Information Selection in Noisy Environments with Large Action Spaces

Information Selection in Noisy Environments with Large Action Spaces Pedro Tsividis (tsividis@mit.edu), Samuel J. Gershman (sjgershm@mit.edu), Joshua B. Tenenbaum (jbt@mit.edu), Laura Schulz (lshulz@mit.edu) Massachusetts Institute of Technology, Department of Brain and Cognitive Sciences, 77 Massachusetts Ave., Cambridge, MA 02139 USA Abstract A critical aspect of human cognition is the ability to effec- tively query the environment for information. The ‘real’ world is large and noisy, and therefore designing effec- tive queries involves prioritizing both scope – the range of hypotheses addressed by the query – and reliability – the likelihood of obtaining a correct answer. Here we de- signed a simple information-search game in which partic- ipants had to select an informative query from a large set of queries, trading off scope and reliability. We find that adults are effective information-searchers even in large, noisy environments, and that their information search is best explained by a model that balances scope and re- liability by selecting queries proportionately to their ex- pected information gain. Keywords: exploration; information search; active learn- ing; information gain. Introduction As scientists, we sometimes encounter (or conduct) experimental work that is stunning in its breadth but dis- appointing in its rigor, or work that is categorically deci- sive but disappointingly narrow in scope. As child or adult intuitive scientists searching for information, we often deal with these epistemic virtues – scope and rigor – as well; we can make general queries that drastically narrow the hypothesis space of answers or make nar- rower ones, and we can seek information from reliable sources that are more likely to give us correct answers, or from sources that are less so. Our success, whether as professional or intuitive scientists, hinges on our abil- ity to balance these two dimensions in order to produce queries whose answers will be informative. Early work on information search seemed to show that people fail to make rational decisions when it comes to information acquisition; in the Wason (1968) selection task, with a fairly small (12) action set, only 4% of sub- jects made the normative information-acquisition selec- tion. However, as Oaksford & Chater (1994) pointed out, the selection made most often by participants in the original Wason task was normative when environmental statistics were taken into account. Specifically, partici- pants’ decisions were best explained as maximizing ex- pected information gain in the service of helping them to decide between competing hypotheses. More recent work on information search has shown that children have strong intuitions about questions’ use- fulness and search adaptively (Nelson et al., 2013) and that adults can value information over explicit reward when the two are put in opposition (Markant & Gureckis, Our interest is in whether these trends persist when people are confronted with the large, noisy information spaces characteristic of the real world. As we explore the world and its affordances, we must select queries that have scope, in that they rule out large numbers of hy- potheses at once. And, inasmuch as we can help it, we should minimize noise by querying reliable sources. In the real world, these are often in opposition. So, we ask: how do people trade off scope and reliability when ex- ploring large, noisy information spaces? And when the potential questions are many, do they ask the right ones? Information-search task To begin to answer these questions, we designed a novel information-search task. Our goal was for it to be as simple as possible, while having as many features approaching natural exploration as possible. Thus we paired a very simple game – identifying a hidden number on a number line – with a relatively complex search pro- cedure. In playing the game, participants make queries that vary in the abstract features of scope and reliabil- ity. Additionally, at each point in the game, partici- pants are faced with a very large number of potential specific queries to choose from. Our task is similar to the Markant & Gureckis (2012) task in that it involves exploring a geometric space to test particular hypothe- ses, but we wanted to make explicit the abstract features of questions, rather than have these be implicit as a func- tion of the hypotheses at hand. Participants play by asking ‘questions’ about the hid- den number’s location, using ‘scanners’ that turn blue if the number is under the scanned region and red if the number is not. In each trial, a participant is given four scanners (Fig. 1). In some conditions, the scanners vary in size. Larger scanners can cover larger regions of the number line, ruling out (or in) a larger set of hypotheses than a smaller scanner. Thus, in the context of this study, the ‘scope’ is directly related to the length of the scan- ner. However, the scanners are not deterministic; they also vary in their reliability, which is the probability of providing an accurate signal about the presence of the hidden number (false positives and false negatives are equally likely). To efficiently find the hidden number, participants have to select scanners that provide a good trade-off be-