Adaptive step size selection for optimization via the ski rental problem

Optimization has been used extensively throughout signal processing in applications including sensor networks and sparsity based compressive sensing. One of the key challenges when implementing iterative optimization algorithms is to choose an appropriate step size for fast algorithms. We pose the problem of choosing step sizes as solving a ski rental problem, a popular class of problems from the computer science literature. This results in a novel algorithm for adaptive step size selection that is agnostic to the choice of the optimization algorithm. Our numerical results show the advantages of using adaptivity for step size selection.