[Paper Review] Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon

Yoshua Bengio, Andrea Lodi+1 more|arXiv (Cornell University)|Nov 14, 2018

Advanced Database Systems and QueriesComputer Science41 citations

TL;DR

A survey outlining how machine learning, especially deep learning, can be used to solve and improve combinatorial optimization problems by learning policies and integrating ML with CO algorithms under a data-distribution view of problem instances.

ABSTRACT

This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art algorithms rely on handcrafted heuristics for making decisions that are otherwise too expensive to compute or mathematically not well defined. Thus, machine learning looks like a natural candidate to make such decisions in a more principled and optimized way. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail a methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.

Motivation & Objective

• Motivate integrating machine learning with combinatorial optimization to automate or augment decision making in CO algorithms.
• Propose a data-driven methodology that treats optimization problems as data points drawn from a distribution.
• Discuss two learning paradigms (imitation and reinforcement learning) for deriving algorithmic policies.
• Highlight how CO structure provides priors and how learning can generalize across problem distributions.

Proposed method

• Describe two orthogonal views: learning policies by imitation of expert decisions and learning policies through experiential reinforcement learning.
• Explain how to represent and process CO problems and algorithm states using machine learning models (e.g., neural networks, GNNs, attention mechanisms).
• Illustrate how to replace or augment heavy CO decisions (e.g., cuts, branching choices) with learned approximations while preserving CO structure as priors.
• Discuss the use of structured data representations (graphs, subproblems) and learned value/policy networks to guide branch-and-bound, cutting planes, and other CO components.
• Address generalization concerns and the importance of distributional assumptions when learning on problem instances.

Experimental results

Research questions

• RQ1 How can ML policies be learned to approximate or replace expensive CO decisions (e.g., branching, cutting planes) within MILP/B&B frameworks?
• RQ2 What are effective learning settings (imitation vs. reinforcement) for deriving decision policies in CO algorithms?
• RQ3 How should problem distributions be defined and used to train ML models so that learned policies generalize to unseen instances?
• RQ4 What ML architectures (e.g., GNNs, attention, deep nets) best handle the structured data typical of CO problems?
• RQ5 What practical challenges arise when integrating ML into CO pipelines, and how can these be addressed?

Key findings

• ML can approximate heavy CO decisions to speed up solving while leveraging CO structure as a prior.
• Two learning paradigms are explored: imitation learning to replicate expert actions and reinforcement learning to discover new policies.
• Graph-based and attention-based neural architectures can process structured CO subproblems and guide decisions such as branching or cutting planes.
• Learning remaining within the CO ecosystem can maintain feasibility and optimality guarantees where appropriate, while improving empirical performance.
• CO problems can be treated as data points from a distribution, enabling learning to tailor algorithms to likely instance types.