Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions, reflecting varying levels of structural uncertainty. Under this fourth notion of uncertainty, choices were no better explained by Bayesian updating than by (model-free) reinforcement learning. Exit questionnaires revealed that participants remained unaware of the presence of unexpected uncertainty and failed to acquire the right model with which to implement Bayesian updating

Searching for rewards in graph-structured spaces

How do people generalize and explore structured spaces? We study human behavior on a multi-armed bandit task, where rewards are influenced by the connectivity structure of a graph. A detailed predictive model comparison shows that a Gaussian Process regression model using a diffusion kernel is able to best describe participant choices, and also predict judgments about expected reward and confidence. This model unifies psychological models of function learning with the Successor Representation used in reinforcement learning, thereby building a bridge between different models of generalization

VIME: Variational Information Maximizing Exploration

Scalable and effective exploration remains a key challenge in reinforcement learning (RL). While there are methods with optimality guarantees in the setting of discrete state and action spaces, these methods cannot be applied in high-dimensional deep RL scenarios. As such, most contemporary RL relies on simple heuristics such as epsilon-greedy exploration or adding Gaussian noise to the controls. This paper introduces Variational Information Maximizing Exploration (VIME), an exploration strategy based on maximization of information gain about the agent's belief of environment dynamics. We propose a practical implementation, using variational inference in Bayesian neural networks which efficiently handles continuous state and action spaces. VIME modifies the MDP reward function, and can be applied with several different underlying RL algorithms. We demonstrate that VIME achieves significantly better performance compared to heuristic exploration methods across a variety of continuous control tasks and algorithms, including tasks with very sparse rewards.Comment: Published in Advances in Neural Information Processing Systems 29 (NIPS), pages 1109-111