Dynamic pricing is a real-time machine learning problem with scarce prior data and a concrete learning cost. While the Kalman Filter can be employed to track hidden demand parameters and extensions to it can facilitate exploration for faster learning, the exploratory nature of Particle Swarm Optimization makes it a natural choice for the dynamic pricing problem. We compare both the Kalman Filter and existing particle swarm adaptations for dynamic and/or noisy environments with a novel approach that time-decays each particle's previous best value; this new strategy provides more graceful and effective transitions between exploitation and exploration, a necessity in the dynamic and noisy environments inherent to the dynamic pricing problem.
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