# Generalization in portfolio-based algorithm selection

arXiv: https://arxiv.org/abs/2012.13315 · HTML: https://mlsanity.com/paper/2012.13315/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [Algorithms with Prediction Portfolios](https://mlsanity.com/paper/2210.12438/) (2022)
- [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023)
- [Binary Search with Distributional Predictions](https://mlsanity.com/paper/2411.16030/) (2024)
- [Learning-Augmented Algorithms with Explicit Predictors](https://mlsanity.com/paper/2403.07413/) (2024)
- [LLMs for Cold-Start Cutting Plane Separator Configuration](https://mlsanity.com/paper/2412.12038/) (2024)
- [Sample Complexity of Algorithm Selection Using Neural Networks and Its Applications to Branch-and-Cut](https://mlsanity.com/paper/2402.02328/) (2024)
- [Generalization Guarantees for Learning Branch-and-Cut Policies in Integer Programming](https://mlsanity.com/paper/2505.11636/) (2025)

## Abstract (arXiv)

Portfolio-based algorithm selection has seen tremendous practical success over the past two decades. This algorithm configuration procedure works by first selecting a portfolio of diverse algorithm parameter settings, and then, on a given problem instance, using an algorithm selector to choose a parameter setting from the portfolio with strong predicted performance. Oftentimes, both the portfolio and the algorithm selector are chosen using a training set of typical problem instances from the application domain at hand. In this paper, we provide the first provable guarantees for portfolio-based algorithm selection. We analyze how large the training set should be to ensure that the resulting algorithm selector's average performance over the training set is close to its future (expected) performance. This involves analyzing three key reasons why these two quantities may diverge: 1) the learning-theoretic complexity of the algorithm selector, 2) the size of the portfolio, and 3) the learning-theoretic complexity of the algorithm's performance as a function of its parameters. We introduce an end-to-end learning-theoretic analysis of the portfolio construction and algorithm selection together. We prove that if the portfolio is large, overfitting is inevitable, even with an extremely simple algorithm selector. With experiments, we illustrate a tradeoff exposed by our theoretical analysis: as we increase the portfolio size, we can hope to include a well-suited parameter setting for every possible problem instance, but it becomes impossible to avoid overfitting.