arXiv subjects

Kevin Glazebrook

Publications and source records attributed to Kevin Glazebrook.

5 recordsLinked to original sources

arXiv2026

Robust Patrol in a Dispersed Environment

We consider a patrol problem in which a patroller moves among several geographically dispersed locations to detect attackers that arrive over time. Once the patroller arrives at a location, they can spend any amount of time searching for attackers at that location---and detect an attacker there with some location-dependent instantaneous detection rate---before moving to a different location. The objective of the patroller is to minimize the expected time an attacker stays undetected at a location, regardless of where and when the attack occurs. In the special case where travel times are negligible, we elucidate an optimal cyclic policy in which the patroller allocates a fixed fraction of their effort to each location continuously. The patrol problem becomes significantly more challenging when travel times cannot be ignored. We introduce two types of cyclic patrol patterns based on common patrol practice for perimeter patrol and border patrol, respectively, and derive formulae for the expected time to detect an attack in both cases. We also provide an algorithm for finding the best search time parameters in both of these cases. We give several examples where these cycle types perform well and numerically demonstrate that the optimal patrol policy depends highly on the structure and parameters of each patrol problem.

math.OC↗

arXiv2022

A New Simheuristic Approach for Stochastic Runway Scheduling

We consider a stochastic, dynamic runway scheduling problem involving aircraft landings on a single runway. Sequencing decisions are made with knowledge of the estimated arrival times (ETAs) of all aircraft due to arrive at the airport, and these ETAs vary according to continuous-time stochastic processes. Time separations between consecutive runway landings are modeled via sequence-dependent Erlang distributions and are affected by weather conditions, which also evolve continuously over time. The resulting multi-stage optimization problem is intractable using exact methods and we propose a novel simheuristic approach, based on the application of methods analogous to variable neighborhood search (VNS) in a high-dimensional stochastic environment. Our model is calibrated using flight tracking data for over 98,000 arrivals at Heathrow Airport. Results from numerical experiments indicate that our proposed simheuristic algorithm outperforms an alternative based on deterministic forecasts under a wide range of parameter values, with the largest benefits being seen when the underlying stochastic processes become more volatile and also when the on-time requirements of individual flights are given greater weight in the objective function.

math.OC↗

arXiv2019

Adaptive Policies for Perimeter Surveillance Problems

Maximising the detection of intrusions is a fundamental and often critical aim of perimeter surveillance. Commonly, this requires a decision-maker to optimally allocate multiple searchers to segments of the perimeter. We consider a scenario where the decision-maker may sequentially update the searchers' allocation, learning from the observed data to improve decisions over time. In this work we propose a formal model and solution methods for this sequential perimeter surveillance problem. Our model is a combinatorial multi-armed bandit (CMAB) with Poisson rewards and a novel filtered feedback mechanism - arising from the failure to detect certain intrusions. Our solution method is an upper confidence bound approach and we derive upper and lower bounds on its expected performance. We prove that the gap between these bounds is of constant order, and demonstrate empirically that our approach is more reliable in simulated problems than competing algorithms.

cs.LG↗

arXiv2017

Combinatorial Multi-Armed Bandits with Filtered Feedback

Motivated by problems in search and detection we present a solution to a Combinatorial Multi-Armed Bandit (CMAB) problem with both heavy-tailed reward distributions and a new class of feedback, filtered semibandit feedback. In a CMAB problem an agent pulls a combination of arms from a set $\{1,...,k\}$ in each round, generating random outcomes from probability distributions associated with these arms and receiving an overall reward. Under semibandit feedback it is assumed that the random outcomes generated are all observed. Filtered semibandit feedback allows the outcomes that are observed to be sampled from a second distribution conditioned on the initial random outcomes. This feedback mechanism is valuable as it allows CMAB methods to be applied to sequential search and detection problems where combinatorial actions are made, but the true rewards (number of objects of interest appearing in the round) are not observed, rather a filtered reward (the number of objects the searcher successfully finds, which must by definition be less than the number that appear). We present an upper confidence bound type algorithm, Robust-F-CUCB, and associated regret bound of order $\mathcal{O}(\ln(n))$ to balance exploration and exploitation in the face of both filtering of reward and heavy tailed reward distributions.

cs.LG↗

arXiv2016

On the Identification and Mitigation of Weaknesses in the Knowledge Gradient Policy for Multi-Armed Bandits

The Knowledge Gradient (KG) policy was originally proposed for online ranking and selection problems but has recently been adapted for use in online decision making in general and multi-armed bandit problems (MABs) in particular. We study its use in a class of exponential family MABs and identify weaknesses, including a propensity to take actions which are dominated with respect to both exploitation and exploration. We propose variants of KG which avoid such errors. These new policies include an index heuristic which deploys a KG approach to develop an approximation to the Gittins index. A numerical study shows this policy to perform well over a range of MABs including those for which index policies are not optimal. While KG does not make dominated actions when bandits are Gaussian, it fails to be index consistent and appears not to enjoy a performance advantage over competitor policies when arms are correlated to compensate for its greater computational demands.

stat.ML↗