  The goal of the paper is to develop a specific application of the convex
optimization based hypothesis testing techniques developed in A. Juditsky, A.
Nemirovski, "Hypothesis testing via affine detectors," Electronic Journal of
Statistics 10:2204--2242, 2016. Namely, we consider the Change Detection
problem as follows: given an evolving in time noisy observations of outputs of
a discrete-time linear dynamical system, we intend to decide, in a sequential
fashion, on the null hypothesis stating that the input to the system is a
nuisance, vs. the alternative stating that the input is a "nontrivial signal,"
with both the nuisances and the nontrivial signals modeled as inputs belonging
to finite unions of some given convex sets. Assuming the observation noises
zero mean sub-Gaussian, we develop "computation-friendly" sequential decision
rules and demonstrate that in our context these rules are provably
near-optimal.
