  Several applications of Reinforcement Learning suffer from instability due to
high variance. This is especially prevalent in high dimensional domains.
Regularization is a commonly used technique in machine learning to reduce
variance, at the cost of introducing some bias. Most existing regularization
techniques focus on spatial (perceptual) regularization. Yet in reinforcement
learning, due to the nature of the Bellman equation, there is an opportunity to
also exploit temporal regularization based on smoothness in value estimates
over trajectories. This paper explores a class of methods for temporal
regularization. We formally characterize the bias induced by this technique
using Markov chain concepts. We illustrate the various characteristics of
temporal regularization via a sequence of simple discrete and continuous MDPs,
and show that the technique provides improvement even in high-dimensional Atari
games.
