  The ability of robots to estimate their location is crucial for a wide
variety of autonomous operations. In settings where GPS is unavailable,
measurements of transmissions from fixed beacons provide an effective means of
estimating a robot's location as it navigates. The accuracy of such a
beacon-based localization system depends both on how beacons are distributed in
the environment, and how the robot's location is inferred based on noisy and
potentially ambiguous measurements. We propose an approach for making these
design decisions automatically and without expert supervision, by explicitly
searching for the placement and inference strategies that, together, are
optimal for a given environment. Since this search is computationally
expensive, our approach encodes beacon placement as a differential neural layer
that interfaces with a neural network for inference. This formulation allows us
to employ standard techniques for training neural networks to carry out the
joint optimization. We evaluate this approach on a variety of environments and
settings, and find that it is able to discover designs that enable high
localization accuracy.
