We study set-valued decision rules in which performance is defined by the inclusion of the top-$p$ hypotheses, rather than only the single best or true hypothesis. This criterion is motivated by sensor selection for target tracking, where inexpensive measurements are used to identify a list of sensor nodes that are likely to be closest to a target. We analyze the performance of top-$p$ versus top-$1$ selection under sequential hypothesis testing, propose a geometry-aware sensor selection algorithm, and validate the approach using real testbed data.

In this paper, we consider a multi-armed bandit (MAB) instance and study how to identify the best arm when arm commands are conveyed from a central learner to a distributed agent over a discrete memoryless channel (DMC). Depending on the agent capabilities, we provide communication schemes along with their analysis, which interestingly relate to the zero-error capacity of the underlying DMC.

We study a distributed multi-armed bandit (MAB) problem over arm erasure channels, motivated by the increasing adoption of MAB algorithms over communication-constrained networks. In this setup, the learner communicates the chosen arm to play to an agent over an erasure channel with probability$\epsilon \in[0,1)$; if an erasure occurs, the agent continues pulling the last successfully received arm; the learner always observes the reward of the arm pulled. In past work, we considered the case where the agent cannot convey feedback to the learner, and thus the learner does not know whether the arm played is the requested or the last successfully received one. In this paper, we instead consider the case where the agent can send feedback to the learner on whether the arm request was received, and thus the learner exactly knows which arm was played. Surprisingly, we prove that erasure feedback does not improve the worst-case regret upper bound order over the previously studied no-feedback setting. In particular, we prove a regret lower bound of$\Omega(\sqrt{K T}+K /(1-\epsilon))$, where$K$is the number of arms and$T$the time horizon, that matches no-feedback lower bound exactly and upper bound (up to logarithmic factors). We note however that the availability of feedback does enable the design of simpler algorithms that may achieve better constants (albeit not better order) regret bounds; we design one such algorithm, and numerically evaluate its performance.

Relative vehicle positioning methods can contribute to safer and more efficient autonomous driving by enabling collision avoidance and platooning applications. For full automation, these applications require cm-level positioning accuracy and greater than 50 Hz update rate. Since sensor-based methods (e.g., LIDAR, cameras) have not been able to reliably satisfy these requirements under all conditions so far, complementary methods are sought. Recently, positioning based on visible light communication signals from vehicle head/tail LED lights (VLP) has shown significant promise as a complementary method attaining cm-level accuracy and near-kHz rate in realistic driving scenarios. Vehicular VLP methods measure relative bearing (angle) or range (distance) of transmitters (i.e., head/tail lights) based on received signals from on-board photodiodes and estimate transmitter relative positions based on those measurements. In this survey, we first review existing vehicular VLP methods and propose a new method that advances the state-of-the-art in positioning performance. Next, we analyze the theoretical and simulated performance of all methods in realistic driving scenarios under challenging noise and weather conditions, real asymmetric light beam patterns and different vehicle dimensions and light placements. Our simulation results show that the newly proposed VLP method is the overall best performer, and can indeed satisfy the accuracy and rate requirements for localization in collision avoidance and platooning applications within practical constraints. Finally, we discuss remaining open challenges that are faced for the deployment of VLP solutions in the automotive sector and further research questions.

We consider a novel multi-arm bandit (MAB) setup, where a learner needs to communicate the actions to distributed agents over erasure channels, while the rewards for the actions are directly available to the learner through external sensors. In our model, while the distributed agents know if an action is erased, the central learner does not (there is no feedback), and thus does not know whether the observed reward resulted from the desired action or not. We propose a scheme that can work on top of any (existing or future) MAB algorithm and make it robust to action erasures. Our scheme results in a worst-case regret over action-erasure channels that is at most a factor of $O(1/\sqrt {1 - \varepsilon } )$ away from the no-erasure worst-case regret of the underlying MAB algorithm, where ϵ is the erasure probability. We also propose a modification of the successive arm elimination algorithm and prove that its worst-case regret is $\tilde O(\sqrt {KT} + K/(1 - \varepsilon ))$, which we prove is optimal by providing a matching lower bound.