On the impact of the cutoff time on the performance of algorithm configurators

Algorithm conigurators are automated methods to optimise the parameters of an algorithm for a class of problems. We evaluate the performance of a simple random local search conigurator (Param- RLS) for tuning the neighbourhood size k of the RLS k algorithm. We measure performance as the expected number of coniguration evaluations required to identify the optimal value for the parameter. We analyse the impact of the cutof time κ (the time spent evaluat- ing a coniguration for a problem instance) on the expected number of coniguration evaluations required to ind the optimal parameter value, where we compare conigurations using either best found itness values (ParamRLS-F) or optimisation times (ParamRLS-T). We consider tuning RLS k for a variant of the Ridge function class ( Ridge* ), where the performance of each parameter value does not change during the run, and for the OneMax function class, where longer runs favour smaller k . We rigorously prove that ParamRLS- F eiciently tunes RLS k for Ridge* for any κ while ParamRLS-T requires at least quadratic κ . For OneMax ParamRLS-F identiies k = 1 as optimal with linear κ while ParamRLS-T requires a κ of at least Ω ( n log n ) . For smaller κ ParamRLS-F identiies that k > 1 performs better while ParamRLS-T returns k chosen uniformly at random.