Summary of Generalization Bounds Of Surrogate Policies For Combinatorial Optimization Problems, by Pierre-cyril Aubin-frankowski and Yohann De Castro and Axel Parmentier and Alessandro Rudi
Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems
by Pierre-Cyril Aubin-Frankowski, Yohann De Castro, Axel Parmentier, Alessandro Rudi
First submitted to arxiv on: 24 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC); Methodology (stat.ME)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates methods to improve learning of structured learning approaches for combinatorial optimization problems with complex objectives in operations research. The approach trains policies that chain a statistical model with a surrogate combinatorial optimization oracle to map any instance of the problem to a feasible solution. To address challenges in risk minimization, the authors propose smoothing the risk by perturbing the policy, which eases optimization and improves generalization. They derive a generalization bound that controls the perturbation bias, statistical learning error, and optimization error. The analysis relies on a uniform weak property that captures the interplay between the statistical model and surrogate combinatorial optimization oracle. This property holds under mild assumptions on the statistical model, surrogate optimization, and instance data distribution. The authors demonstrate their results on applications such as stochastic vehicle scheduling. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps machines learn better for complex problems in operations research. It trains special policies that work well with complex objectives. To make it easier to learn, the approach smooths out the risks by changing the policy a little bit. This makes optimization easier and improves results. The authors show how their method works and provide a guarantee that it will generalize well to new situations. They also test their method on real-world problems like scheduling vehicles. |
Keywords
» Artificial intelligence » Generalization » Optimization » Statistical model
