  A sequential decision process in which an adaptive radar system repeatedly
interacts with a finite-state target channel is studied. The radar is capable
of passively sensing the spectrum at regular intervals, which provides side
information for the waveform selection process. The radar transmitter uses the
sequence of spectrum observations as well as feedback from a collocated
receiver to select waveforms which accurately estimate target parameters. It is
shown that the waveform selection problem can be effectively addressed using a
linear contextual bandit formulation in a manner that is both computationally
feasible and sample efficient. Stochastic and adversarial linear contextual
bandit models are introduced, allowing the radar to achieve effective
performance in broad classes of physical environments. Simulations in a
radar-communication coexistence scenario, as well as in an adversarial
radar-jammer scenario, demonstrate that the proposed formulation provides a
substantial improvement in target detection performance when Thompson Sampling
and EXP3 algorithms are used to drive the waveform selection process. Further,
it is shown that the harmful impacts of pulse-agile behavior on coherently
processed radar data can be mitigated by adopting a time-varying constraint on
the radar's waveform catalog.
