Generalization in Portfolio-Based Algorithm Selection
Year: 2021
Type: conference-paper
Abstract: 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.
Institution: Carnegie Mellon University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Awards: AitF: FULL: From Worst-Case to Realistic-Case Analysis for Large Scale Machine Learning Algorithms, Attitude towards information in multi-agent settings: Understanding and mitigating Avoidance and Over-Evaluation, RI: AF: Small: Collaborative Research: Differentially Private Learning: From Theory To Applications, AF: Small: Learning Theory for a Modern World: Transfer Learning, Unsupervised Learning, and Beyond Prediction, AitF: Algorithms and Mechanisms for Kidney Exchange, RI: Medium: Learning to Search: Provable Guarantees and Applications, RI: Small: New Computational Techniques and Market Designs for Kidney Exchanges and Other Barter Markets, G6869609206, RI: Small: Computational Techniques for Large Multi-Step Incomplete-Information Games, G8601312861
OpenAlex ID: W3114917398