  Despite the empirical success of meta reinforcement learning (meta-RL), there
are still a number poorly-understood discrepancies between theory and practice.
Critically, biased gradient estimates are almost always implemented in
practice, whereas prior theory on meta-RL only establishes convergence under
unbiased gradient estimates. In this work, we investigate such a discrepancy.
In particular, (1) We show that unbiased gradient estimates have variance
$\Theta(N)$ which linearly depends on the sample size $N$ of the inner loop
updates; (2) We propose linearized score function (LSF) gradient estimates,
which have bias $\mathcal{O}(1/\sqrt{N})$ and variance $\mathcal{O}(1/N)$; (3)
We show that most empirical prior work in fact implements variants of the LSF
gradient estimates. This implies that practical algorithms "accidentally"
introduce bias to achieve better performance; (4) We establish theoretical
guarantees for the LSF gradient estimates in meta-RL regarding its convergence
to stationary points, showing better dependency on $N$ than prior work when $N$
is large.
