  Classical univariate isotonic regression involves nonparametric estimation
under a monotonicity constraint of the true signal. We consider a variation of
this generating process, which we term adversarial sign-corrupted isotonic
(\texttt{ASCI}) regression. Under this \texttt{ASCI} setting, the adversary has
full access to the true isotonic responses, and is free to sign-corrupt them.
Estimating the true monotonic signal given these sign-corrupted responses is a
highly challenging task. Notably, the sign-corruptions are designed to violate
monotonicity, and possibly induce heavy dependence between the corrupted
response terms. In this sense, \texttt{ASCI} regression may be viewed as an
adversarial stress test for isotonic regression. Our motivation is driven by
understanding whether efficient robust estimation of the monotone signal is
feasible under this adversarial setting. We develop \texttt{ASCIFIT}, a
three-step estimation procedure under the \texttt{ASCI} setting. The
\texttt{ASCIFIT} procedure is conceptually simple, easy to implement with
existing software, and consists of applying the \texttt{PAVA} with crucial pre-
and post-processing corrections. We formalize this procedure, and demonstrate
its theoretical guarantees in the form of sharp high probability upper bounds
and minimax lower bounds. We illustrate our findings with detailed simulations.
