Optimal search in discrete locations:extensions and new findings

A hidden target needs to be found by a searcher in many real-life situations, some of which involve large costs and significant consequences with failure. Therefore, efficient search methods are paramount. In our search model, the target lies in one of several discrete locations according to some hiding distribution, and the searcher's goal is to discover the target in minimum expected time by making successive searches of individual locations. In Part I of the thesis, the searcher knows the hiding distribution. Here, if there is only one way to search each location, the solution to the search problem, discovered in the 1960s, is simple; search next any location with a maximal probability per unit time of detecting the target. An equivalent solution is derived by viewing the search problem as a multi-armed bandit and following a Gittins index policy. Motivated by modern search technology, we introduce two modes---fast and slow---to search each location. The fast mode takes less time, but the slow mode is more likely to find the target. An optimal policy is difficult to obtain in general, because it requires an optimal sequence of search modes for each location, in addition to a set of sequence-dependent Gittins indices for choosing between locations. For each mode, we identify a sufficient condition for a location to use only that search mode in an optimal policy. For locations meeting neither sufficient condition, an optimal choice of search mode is extremely complicated, depending both on the hiding distribution and the search parameters of the other locations. We propose several heuristic policies motivated by our analysis, and demonstrate their near-optimal performance in an extensive numerical study. In Part II of the thesis, the searcher has only one search mode per location, but does not know the hiding distribution, which is chosen by an intelligent hider who aims to maximise the expected time until the target is discovered. Such a search game, modelled via two-person, zero-sum game theory, is relevant if the target is a bomb, intruder, or, of increasing importance due to advances in technology, a computer hacker. By Part I, if the hiding distribution is known, an optimal counter strategy for the searcher is any corresponding Gittins index policy. To develop an optimal search strategy in the search game, the searcher must account for the hider’s motivation to choose an optimal hiding distribution, and consider the set of corresponding Gittins index policies. %It follows that an optimal search strategy in the search game must be some Gittins index policy if the hiding distribution is assumed to be chosen optimally by the hider. However, the searcher must choose carefully from this set of Gittins index policies to ensure the same expected time to discover the target regardless of where it is hidden by the hider. %It follows that an optimal search strategy in the search game must be a Gittins index policy applied to a hiding distribution which is optimal from the hider's perspective. However, to avoid giving the hider any advantage, the searcher must carefully choose such a Gittins index policy among the many available. As a result, finding an optimal search strategy, or even proving one exists, is difficult. We extend several results for special cases from the literature to the fully-general search game; in particular, we show an optimal search strategy exists and may take a simple form. Using a novel test, we investigate the frequency of the optimality of a particular hiding strategy that gives the searcher no preference over any location at the beginning of the search

Three essays on sequential learning in search - pursuit games and jury voting problems

This thesis consists of three papers on different topics on the sequential learning problem. The first paper is a stochastic game model of predator-prey interaction that combines search and pursuit in a single game. In this paper I introduce a novel learning model in which certain parameters of the model could in theory be learned sequentially over time. The second paper in this thesis focuses on the deterministic version of the similar search and pursuit problem. By relaxing the assumption made since Gal and Casas [36], I introduce three sub-problems to the original model and provide general propositions to each of them. The third paper departs from the area of search games and analyzes the optimal voting ordering in sequential juries. Together with Steve Alpern, Bo Chen, and Chenxin Pan, we studied a new version of the Alpern{Chen model [2]. Our paper makes the notion of \ability" more specific by introducing the sealed card model in which the state of Nature (equivalent to innocent or guilty for a legal jury) is the color of a sealed card and the jurors sample other cards in the deck as their `signals' and they vote sequentially. I show that under this model, by voting in Alpern-Chen ordering (median ability, high ability, low ability), the jury ensures the highest average reliability and optimality fraction

