Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rate-matching the regret lower-bound in the linear quadratic regulator
  with unknown dynamics   The theory of reinforcement learning currently suffers from a mismatch
between its empirical performance and the theoretical characterization of its
performance, with consequences for, e.g., the understanding of sample
efficiency, safety, and robustness. The linear quadratic regulator with unknown
dynamics is a fundamental reinforcement learning setting with significant
structure in its dynamics and cost function, yet even in this setting there is
a gap between the best known regret lower-bound of $\Omega_p(\sqrt{T})$ and the
best known upper-bound of $O_p(\sqrt{T}\,\text{polylog}(T))$. The contribution
of this paper is to close that gap by establishing a novel regret upper-bound
of $O_p(\sqrt{T})$. Our proof is constructive in that it analyzes the regret of
a concrete algorithm, and simultaneously establishes an estimation error bound
on the dynamics of $O_p(T^{-1/4})$ which is also the first to match the rate of
a known lower-bound. The two keys to our improved proof technique are (1) a
more precise upper- and lower-bound on the system Gram matrix and (2) a
self-bounding argument for the expected estimation error of the optimal
controller.

37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics