  We propose a novel approach to allocating resources for expensive simulations
of high fidelity models when used in a multifidelity framework. Allocation
decisions that distribute computational resources across several simulation
models become extremely important in situations where only a small number of
expensive high fidelity simulations can be run. We identify this allocation
decision as a problem in optimal subset selection, and subsequently regularize
this problem so that solutions can be computed. Our regularized formulation
yields a type of group lasso problem that has been studied in the literature to
accomplish subset selection. Our numerical results compare performance of
algorithms that solve the group lasso problem for algorithmic allocation
against a variety of other strategies, including those based on classical
linear algebraic pivoting routines and those derived from more modern machine
learning-based methods. We demonstrate on well known synthetic problems and
more difficult real-world simulations that this group lasso solution to the
relaxed optimal subset selection problem performs better than the alternatives.