Allocating patrolling resources to effectively thwart intelligent attackers

This thesis considers the allocation of patrolling resources deployed in an effort to thwart intelligent attackers, who are committing malicious acts at unknown locations which take a specified length of time to complete. This thesis considers patrolling games which depend on three parameters; a graph, a game length and an attack length. For patrolling games, the graph models the locations and how they are connected, the game length corresponds to the time-horizon in which two players, known as the patroller and attacker, act and the attack length is the time it takes an attacker to complete their malicious act. This thesis defines patrolling games (as first seen in [16]) and explains its known properties and how such games are solved. While any patrolling game can be solved by a linear program (LP) when the number of locations or game length is small, this becomes infeasible when either of these parameters are of moderate size. Therefore, strategies are often evaluated by knowing an opponent’s response and with this, patroller and attacker strategies give lower and upper bounds on the optimal value. Moreover, when tight bounds are given by strategies these are optimal strategies. This thesis states known strategies giving these bounds and classes for which patrolling games have been solved. Firstly, this thesis introduces new techniques which can be used to evaluate strategies, by reducing the strategy space for best responses from an opponent. Extensions to known strategies are developed and their respective bounds are given using known results. In addition we develop a patroller improvement program (PIP) which improves current patroller strategies by considering which locations are currently under performing. Secondly, these general techniques and strategies are applied to find solutions to a certain class of patrolling games which are not previously solved. In particular, classes of the patrolling game are solved when the graph is multipartite or is an extension of a star graph. Thirdly, this thesis conjectures that a developed patroller strategy known as the random minimal full-node cycle is optimal for a large class of patrolling games, when the graph is a tree. Intuitive reasoning behind the conjecture is given along with computational evidence, showing the conjecture holds when the number of locations in the graph is less than 9. Finally, this thesis looks at three extensions to the scenario modelled by the patrolling game. One extension models varying distances between locations rather than assuming locations are a unitary distance apart. Another extension allows the time needed for an attacker to complete their malicious act to vary depending on the vulnerability of the location. For the final extension of multiple players we look at four variants depending on how multiple attackers succeed in the extension. In each extension we find some properties of the game and show that it possible to relate # extensions to the classic patrolling game in order to find the value and optimal strategies for certain classes of such games

Allocating patrolling resources to effectively thwart intelligent attackers

This thesis considers the allocation of patrolling resources deployed in an effort to thwart intelligent attackers, who are committing malicious acts at unknown locations which take a specified length of time to complete. This thesis considers patrolling games which depend on three parameters; a graph, a game length and an attack length. For patrolling games, the graph models the locations and how they are connected, the game length corresponds to the time-horizon in which two players, known as the patroller and attacker, act and the attack length is the time it takes an attacker to complete their malicious act. This thesis defines patrolling games (as first seen in [16]) and explains its known properties and how such games are solved. While any patrolling game can be solved by a linear program (LP) when the number of locations or game length is small, this becomes infeasible when either of these parameters are of moderate size. Therefore, strategies are often evaluated by knowing an opponent’s response and with this, patroller and attacker strategies give lower and upper bounds on the optimal value. Moreover, when tight bounds are given by strategies these are optimal strategies. This thesis states known strategies giving these bounds and classes for which patrolling games have been solved. Firstly, this thesis introduces new techniques which can be used to evaluate strategies, by reducing the strategy space for best responses from an opponent. Extensions to known strategies are developed and their respective bounds are given using known results. In addition we develop a patroller improvement program (PIP) which improves current patroller strategies by considering which locations are currently under performing. Secondly, these general techniques and strategies are applied to find solutions to a certain class of patrolling games which are not previously solved. In particular, classes of the patrolling game are solved when the graph is multipartite or is an extension of a star graph. Thirdly, this thesis conjectures that a developed patroller strategy known as the random minimal full-node cycle is optimal for a large class of patrolling games, when the graph is a tree. Intuitive reasoning behind the conjecture is given along with computational evidence, showing the conjecture holds when the number of locations in the graph is less than 9. Finally, this thesis looks at three extensions to the scenario modelled by the patrolling game. One extension models varying distances between locations rather than assuming locations are a unitary distance apart. Another extension allows the time needed for an attacker to complete their malicious act to vary depending on the vulnerability of the location. For the final extension of multiple players we look at four variants depending on how multiple attackers succeed in the extension. In each extension we find some properties of the game and show that it possible to relate # extensions to the classic patrolling game in order to find the value and optimal strategies for certain classes of such games

