Bounded Rationality, Abstraction, and Hierarchical Decision-Making: An Information-Theoretic Optimality Principle

Abstract

Abstraction and hierarchical information processing are hallmarks of human and animal intelligence underlying the unrivaled flexibility of behavior in biological systems. Achieving such flexibility in artificial systems is challenging, even with more and more computational power. Here, we investigate the hypothesis that abstraction and hierarchical information processing might in fact be the consequence of limitations in information-processing power. In particular, we study an information-theoretic framework of bounded rational decision-making that trades off utility maximization against information-processing costs. We apply the basic principle of this framework to perception-action systems with multiple information-processing nodes and derive bounded-optimal solutions. We show how the formation of abstractions and decision-making hierarchies depends on information-processing costs. We illustrate the theoretical ideas with example simulations and conclude by formalizing a mathematically unifying optimization principle that could potentially be extended to more complex systems.

An information-theoretic perspective on the costs of cognition

“…This lack of knowledge of statistical properties of the task leads to non-optimal encoding and large information costs. This is because participants will have to start from uninformative prior distributions p 0 (z), p 0 (y) and p 0 (y|z) that may be far from the true marginal distributions of the task, which they will have to learn across trial repetitions (Genewein et al, 2015;. In this case the additional cost of starting with the wrong priors can be formalized as:…”

“…Beyond this level of compression, relevant information is necessarily discarded and distortion starts to increase, leading to lossy compression. This trade-off is usually implemented as a parameter that constraints the capacity (or maximal mutual information) of the system (Alemi et al, 2016;Denève et al, 2017;Genewein et al, 2015;Kingma and Welling, 2013;Ortega and Braun, 2013;Tishby et al, 2000): , where U represents some utility measure and is a (Lagrangian) factor that adjusts the trade-off between costs and performance. In order to apply this framework to behavioural data, this parameter then has to be fit to observed performance data (Sims, 2016).…”

“…Serial processing has the major drawback that total information capacity of the system is equal to the information capacity of its weakest link (Genewein et al, 2015). In contrast, parallel processing consists in architectures in which the outputs from high-level processes provide priors, rather than inputs, to low-level processes (Genewein et al, 2015) and in which the information capacities of the individual parts sum up. Here, while we consider perceptual processing as a serial process (information is first stored in a variable z and then processed further to provide response y) automatic and context-dependent processes follow a parallel architecture, in which the outcome of the automatic process is fed as a prior into the contextdependent one.…”

“…These views shed light on the potential adaptive value of cost-avoidance mechanisms.Keywords: cognitive effort, information theory, active inference, predictive coding, efficient coding, computational neuroscience Recent advances in artificial intelligence and computational neuroscience have led to formalization of cognition as a bounded rationality process (Friston, 2010;Kingma and Welling, 2013;Ortega and Braun, 2013;Tishby et al, 2000;Tkačik and Bialek, 2014).According to this view, rather than aiming systematically at the optimal solution to computational problems, cognitive processes trade off performance with computational costs.Remarkably, the way computational costs are formalized across these different studies is very consistent, despite their different approaches. In fact, whether one starts from an inference problem, in which the evidence for a model is maximized given some data (Genewein et al, 2015;Kingma and Welling, 2013;Tishby et al, 2000), or whether one is more generally attempting to minimize the entropy of future states (Friston, 2010), or whether one takes a decision making perspective, in which expected utility is maximized (Ortega et al, 2015), or even from the point of view of thermodynamics (Ortega and Braun, 2013;Sengupta et al, 2013), information cost is framed as a measure of divergence between an initial belief (or prior probability distribution over a variable of interest x, such as expected reward) and an updated belief (or posterior probability distribution over the same variable x) obtained after receiving new data. This measure of difference between probability distributions, called the Kullback-Leibler (KL) divergence, represents the amount of information one needs to collect in order to update the prior to the posterior ( for probability distributions P and Q).…”

“…Remarkably, the way computational costs are formalized across these different studies is very consistent, despite their different approaches. In fact, whether one starts from an inference problem, in which the evidence for a model is maximized given some data (Genewein et al, 2015;Kingma and Welling, 2013;Tishby et al, 2000), or whether one is more generally attempting to minimize the entropy of future states (Friston, 2010), or whether one takes a decision making perspective, in which expected utility is maximized (Ortega et al, 2015), or even from the point of view of thermodynamics (Ortega and Braun, 2013;Sengupta et al, 2013), information cost is framed as a measure of divergence between an initial belief (or prior probability distribution over a variable of interest x, such as expected reward) and an updated belief (or posterior probability distribution over the same variable x) obtained after receiving new data. This measure of difference between probability distributions, called the Kullback-Leibler (KL) divergence, represents the amount of information one needs to collect in order to update the prior to the posterior ( for probability distributions P and Q).…”