Extensions of regret-minimization algorithm for optimal design

We explore extensions and applications of the regret minimization framework introduced by~\cite{design} for solving optimal experimental design problems. Specifically, we incorporate the entropy regularizer into this framework, leading to a novel sample selection objective and a provable sample complexity bound that guarantees a $(1+\epsilon)$-near optimal solution. We further extend the method to handle regularized optimal design settings. As an application, we use our algorithm to select a small set of representative samples from image classification datasets without relying on label information. To evaluate the quality of the selected samples, we train a logistic regression model and compare performance against several baseline sampling strategies. Experimental results on MNIST, CIFAR-10, and a 50-class subset of ImageNet show that our approach consistently outperforms competing methods in most cases.