Bayesian Brains and the Rényi Divergence

Area of Science:

• Cognitive Neuroscience
• Computational Psychiatry
• Decision Theory

Background:

• Behavioral variability in decision-making is often explained by differing prior beliefs in the Bayesian brain hypothesis.
• Greedy preferences can arise from confident beliefs about specific outcomes.

Purpose of the Study:

• To propose an alternative framework for understanding behavioral variability using Rényi divergences and variational bounds.
• To demonstrate how a single parameter (α) can account for diverse behavioral preferences and posterior estimates.

Main Methods:

• Utilized Rényi divergences and their associated variational bounds, analogous to variational free energy.
• Introduced a continuous parameter α to modulate the variational bounds and influence posterior estimates.
• Simulated the multiarmed bandit task to exemplify the proposed formulation.

Main Results:

• Changes in the α parameter systematically alter variational bounds, leading to different posterior estimates and behavioral variations.
• α→0+ optimization results in mass-covering variational estimates and increased choice variability.
• α→+∞ optimization leads to mass-seeking variational posteriors and greedy preferences.

Conclusions:

• Rényi bounds offer a formal mechanism to explain behavioral differences through variations in the α parameter, independent of differing priors.
• This framework provides a potentially useful explanation for individual differences in behavior for both biological and artificial agents assuming variational Bayesian inference.
• The α parameterization is particularly relevant when the true posterior distribution differs from the assumed approximate density.