Not all uncertainty is alike: volatility, stochasticity, and exploration

TL;DR

This paper distinguishes different sources of environmental uncertainty, showing that volatility promotes exploration while stochasticity suppresses it, and introduces a new exploration method called CAUSE that leverages this insight.

Contribution

It formally characterizes the opposite effects of volatility and stochasticity on exploration and develops CAUSE, a novel exploration bonus based on control-as-inference.

Findings

Volatility enhances exploration, stochasticity suppresses it.

CAUSE outperforms standard strategies in noisy environments.

Reversed exploration occurs with pathological noise inference.

Abstract

Adaptive decision-making in biological and artificial intelligence requires balancing the exploitation of known outcomes with the exploration of uncertain alternatives. Although prior work suggests that uncertainty generally promotes exploration, it has typically treated distinct sources of environmental uncertainty as equivalent. We consider environments with latent reward states that drift over time (volatility) and are observed through noisy outcomes (stochasticity). Both increase posterior uncertainty, yet we show they drive optimal exploration in opposite directions: volatility enhances it, stochasticity suppresses it. We establish this asymmetry formally by extending the Gittins index framework to Gaussian state-space bandits with latent dynamics. We further derive Cause-Aware Uncertainty-Sensitive Exploration (CAUSE), a closed-form exploration bonus obtained via control-as-inference that inherits the same monotonicities. CAUSE outperforms standard exploration strategies in environments with heterogeneous noise structure, and also improves on a Gittins-per-arm policy whose rested-bandit optimality does not transfer to restless settings. Learning and exploration are governed by the same noise-inference asymmetry, and the framework predicts that pathological noise inference produces \emph{reversed} rather than merely impaired exploration, with implications for computational accounts of psychiatric conditions.