Searching for Fundamentals and Commonalities of Search

This chapter reports the discussion of a group of mostly behavioral biologists, who attempt to put research on search from their own discipline into a framework that might help identify parallels with cognitive search. Essential components of search are a functional goal, uncertainty about goal location, the adaptive varying of position, and often a stopping rule. The chapter considers a diversity of cases where search is in domains other than spatial and lists other important dimensions in which search problems differ. One dimension examined in detail is social interactions between searchers and searchers, targets and targets, and targets and searchers. The producer-scrounger game is presented as an example; despite the extensive empirical and theoretical work on the equilibrium between the strategies, it is largely an open problem how animals decide when to adopt each strategy, and thus how real equilibria are attained. Another dimension that explains some of the diversity of search behavior is the modality of the information utilized (e.g., visual, auditory, olfactory). The chapter concludes by highlighting further parallels between search in the external environment and cognitive search. These suggest some novel avenues of research. Evolutionary Biology of Search To begin, it may be useful to say something about the perspective we bring to the study of search. Our group is predominantly whole-organism biologists who investigate the mechanisms and adaptive signifi cance of behavior. In doing this, behavioral ecologists commonly appeal to optimality or game-theoretical models, and these models, along with knowledge about animal genetics, From “Cognitive Search: Evolution, Algorithms, and the Brain,” edited by Peter M. Todd, Thomas T. Hills, and Trevor W. Robbins. 2012. Strüngmann Forum Report, vol. 9, J. Lupp, series ed. Cambridge, MA: MIT Press. ISBN 978-0-262-01809-8. 48 J. M. C. Hutchinson et al. physiology, neurobiology, phylogeny and development, have guided our thinking about search. For example, a classic optimality model considers when a foraging animal should stop feeding in a patch being depleted of prey and switch to a new patch, despite the cost of moving (Charnov 1976). The prediction most often tested is that increasing the travel time between patches should increase the time spent in each patch. This prediction has generally been confi rmed, but less successful have been predictions about the absolute time spent in a patch (Nonacs 2001) and what cues to attend to so as to decide when to leave a patch (e.g., Roche et al. 1998; Hutchinson et al. 2008). Failures like this lead biologists to change or elaborate the basic model, for instance by incorporating additional aspects of the environment or by invoking some informational or cognitive constraint (e.g., Nonacs 2001; Hills and Adler 2002). Ideally, predictions are tested by manipulating the environment of an individual in the hope of a real-time response, but alternatives are to utilize variation among species or natural variation among individuals of a single species. If what follows manages to say anything novel of interest to workers on cognitive search, we suspect that it will be because of, not despite, this perspective of the adaptation of behavior. Our biological perspective also brings to the table a greater diversity of search problems faced by different animals, and plants too (de Kroon and Mommer 2006), than by humans and our machines. The Essence of Search How would you defi ne search? It is all too easy for a defi nition to use a near synonym like “locate,” which does not gain us much, or unintentionally to exclude phenomena such as searching internally for a solution to an anagram. Seeking a defi nition moved us beyond sterile questions of semantics, because it enabled us to recognize the essence of the search process that makes it distinct. We agreed that it would not be useful to defi ne the term so broadly that it covered all adaptive processes. Luc-Alain Giraldeau provided the initial insight. He proposed that for something to qualify as search there must fi rst be a defi ned goal, such as food, mates, or particular information. The search itself then consists of acting to vary position according to some scheme that facilitates fi nding the goal. We defi nitely do not mean to restrict “vary position” to moving in space; rather, we include movement in other dimensions, such as sampling at different times of day or shifting attention somehow in one’s brain. It seems an important component of the defi nition that the varying of the position is adapted toward effi cient location of the goal, hence the importance of defi ning the goal fi rst. Thus we would not consider as search the process by which sand grains get deposited by the wind on the lee side of a dune. Nor is it search if animals explore and learn about the environment incidentally, ahead of starting to seek a From “Cognitive Search: Evolution, Algorithms, and the Brain,” edited by Peter M. Todd, Thomas T. Hills, and Trevor W. Robbins. 