Adaptive information-theoretic bounded rational decision-making with parametric priors
This provides a more realistic model of human decision-making processes, though it is incremental as it builds on existing information-theoretic frameworks.
The paper tackles the problem of modeling bounded rational decision-making with information-processing costs by deriving a sampling-based update rule that avoids infeasible operations like partition sums, showing convergence to the optimal prior in simulations for discrete domains.
Deviations from rational decision-making due to limited computational resources have been studied in the field of bounded rationality, originally proposed by Herbert Simon. There have been a number of different approaches to model bounded rationality ranging from optimality principles to heuristics. Here we take an information-theoretic approach to bounded rationality, where information-processing costs are measured by the relative entropy between a posterior decision strategy and a given fixed prior strategy. In the case of multiple environments, it can be shown that there is an optimal prior rendering the bounded rationality problem equivalent to the rate distortion problem for lossy compression in information theory. Accordingly, the optimal prior and posterior strategies can be computed by the well-known Blahut-Arimoto algorithm which requires the computation of partition sums over all possible outcomes and cannot be applied straightforwardly to continuous problems. Here we derive a sampling-based alternative update rule for the adaptation of prior behaviors of decision-makers and we show convergence to the optimal prior predicted by rate distortion theory. Importantly, the update rule avoids typical infeasible operations such as the computation of partition sums. We show in simulations a proof of concept for discrete action and environment domains. This approach is not only interesting as a generic computational method, but might also provide a more realistic model of human decision-making processes occurring on a fast and a slow time scale.