Data-driven algorithm selection and tuning in optimization and signal processing - De Loera, Jesús A.; Haddock, Jamie; Ma, Anna; Needell, Deanna (Annals of mathematics and artificial intelligence, 2021)
Machine learning algorithms typically rely on optimization subroutines and are well known to provide very effective outcomes for many types of problems. Here, we flip the reliance and ask the reverse question: can machine learning algorithms lead to more effective outcomes for optimization problems? Our goal is to train machine learning methods to automatically improve the performance of optimization and signal processing algorithms. As a proof of concept, we use our approach to improve two popular data processing subroutines in data science: stochastic gradient descent and greedy methods in compressed sensing. We provide experimental results that demonstrate the answer is “yes”, machine learning algorithms do lead to more effective outcomes for optimization problems, and show the future potential for this research direction. In addition to our experimental work, we prove relevant Probably Approximately Correct (PAC) learning theorems for our problems of interest. More precisely, we show that there exists a learning algorithm that, with high probability, will select the algorithm that optimizes the average performance on an input set of problem instances with a given distribution.