Rethinking and Benchmarking Predict-then-Optimize Paradigm for Combinatorial Optimization Problems

Numerous web applications rely on solving combinatorial optimization problems, such as energy cost-aware scheduling, budget allocation on web advertising, and graph matching on social networks. However, many optimization problems involve unknown coefficients, and improper predictions of these factors may lead to inferior decisions which may cause energy wastage, inefficient resource allocation, inappropriate matching in social networks, etc. Such a research topic is referred to as "Predict-Then-Optimize (PTO)" which considers the performance of prediction and decision-making in a unified system. A noteworthy recent development is the end-to-end methods by directly optimizing the ultimate decision quality which claims to yield better results in contrast to the traditional two-stage approach. However, the evaluation benchmarks in this field are fragmented and the effectiveness of various models in different scenarios remains unclear, hindering the comprehensive assessment and fast deployment of these methods. To address these issues, we provide a comprehensive categorization of current approaches and integrate existing experimental scenarios to establish a unified benchmark, elucidating the circumstances under which end-to-end training yields improvements, as well as the contexts in which it performs ineffectively. We also introduce a new dataset for the industrial combinatorial advertising problem for inclusive finance to open-source. We hope the rethinking and benchmarking of PTO could facilitate more convenient evaluation and deployment, and inspire further improvements both in the academy and industry within this field.