  Meta reinforcement learning sets a distribution over a set of tasks on which
the agent can train at will, then is asked to learn an optimal policy for any
test task efficiently. In this paper, we consider a finite set of tasks modeled
through Markov decision processes with various dynamics. We assume to have
endured a long training phase, from which the set of tasks is perfectly
recovered, and we focus on regret minimization against the optimal policy in
the unknown test task. Under a separation condition that states the existence
of a state-action pair revealing a task against another, Chen et al. (2022)
show that $O(M^2 \log(H))$ regret can be achieved, where $M, H$ are the number
of tasks in the set and test episodes, respectively. In our first contribution,
we demonstrate that the latter rate is nearly optimal by developing a novel
lower bound for test-time regret minimization under separation, showing that a
linear dependence with $M$ is unavoidable. Then, we present a family of
stronger yet reasonable assumptions beyond separation, which we call strong
identifiability, enabling algorithms achieving fast rates $\log (H)$ and
sublinear dependence with $M$ simultaneously. Our paper provides a new
understanding of the statistical barriers of test-time regret minimization and
when fast rates can be achieved.
