Sequential Change Detection with Simulators

Music City Center 

We consider the problem of sequential change detection in the presence of simulators of the
pre- and post-change distributions. Formally, given a stream of observations $(U_t, V_t, X_t)_{t
\geq 1}$, with $(U_t)_{t \geq 1}$ and $(V_t)_{t \geq 1}$ generated by simulators, and $(X_t)_{t
\geq 1}$ denoting the real sequence, we develop a general strategy for quickly detecting
changes in the distribution of $X_t$ from an (unknown) $P_0$ to another (unknown) distribution
$P_1 \neq P_0$ at some unknown time $T$. We have additional information that $U_t \sim
Q_0$ and $V_t \sim Q_1$, with $Q_0 \approx P_0$ and $Q_1 \approx P_1$.
We show that this problem can be reduced to that of detecting changes in the sign of the
mean of the stream of observations. This allows us to take advantage of recent progress in the
design of methods for estimating and testing for the mean of random variables in the sequential
setting to construct powerful change detection schemes. We discuss several instantiations of
our general change detection scheme and end the presentation with some numerical
experiments.