Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adversarial Tradeoffs in Linear Inverse Problems and Robust State
  Estimation   Adversarially robust training has been shown to reduce the susceptibility of
learned models to targeted input data perturbations. However, it has also been
observed that such adversarially robust models suffer a degradation in accuracy
when applied to unperturbed data sets, leading to a robustness-accuracy
tradeoff. In this paper, we provide sharp and interpretable characterizations
of such robustness-accuracy tradeoffs for linear inverse problems. In
particular, we provide an algorithm to find the optimal adversarial
perturbation given data, and develop tight upper and lower bounds on the
adversarial loss in terms of the standard (non-adversarial) loss and the
spectral properties of the resulting estimator. Further, motivated by the use
of adversarial training in reinforcement learning, we define and analyze the
\emph{adversarially robust Kalman Filtering problem.} We apply a refined
version of our general theory to this problem, and provide the first
characterization of robustness-accuracy tradeoffs in a setting where the data
is generated by a dynamical system. In doing so, we show a natural connection
between a filter's robustness to adversarial perturbation and underlying
control theoretic properties of the system being observed, namely the spectral
properties of its observability gramian.

15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci