A theoretical comparison of batch-mode, on-line, cyclic, and almost-cyclic learning

We study and compare different neural network learning strategies: batch-mode learning, online learning, cyclic learning, and almost-cyclic learning. Incremental learning strategies require less storage capacity than batch-mode learning. However, due to the arbitrariness in the presentation order of the training patterns, incremental learning is a stochastic process; whereas batch-mode learning is deterministic. In zeroth order, i.e., as the learning parameter eta tends to zero, all learning strategies approximate the same ordinary differential equation for convenience referred to as the "ideal behavior". Using stochastic methods valid for small learning parameters eta, we derive differential equations describing the evolution of the lowest-order deviations from this ideal behavior. We compute how the asymptotic misadjustment, measuring the average asymptotic distance from a stable fixed point of the ideal behavior, scales as a function of the learning parameter and the number of training patterns. Knowing the asymptotic misadjustment, we calculate the typical number of learning steps necessary to generate a weight within order epsilon of this fixed point, both with fixed and time-dependent learning parameters. We conclude that almost-cyclic learning (learning with random cycles) is a better alternative for batch-mode learning than cyclic learning (learning with a fixed cycle).