn a representation that maps the original optimization problem onto a simpler proxy problem that can be efficiently differentiated through. Experimental results show that our ClusterNet system outperforms both pure end-to-end approaches (that directly predict the optimal solution) and standard approaches that entirely separate learning and optimization. Code for our system is available at https://github.com/bwilder0/clusternet.

• The paper presents ClusterNet, which integrates learning and optimization by embedding a differentiable k-means clustering layer into the graph decision-making process.
• It demonstrates superior performance over traditional two-stage and pure end-to-end methods on tasks like community detection and facility location across multiple datasets.
• The approach minimizes data requirements and offers a scalable blueprint for embedding optimization within machine learning systems for complex graph challenges.

Decision-Focused Learning for Graph Optimization

The research paper "End to End Learning and Optimization on Graphs" by Wilder et al. presents an innovative approach to addressing the combined challenges of learning and optimization in graph-based problems. Traditional approaches have often treated learning and optimization as distinct tasks, leading to suboptimal solutions when graphs or their attributes are only partially observed. This study aims to integrate these processes by proposing a decision-focused learning framework, specifically through a system dubbed ClusterNet.

Synthesis of Learning and Optimization

The paper highlights the limitations of two-stage approaches that separate the learning and optimization processes, as well as the shortcomings of end-to-end methods that predict optimal solutions without engaging with the intricacies of the optimization tasks. Contrary to these existing strategies, ClusterNet introduces a novel differentiable proxy for typical graph optimization problems, leveraging a differentiable $k$-means clustering system as an interpretable layer within the learning framework.

Methodology

ClusterNet distinguishes itself by embedding algorithmic structures into the learning framework. It avoids the need for vast amounts of training data, which would be required for pure end-to-end learning approaches to discover algorithmic structure from scratch. Instead, ClusterNet reduces a complex optimization problem to a simpler one (i.e., $k$-means clustering) and leverages the learned representation of the data to map this simpler problem back to the original optimization problem.

The proposed system is instantiated for problems requiring either partitioning of graphs or selection of node subsets. The differentiation through the clustering method allows integrating optimization in a decision-centric learning process, where the primary loss function is derived from the performance of the optimization outcome, rather than merely predictive accuracy.

Empirical Validation

The paper provides an extensive empirical evaluation across two main graph optimization problems: community detection and facility location. Experimental results demonstrate that ClusterNet outperforms both two-stage methods and pure end-to-end methods on a range of datasets including Cora, Citeseer, Protein, Adolescent Health, and Facebook networks. A crucial insight is that ClusterNet not only attains higher solution quality in the presence of partially observed graphs but also contends with expert-designed optimization algorithms when complete information is available.

For community detection, ClusterNet’s achieved modularity surpasses conventional approaches, showcasing its capability in network clustering tasks. In facility location optimization, it proves efficient in minimizing the maximum distance from any node to a selected facility, surpassing standard approximation algorithms. These results affirm that the model does not merely predict edges but effectively learns to produce meaningful decision-oriented solutions that generalize across different instances.

Future Directions

The study opens potential pathways for extending decision-focused learning to other complex graph-based and combinatorial optimization tasks, potentially influencing the design of AI systems that require intricate decision-making capabilities. The framework's adaptability suggests utility for a range of applications such as supply chain optimization, resource allocation, and network resilience planning.

Conclusion

ClusterNet represents a significant step forward in integrating the strengths of both learning and optimization in graph problems. By demonstrating that a decision-focused learning approach can yield superior results, the paper makes a compelling case for embedding optimization solvers as layers in machine learning systems, thereby offering a blueprint for future developments in AI-based graph optimization tasks. Such integration not only enhances performance but also fosters more efficient and flexible systems capable of addressing real-world decision-making challenges grounded in complex data environments.