  This paper proposes a new robust update rule of target network for deep
reinforcement learning (DRL), to replace the conventional update rule, given as
an exponential moving average. The target network is for smoothly generating
the reference signals for a main network in DRL, thereby reducing learning
variance. The problem with its conventional update rule is the fact that all
the parameters are smoothly copied with the same speed from the main network,
even when some of them are trying to update toward the wrong directions. This
behavior increases the risk of generating the wrong reference signals. Although
slowing down the overall update speed is a naive way to mitigate wrong updates,
it would decrease learning speed. To robustly update the parameters while
keeping learning speed, a t-soft update method, which is inspired by student-t
distribution, is derived with reference to the analogy between the exponential
moving average and the normal distribution. Through the analysis of the derived
t-soft update, we show that it takes over the properties of the student-t
distribution. Specifically, with a heavy-tailed property of the student-t
distribution, the t-soft update automatically excludes extreme updates that
differ from past experiences. In addition, when the updates are similar to the
past experiences, it can mitigate the learning delay by increasing the amount
of updates. In PyBullet robotics simulations for DRL, an online actor-critic
algorithm with the t-soft update outperformed the conventional methods in terms
of the obtained return and/or its variance. From the training process by the
t-soft update, we found that the t-soft update is globally consistent with the
standard soft update, and the update rates are locally adjusted for
acceleration or suppression.
