Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems   This paper presents local minimax regret lower bounds for adaptively
controlling linear-quadratic-Gaussian (LQG) systems. We consider smoothly
parametrized instances and provide an understanding of when logarithmic regret
is impossible which is both instance specific and flexible enough to take
problem structure into account. This understanding relies on two key notions:
That of local-uninformativeness; when the optimal policy does not provide
sufficient excitation for identification of the optimal policy, and yields a
degenerate Fisher information matrix; and that of
information-regret-boundedness, when the small eigenvalues of a
policy-dependent information matrix are boundable in terms of the regret of
that policy. Combined with a reduction to Bayesian estimation and application
of Van Trees' inequality, these two conditions are sufficient for proving
regret bounds on order of magnitude $\sqrt{T}$ in the time horizon, $T$. This
method yields lower bounds that exhibit tight dimensional dependencies and
scale naturally with control-theoretic problem constants. For instance, we are
able to prove that systems operating near marginal stability are fundamentally
hard to learn to control. We further show that large classes of systems satisfy
these conditions, among them any state-feedback system with both $A$- and
$B$-matrices unknown. Most importantly, we also establish that a nontrivial
class of partially observable systems, essentially those that are
over-actuated, satisfy these conditions, thus providing a $\sqrt{T}$ lower
bound also valid for partially observable systems. Finally, we turn to two
simple examples which demonstrate that our lower bound captures classical
control-theoretic intuition: our lower bounds diverge for systems operating
near marginal stability or with large filter gain -- these can be arbitrarily
hard to (learn to) control.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga