Secure ranging refers to the capability of upper-bounding the actual physical distance between two devices with reliability. This is essential in a variety of applications, including to unlock physical systems. In this work, we will look at secure ranging in the context of ultra-wideband impulse radio (UWB-IR) as specified in IEEE 802.15.4z (a.k.a. 4z). In particular, an encrypted waveform, i.e. the scrambled timestamp sequence (STS), is defined in the high rate pulse repetition frequency (HRP) mode of operation in 4z for secure ranging. This work demonstrates the security analysis of 4z HRP when implemented with an adequate receiver design and shows the STS waveform can enable secure ranging. We first review the STS receivers adopted in previous studies and analyze their security vulnerabilities. Then we present a reference STS receiver and prove that secure ranging can be achieved by employing the STS waveform in 4z HRP. The performance bounds of the reference secure STS receiver are also characterized. Numerical experiments corroborate the analyses and demonstrate the security of the reference STS receiver.

We study the asymptotic performance of the Thompson sampling algorithm in the batched multi-armed bandit setting where the time horizon$T$is divided into batches, and the agent is not able to observe the rewards of her actions until the end of each batch. We show that in this batched setting, Thompson sampling achieves the same asymptotic performance as in the case where instantaneous feedback is available after each action, provided that the batch sizes increase subexponentially. This result implies that Thompson sampling can maintain its performance even if it receives delayed feedback in$\omega (\log T)$batches. We further propose an adaptive batching scheme that reduces the number of batches to$O(\log \log T)$while maintaining the same performance. Although the batched multi-armed bandit setting has been considered in several recent works, previous results rely on tailored algorithms for the batched setting, which optimize the batch structure and prioritize exploration in the beginning of the experiment to eliminate suboptimal actions. We show that Thompson sampling, on the other hand, is able to achieve a similar asymptotic performance in the batched setting without any modifications.

We study the asymptotic performance of the Thompson sampling algorithm in the batched multi-armed bandit setting where the time horizon$T$is divided into batches, and the agent is not able to observe the rewards of her actions until the end of each batch. We show that in this batched setting, Thompson sampling achieves the same asymptotic performance as in the case where instantaneous feedback is available after each action, provided that the batch sizes increase subexponentially. This result implies that Thompson sampling can maintain its performance even if it receives delayed feedback in ω(log T) batches. We further propose an adaptive batching scheme that reduces the number of batches to Θ(log T) while maintaining the same performance. Although the batched multi-armed bandit setting has been considered in several recent works, previous results rely on tailored algorithms for the batched setting, which optimize the batch structure and prioritize exploration in the beginning of the experiment to eliminate suboptimal actions. We show that Thompson sampling, on the other hand, is able to achieve a similar asymptotic performance in the batched setting without any modifications.

We introduce a novel anytime batched Thompson sampling policy for multi-armed bandits where the agent observes the rewards of her actions and adjusts her policy only at the end of a small number of batches. We show that this policy simultaneously achieves a problem dependent regret of order $O(\log(T))$ and a minimax regret of order $O(\sqrt{T\log(T)})$ while the number of batches can be bounded by $O(\log(T))$ independent of the problem instance over a time horizon $T$. We also prove that in expectation the instance dependent batch complexity of our policy is of order $O(\log\log(T))$. These results indicate that Thompson sampling performs competitively with recently proposed algorithms for the batched setting, which optimize the batch structure for a given time horizon $T$ and prioritize exploration in the beginning of the experiment to eliminate suboptimal actions. Unlike these algorithms, the batched Thompson sampling algorithm we propose is an anytime policy, i.e. it operates without the knowledge of the time horizon $T$, and as such it is the only anytime algorithm that achieves optimal regret with $O(\log\log(T))$ expected batch complexity. This is achieved through a dynamic batching strategy, which uses the agents estimates to adaptively increase the batch duration.

Thompson sampling has been of significant recent interest due to its wide range of applicability to online learning problems and its good empirical and theoretical performance. In this paper, we analyze the performance of Thompson sampling in the canonical Gaussian linear bandit setting. We prove that the Bayesian regret of Thompson sampling in this setting is bounded by O(√T log (T)) improving on an earlier bound of O(√T log (T)) n the literature for the case of the infinite, and compact action set. Our proof relies on a Cauchy-Schwarz type inequality which can be of interest in its own right.