  We focus on parameterized policy search for reinforcement learning over
continuous action spaces. Typically, one assumes the score function associated
with a policy is bounded, which fails to hold even for Gaussian policies. To
properly address this issue, one must introduce an exploration tolerance
parameter to quantify the region in which it is bounded. Doing so incurs a
persistent bias that appears in the attenuation rate of the expected policy
gradient norm, which is inversely proportional to the radius of the action
space. To mitigate this hidden bias, heavy-tailed policy parameterizations may
be used, which exhibit a bounded score function, but doing so can cause
instability in algorithmic updates. To address these issues, in this work, we
study the convergence of policy gradient algorithms under heavy-tailed
parameterizations, which we propose to stabilize with a combination of mirror
ascent-type updates and gradient tracking. Our main theoretical contribution is
the establishment that this scheme converges with constant step and batch
sizes, whereas prior works require these parameters to respectively shrink to
null or grow to infinity. Experimentally, this scheme under a heavy-tailed
policy parameterization yields improved reward accumulation across a variety of
settings as compared with standard benchmarks.
