Towards a theory of heuristic and optimal planning for sequential information search

Abstract

How should tests (or queries, questions, or experiments) be selected? Does it matter if only a single test is allowed, or if a sequential test strategy can be planned in advance? This article contributes two sets of theoretical results bearing on these questions. First, for selecting a single test, several Optimal Experimental Design (OED) ideas have been proposed in statistics and other disciplines. The OED models are mathematically nontrivial. How is it that they often predict human behavior well? One possibility is that simple heuristics can approximate or exactly implement OED models. We prove that heuristics can identify the highest information value queries (as quantified by OED models) in several situations, thus providing a possible algorithmic-level theory of human behavior. Second, we address whether OED models are optimal for sequential search, as is frequently presumed. We consider the Person Game, a 20-questions scenario, as well as a two-category, binary feature scenario, both of which have been widely used in psychological research. In each task, we demonstrate via specific examples and extended computational simulations that neither the OED models nor the heuristics considered in the literature are optimal. Little research addresses human behavior in such situations. We call for experimental research into how people approach the sequential planning of tests, and theoretical research on what sequential planning procedures are most successful, and we offer a number of testable predictions for discriminating among candidate models.

Stepwise versus globally optimal search in children and adults

“…However, crucially, a stepwise-optimal query is not necessarily the best first query when multiple queries can be conducted, because the feedback on one query affects and constrains the informativeness of subsequent queries. Sequential search is particularly interesting from a computational standpoint, because the problem of identifying the globally optimal strategy is generally intractable (Hyafil & Rivest, 1976;Nelson et al, 2018). From a psychological perspective, sequential search relates to many real-world situations (e.g., medical diagnosis involving multiple tests) and it is methodologically critical for differentiating between competing descriptive and normative models of human search.…”

“…where IG is the expected information gain and the term in the brackets is the expected entropy after asking the question. Selecting questions by maximizing information gain in accordance with Equation 1 reduces uncertainty in a stepwise-optimal fashion (for an analysis of multistep methods see Nelson et al, 2018).…”

“…Because they disregard future queries and do not plan ahead they are also referred to as greedy or myopic models. Obtaining information in a stepwise-optimal fashion is often an efficient approach to information acquisition, but it is not generally guaranteed to identify the most efficient strategy when multiple queries can be conducted (Hyafil & Rivest, 1976;Nelson et al, 2018). This has important theoretical implications for both computational-level and mechanistic analyses of human search behavior.…”

“…This has important theoretical implications for both computational-level and mechanistic analyses of human search behavior. At the computational level, almost all psychological research to date has tacitly assumed that sequential search is governed by the same normative principles that govern oneshot scenarios, in which only a single piece of information can be obtained (but see Bramley et al, 2015;Meier & Blair, 2013;Nelson et al, 2018). At the mechanistic level, stepwise strategies engage a fundamentally different form of cognitive processing than methods that are sensitive to long-run efficiency, the former involving valuation of individual queries and the latter requiring explicit planning to evaluate alternative decision trees.…”

Why do you ask? The informational dynamics of questions and answers

“…OED policies based on global planning, compared to locally 'greedy' policies, are not yet well-understood even in the simpler non-pragmatic case of sequentially querying an oracle, though seeNelson, Meder, and Jones (2018) for recent theoretical progress.…”