Model-Based Uncertainty in Value Functions

TL;DR

This paper introduces a new uncertainty Bellman equation for better quantification of value function uncertainty in model-based reinforcement learning, leading to improved exploration and sample efficiency.

Contribution

It presents a novel uncertainty Bellman equation that accurately estimates posterior variance over values, enhancing exploration strategies in RL.

Findings

Sharper uncertainty estimates improve sample efficiency.

Method scales to deep RL architectures.

Enhanced exploration in complex tasks.

Abstract

We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertainty quantification technique is easily integrated into common exploration strategies and scales naturally beyond the tabular setting by using standard deep reinforcement learning architectures. Experiments in difficult exploration tasks, both in tabular and continuous control settings, show that our sharper uncertainty estimates improve sample-efficiency.