Particle Swarm Optimization (PSO) is an outstanding evolutionary algorithm designed to tackle various optimization problems. However, its performance deteriorates significantly in noisy environments. Some studies have addressed this issue by introducing a resampling method. Most existing methods allocate a fixed and predetermined budget of re-evaluations for every iteration, but cannot change the budget according to different environments adaptively. Our previous work proposed a PSO-LA to integrate PSO with a Learning Automaton (LA) variant. PSO-LA utilizes LA's flexible self-adaption and automatic learning capability to learn the budget allocation for each iteration. This work further improves PSO-LA by the introduction of a subset scheme based LA (subLA) into PSO to further increase the probability of correctly finding the best particle through the pursuit on the a subset of particles with better performance, yielding a new method called LAPSO. LAPSO does not record the historical global best solution but finds it from the subset learned by subLA to jump out of the trapped area that may have a false global best solution. It can also adaptively consume computing budgets for every particle per iteration and, accordingly, total iteration times. Through experiments on 20 large-scale benchmark functions subject to different levels of noise, this work convincingly shows that LAPSO outperforms the existing ones in both accuracy and convergence rate of the optimization problems in noisy environments.