  We consider a task of surveillance-evading path-planning in a continuous
setting. An Evader strives to escape from a 2D domain while minimizing the risk
of detection (and immediate capture). The probability of detection is
path-dependent and determined by the spatially inhomogeneous surveillance
intensity, which is fixed but a priori unknown and gradually learned in the
multi-episodic setting. We introduce a Bayesian reinforcement learning
algorithm that relies on a Gaussian Process regression (to model the
surveillance intensity function based on the information from prior episodes),
numerical methods for Hamilton-Jacobi PDEs (to plan the best continuous
trajectories based on the current model), and Confidence Bounds (to balance the
exploration vs exploitation). We use numerical experiments and regret metrics
to highlight the significant advantages of our approach compared to traditional
graph-based algorithms of reinforcement learning.
