  High level declarative constraints provide a powerful (and popular) way to
define and construct control policies; however, most synthesis algorithms do
not support specifying the degree of randomness (unpredictability) of the
resulting controller. In many contexts, e.g., patrolling, testing, behavior
prediction, and planning on idealized models, predictable or biased controllers
are undesirable. To address these concerns, we introduce the \emph{Entropic
Reactive Control Improvisation} (ERCI) framework and algorithm that supports
synthesizing control policies for stochastic games that are declaratively
specified by (i) a \emph{hard constraint} specifying what must occur (ii) a
\emph{soft constraint} specifying what typically occurs, and (iii) a
\emph{randomization constraint} specifying the unpredictability and variety of
the controller, as quantified using causal entropy. This framework, which
extends the state-of-the-art by supporting arbitrary combinations of
adversarial and probabilistic uncertainty in the environment, enables a
flexible modeling formalism which we argue, theoretically and empirically,
remains tractable.
