Heuristics and optimal solutions to the breadth–depth dilemma

Abstract

In multialternative risky choice, we are often faced with the opportunity to allocate our limited information-gathering capacity between several options before receiving feedback. In such cases, we face a natural trade-off between breadth—spreading our capacity across many options—and depth—gaining more information about a smaller number of options. Despite its broad relevance to daily life, including in many naturalistic foraging situations, the optimal strategy in the breadth–depth trade-off has not been delineated. Here, we formalize the breadth–depth dilemma through a finite-sample capacity model. We find that, if capacity is small (∼10 samples), it is optimal to draw one sample per alternative, favoring breadth. However, for larger capacities, a sharp transition is observed, and it becomes best to deeply sample a very small fraction of alternatives, which roughly decreases with the square root of capacity. Thus, ignoring most options, even when capacity is large enough to shallowly sample all of them, is a signature of optimal behavior. Our results also provide a rich casuistic for metareasoning in multialternative decisions with bounded capacity using close-to-optimal heuristics.

Monkey Plays Pac-Man with Compositional Strategies and Hierarchical Decision-making

“…Finally, the model, without being specified so, revealed that a single strategy dominates monkeys' decision-making during most of the game. This is consistent with the idea that the strategy-using as the method that the brain uses to simplify decision making by ignoring irrelevant game aspects to solve complex tasks (Binz et al, 2020;Moreno-Bote et al, 2020).…”

Decision Prioritization and Causal Reasoning in Decision Hierarchies

“…Therefore, the need to decide which memory, feeling or thought to use to inform a decision may be subject to the same type of arbitration rules that we have identified here. More fundamental differences are that the number of possible sources of evidence bearing on a decision can be vast (Moreno-Bote et al, 2020;Moreno-Bote and Mastrogiuseppe, 2021), that the hypothesis space may need to be expanded during the decision process (Christie and Gentner, 2010;Kemp and Tenenbaum, 2008), and that richer internal models need to be queried to relate individual evaluations to the agent's goals (Coenen et al, 2019). It might be fruitful to extend the paradigm presented here to approximate these more complex aspects of reasoning.…”

Humans balance breadth and depth: Near-optimal performance in many-alternative decision making

“…Despite its relevance to understand how humans make decisions under finite resources, it is remarkable that the breadth-depth dilemma has mostly been investigated outside cognitive neuroscience (Moreno-Bote et al, 2020), in contrast to other well-studied trade-offs like speed-accuracy and exploration-exploitation (J. D. Cohen et al, 2007;Costa et al, 2019;Daw et al, 2006;Ebitz et al, 2018;Wilson et al, 2014). The breadthdepth dilemma underlies virtually all cognitive problems, from allocating attention amongst multiple alternatives in multi-choice decision making (Busemeyer et al, 2019;Hick, 1952;Proctor & Schneider, 2018), splitting encoding precision to items in working memory (Joseph et al, 2016;Ma et al, 2014), to dividing cognitive effort into several ongoing subtasks (Feng et al, 2014;Musslick & Cohen, 2021;Shenhav et al, 2013).…”

“…Previous theoretical work has shown how to optimally trade-off breadth and depth over multi-alternative problems in the situations described above, where resources are allocated all at once before feedback is received (Moreno-Bote et al, 2020;Moreno-Bote & Mastrogiuseppe, 2021;Ramírez-Ruiz & Moreno-Bote, 2021). A central result is that the optimal trade-off depends on the search capacity of the agent: while at low capacity resources should be split in as many alternatives as capacity permits (breadth), at high capacity resources should be focused on a relatively small number of selected alternatives so that available resources are more focused (depth) (Moreno-Bote et al, 2020). In rich environments, where finding options rendering good outcomes is more likely, depth should be further favoured.…”

“…Despite of the existence of precise predictions describing ideal behaviours in these scenarios, how humans solve breadth-depth trade-offs in manyalternative decision making is largely unknown (Brown et al, 2009;Callaway et al, 2021;Chau et al, 2014;A. L. Cohen et al, 2017;Hawkins et al, 2012;Moreno-Bote et al, 2020;Roe et al, 2001;Usher & Mcclelland, 2004;Vul et al, 2014).…”