Understanding the Cost of Fitness Evaluation for Subset Selection: Markov Chain Analysis of Stochastic Local Search

With a focus on both the fitness and cost of subset selection, we study stochastic local search (SLS) heuristics in this paper. In particular, we consider subset selection problems where the cost of fitness function evaluation needs to be accounted for. Here, cost can be fitness evaluation's computation time or energy cost. We propose and study an SLS method, SLS4CFF, tailored to such problems. SLS4CFF ("SLS for costly fitness functions") is an amalgamation of several existing heuristics. We develop a homogeneous Markov chain model that explicitly represents both fitness and cost of subset selection with SLS4CFF. This Markov chain, which can be lumped or compressed for certain fitness and cost functions, enables us to better understand and analyze hyperparameter optimization in a principled manner, via expected hitting times. Studies with synthetic and real-world problems improve the understanding of SLS and demonstrate the importance of cost-awareness.