Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Koopman Spectrum Nonlinear Regulator and Provably Efficient Online
  Learning   Most modern reinforcement learning algorithms optimize a cumulative
single-step cost along a trajectory. The optimized motions are often
'unnatural', representing, for example, behaviors with sudden accelerations
that waste energy and lack predictability. In this work, we present a novel
paradigm of controlling nonlinear systems via the minimization of the Koopman
spectrum cost: a cost over the Koopman operator of the controlled dynamics.
This induces a broader class of dynamical behaviors that evolve over stable
manifolds such as nonlinear oscillators, closed loops, and smooth movements. We
demonstrate that some dynamics realizations that are not possible with a
cumulative cost are feasible in this paradigm. Moreover, we present a provably
efficient online learning algorithm for our problem that enjoys a sub-linear
regret bound under some structural assumptions.

16
The categories of this paper are: stat
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph