Empirical Hardness Models for Algorithm Runtime Prediction
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Solution Overview
Problem
Existing methods for comparing and predicting the performance of algorithms, especially heuristic ones, are time-consuming and lack performance guarantees, as empirical runtimes of identical problem instances can vary significantly, making it difficult to select the best algorithm for a task.
Innovation Solution
The development of empirical hardness models using supervised machine learning to predict algorithm runtime by defining features for problem instances, training models without explicitly running the algorithms, and using these models to estimate performance across various problem instances.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If empirical analysis is used to compare heuristic algorithms, then performance prediction accuracy is improved, but time consumption increases significantly
Solution Approach 1:
The patent applies preliminary action by pre-training machine learning models on historical algorithm performance data before actual runtime prediction is needed. The models are trained offline using supervised learning on datasets containing problem instance features and corresponding algorithm runtimes, so that when runtime prediction is required, the pre-trained model can provide accurate predictions immediately without performing time-consuming empirical analysis at runtime.
2Reliability
If algorithm performance is evaluated through explicit computation and empirical analysis, then reliability of performance guarantees is improved, but device complexity increases
Solution Approach 1:
The patent introduces an intermediary machine learning model that acts as a mediator between problem instance features and algorithm runtime predictions. Instead of directly computing algorithm performance through complex empirical analysis, the feature representation model extracts relevant features from problem instances, and the regression model predicts runtime based on these features, thereby simplifying the overall system while maintaining prediction reliability.
3Measurement precision
If multiple algorithms are explicitly modeled and compared, then selection accuracy is improved, but ease of operation deteriorates
Solution Approach 1:
The patent applies universality by creating a unified machine learning framework that can handle multiple algorithms through a single system. The regression model is trained on data from multiple different heuristic algorithms, allowing it to learn general patterns in algorithm performance. This single multi-functional model can then predict and compare the runtime of different algorithms on new problem instances, eliminating the need for separate analysis procedures for each algorithm and greatly simplifying the algorithm selection process.
Data Source
AI summary
A method and system are provided for modeling the relative performance of algorithms, including quantum algorithms, over a set of problem instances. The model, referred to as a performance estimator, is generated from a selected algorithm and a set a set of problem instances as input, resulting in a generated model. Unlike prior methods, which model the performance of a fixed algorithm on a set of instances, embodiments of the present technology produce a performance estimate without needing to explicitly model the underlying algorithm. The model, once generated by the disclosed technology, may then be utilized to estimate the performance of new algorithms that the model has not been trained on.