  The deadly triad refers to the instability of a reinforcement learning
algorithm when it employs off-policy learning, function approximation, and
bootstrapping simultaneously. In this paper, we investigate the target network
as a tool for breaking the deadly triad, providing theoretical support for the
conventional wisdom that a target network stabilizes training. We first propose
and analyze a novel target network update rule which augments the commonly used
Polyak-averaging style update with two projections. We then apply the target
network and ridge regularization in several divergent algorithms and show their
convergence to regularized TD fixed points. Those algorithms are off-policy
with linear function approximation and bootstrapping, spanning both policy
evaluation and control, as well as both discounted and average-reward settings.
In particular, we provide the first convergent linear $Q$-learning algorithms
under nonrestrictive and changing behavior policies without bi-level
optimization.
