Efficient sampling and noisy decisions

Abstract

16Noise and information sampling are ubiquitous components determining the precision 17 in our ability to discriminate between decision alternatives, however, the source and 18 nature of these imprecisions is unclear. Moreover, how the nervous system 19 simultaneously considers regularities in the environment, goals of the organism, and 20 capacity constraints to guide goal-directed behavior, remains unknown. To address 21 these issues, we elaborate a biologically-and cognitive-relevant efficient coding 22 mechanism for discrimination, which takes into consideration resource limitations 23 when forming percepts based on information sampling. Crucially, we show that this 24 theory makes it formally explicit why a system that evolved to encode information 25 based on a limited set of discrete samples must rely on noise to optimize decision 26 behavior. Thus, contrary to common assumptions, we demonstrate noise does not 27 necessarily degrade performance, but is an essential component to optimize distinct 28 organism's goals in capacity-limited systems, for instance, maximize the amount of 29 correct responses, or maximize expected fitness. Our theory allowed us to test 30 empirically the hypothesis that humans may efficiently adapt their number sense to 31 maximize fitness, thus providing an evolutionary advantage. Surprisingly, we found 32 that humans employ a less optimal but more flexible sampling mechanism that relies 33 on limited samples drawn from memory of encountered stimuli, irrespective of 34 incentivized goals. Together, these theoretical and empirical findings provide a general 35 mechanistic framework for understanding decision behavior while accounting for 36 biological restrictions of information coding. 37 38 39 40 Page 3 of 33Main text 41 It has been suggested that the rules guiding behavior are not arbitrary, but should 42 follow fundamental principles of acquiring information from environmental 43 regularities in order to make the best decisions. Moreover, these principles should 44 incorporate strategies of information coding that take into consideration the cost of 45 making decisions as well as biological constraints of information acquisition. Therefore, 46 the elaboration and understanding of such unifying theories could help to establish 47 65 precision of discrimination of stimulus features of the latter kind; in particular, the 66 values that must be represented in the case of reward-based decision making(2, 4, 7), 67 which could in turn be beneficial to develop strategies for reward or fitness 68 maximization. Can a unifying theory of efficient coding be developed that reflects 69 constraints on feasible internal representations that is relevant to both cases? 70 Another hallmark in neural systems is the well-known observation that neural 71 activity and behavior are considerably variable trial-to-trial, even when input stimuli is 72 maintained as constant as possible(8-10). However, it remains unclear what actually 73 causes behavioral variability, which is u...

Efficient Coding and Risky Choice

“…4 As emphasized in Ma and Woodford (2020), there are differences in the way that resource constraints are imposed across different models of efficient coding. While we use a specific constraint levied by the Heng et al (2020) model, the main prediction we test is qualitatively similar to other models of efficient coding in sensory perception that assume different constraints, such as Wei and Stocker (2015).…”

“…First, the foundation of our framework is the KLW model, which assumes that the DM observes noisy signals of lottery payoffs and subsequently forms optimal estimates of these payoffs through Bayesian inference. Second, we rely on the efficient coding model from Heng, Woodford, and Polanía (2020) (henceforth HWP) to endogenize the conditional distribution of noisy signals-which is called the "efficient code." As in KLW, our framework generates the probability of choosing a risky lottery over a certain option; but, crucially, by adding the efficient coding mechanism from HWP, we can assess how the probability of choosing the risky lottery varies with the environment.…”

“…3 See also related theoretical work on how efficient coding can serve as a normative foundation for decision-bysampling (Bhui and Gershman, 2018;Heng et al, 2020) and a specific model of normalization (Rustichini, Conen, Cai, and Padoa-Schioppa, 2017). 4 As emphasized in Ma and Woodford (2020), there are differences in the way that resource constraints are imposed across different models of efficient coding.…”

“…For experimental evidence consistent with efficient coding in sensory perception, seeGirshick, Landy, and Simoncelli (2011), Stocker (2015, 2017), Payzan-LeNestour and Woodford (2020), andHeng, Woodford, and Polanía (2020). See also the evidence fromPolanía, Woodford, and Ruff (2019) on efficient coding in choice between food items.…”

Cognitive Imprecision and Stake-Dependent Risk Attitudes

“…Thus the statistics presented in the figures measure the degree of discrepancy with respect to this benchmark, for those trials on which the subject submits a (non-zero) bid. 17 In the case of each lottery, the dot indicates the mean value of log(W T P/EV ), pooling all subjects. The vertical whiskers mark an interval ±s around the mean, where s is the standard deviation of log(W T P ) for an "average" subject, computed as the mean of s.d.…”