Population-based learning techniques have been proven to be effective in dealing with noise in numerical benchmark functions and are thus promising tools for the high-dimensional optimization of controllers for multiple robots with limited sensing capabilities, which have inherently noisy performance evaluations. In this article, we apply a statistical technique called Optimal Computing Budget Allocation to improve the performance of Particle Swarm Optimization in the presence of noise for a multi-robot obstacle avoidance benchmark task. We present a new distributed PSO OCBA algorithm suitable for resource-constrained mobile robots due to its low requirements in terms of memory and limited local communication. Our results from simulation show that PSO OCBA outperforms other techniques for dealing with noise, achieving a more consistent progress and a better estimate of the ground-truth performance of candidate solutions. We then validate our simulations with real robot experiments where we compare the controller learned with our proposed algorithm to a potential field controller for obstacle avoidance in a cluttered environment. We show that they both achieve a high performance through different avoidance behaviors.