User redefinition of search goals through interaction with an information retrieval system

Search goals of users of information retrieval systems have commonly been assumed to be static and well-formed. However, a significant amount of goal redefinition is detected in the studies described. A pilot study examined user behaviour at a library OPAC, showing that search results would quite frequently induce users to reconsider and revise their search goals, sometimes following up with a new search based on this revision (labeled "strong" goal redefinition). The main analysis employed transaction logs from the OCLC FirstSearch service, investigating what factors, if any, might affect the amount of goal redefinition that takes place during a search session. To this end, ten hypotheses were proposed and considered. Within each search session, logged queries were coded according to their conceptual differences or similarities, in order for indices of strong goal redefinition to be constructed: a chronological content analysis was thus performed on the transaction logs. The indices of redefinition for search sessions on different FirstSearch databases were compared. It was found that different databases induced goal redefinition to different extents. Further analysis showed that the metadata displayed by a database appeared to affect the amount of goal redefinition, and that the presence of abstracts in results was a positive factor, as was the presence of descriptors and identifiers, perhaps because of the former's hyperlinking nature on the FirstSearch interface. On the other hand, no evidence was found to indicate that abstract length has much of an effect on goal redefinition, nor hit rate or levels of precision and recall. Of the two indices of redefinition that were produced, the "refined" index showed signs of greater precision. Implications of the findings are discussed. It is suggested that goal redefinition should be considered a positive result of system feedback, and that systems should readily allow users to follow up on redefined goals. Abstracts and summaries of documents should be presented to the user as frequently as possible, and hyperlinks from key terms in the metadata should also be created to assist evolving searches. The importance of how system feedback is encountered by the user is emphasized in a new model of information retrieval, which embraces the nonconscious as part of the "cognitive viewpoint," allowing for nonconscious information wants to enter into a user's consciousness through cues encountered during the scanning of search results, triggering a redefinition of search goal. This thesis paves the way for a considerable amount of potentially important research, including: further testing and development of the index of goal redefinition; deeper transaction log analyses, perhaps using screen recorders, examining semantic content and contextualizing at the level of the query; and further identification and analysis of the factors affecting goal redefinition, across different types of information retrieval system

Electronic Warfare Receiver Resource Management and Optimization

Optimization of electronic warfare (EW) receiver scan strategies is critical to improving the probability of surviving military missions in hostile environments. The problem is that the limited understanding of how dynamic variations in radar and EW receiver characteristics has influenced the response time to detect enemy threats. The dependent variable was the EW receiver response time and the 4 independent variables were EW receiver revisit interval, EW receiver dwell time, radar scan time, and radar illumination time. Previous researchers have not explained how dynamic variations of independent variables affected response time. The purpose of this experimental study was to develop a model to understand how dynamic variations of the independent variables influenced response time. Queuing theory provided the theoretical foundation for the study using Little\u27s formula to determine the ideal EW receiver revisit interval as it states the mathematical relationship among the variables. Findings from a simulation that produced 17,000 data points indicated that Little\u27s formula was valid for use in EW receivers. Findings also demonstrated that variation of the independent variables had a small but statistically significant effect on the average response time. The most significant finding was the sensitivity in the variance of response time given minor differences of the test conditions, which can lead to unexpectedly long response times. Military users and designers of EW systems benefit most from this study by optimizing system response time, thus improving survivability. Additionally, this research demonstrated a method that may improve EW product development times and reduce the cost to taxpayers through more efficient test and evaluation techniques