Scaling of Probability-Based Optimization Algorithms

Population-based Incremental Learning is shown require very sensitive scalingof its learning rate. The learning rate must scale with the system size in a problem-dependent way. This is shown in two problems: the needle-in-a haystack, in which the learning rate must vanish exponentially in the system size, and in a smooth function in which the learning rate must vanish like the square root of the system size. Two methods are proposed for removing this sensitivity. Alearning dynamics which obeys detailed balance is shown to give consistent performance over the entire range of learning rates. An analog of mutation is shown to require a learning rate which scales as the inverse system size, but is problem independent.