2012. Strüngmann Forum Report, vol. 9, J. Lupp, series ed. Cambridge, MA: MIT Press. ISBN 978-0-262-01809-8. Searching for Fundamentals and Commonalities of Search 49 goal (latent learning: Thistlethwaite 1951). Our opinion is that search does not start until that goal seeking starts. The goal that we invoke here is the function of the behavior. Without getting into philosophical debates about teleology, biologists are happy to say that a character has a particular ultimate function if design considerations suggest that natural selection has adapted it for that purpose. We are not talking about the proximate goal that one must identify to understand the mechanism of a control problem such as search. In this perhaps we differ from some other groups in this volume. To bring out the distinction, consider the princess and monster game, a classic example from the theory of search games (Isaacs 1965). A princess and a monster are free to move around in a darkened room or other space. The monster’s goal, in the sense we intend, is to catch the princess; but, since neither can detect the other until they collide, its proximate goal cannot be capture but merely to move in particular prespecifi ed directions. Formally there may be an additional part of the search process: the application of a stopping rule to decide when the goal has been attained. Some valid sorts of search may lack a stopping rule. For instance, one can imagine a chemotactic bacterium following a gradient to the source; when it reaches the source it need not apply a stopping rule but oscillate around the source, its goal seeking continuing. If there is a stopping rule, its application is itself part of the search process. Note that a stopping rule may test the environment repeatedly during a search even though it triggers stopping of the task only once. One important aspect of search is that there is some uncertainty in the location of the goal. If you can see the target and then walk straight toward it, that does not seem like search, although others coined the phrase “nonexploratory search” to cover situations where there is no uncertainty. Compare leafi ng through a book to fi nd a particular passage with using the subject index: the former represents search with uncertainty, whereas an index is like a lookup table in computer programming, which is constructed to avoid repeated search or calculation. What about a blind organism that can apply a deterministic algorithm to locate a target reliably, say by chemotaxis? If it is absolutely always able to fi nd the target, this behavior seems analogous to walking straight toward a visible target. Now consider the ability of some ants to return straight to their nests using solely path integration of their wiggly outward route (Müller and Wehner 1988). That does not initially sound like search, but actually their method of path integration is a clever approximation rather than exact (Müller and Wehner 1988), and they routinely must apply backup search mechanisms (Wehner 2003; Merkle and Wehner 2010). So, if we defi ne search as involving uncertainty, recognizing a phenomenon as search may require us to know about the proximate mechanism and its performance. We wondered whether a characteristic of search is that uncertainty tends to be reduced, or at least not to increase, at each step. One exception is the case when the search is for a mobile target known to be initially within some distance but able to move away (Foreman 1977), although perhaps search still From “Cognitive Search: Evolution, Algorithms, and the Brain,” edited by Peter M. Todd, Thomas T. Hills, and Trevor W. Robbins. 2012. Strüngmann Forum Report, vol. 9, J. Lupp, series ed. Cambridge, MA: MIT Press. ISBN 978-0-262-01809-8. 50 J. M. C. Hutchinson et al. tends to delay the increase of uncertainty compared to random movement by the searcher. Real searches for a particular mobile prey can often fail, but this should not stop us considering the strategy that maximizes the probability of capture as a search. Another aspect of most search is that it is sequential. By this we do not mean to exclude cases of multiple agents working in parallel and maybe sharing information; still each agent individually is searching sequentially. By “sequential” we intend to capture the idea that several steps must be taken to reach the target; a single-step process of selection between options is not search. The options change at each step and information gained from earlier phases should inform the choices made at later steps. A revealing example in this context is the secretary problem (Freeman 1983), the archetypal case of sequential search, which has been applied to model mate choice. Candidates of different qualities appear in random order one at a time; the object is to select a candidate of good quality, and each of a sequence of decisions is whether to accept the current candidate or continue inspecting further candidates. In this case, the only scope for varying “position” is the gain in information from inspecting the next candidate, but the crucial aspect is that information on the qualities of candidates inspected at earlier steps should determine whether search is terminated at later steps. We tried, but failed, to agree on a single-sentence defi nition of search, preferring instead to list the key components: a functional goal, uncertainty about goal location, the adaptive varying of position, and often a stopping rule.