Hyperbolic Discounting and Learning over Multiple Horizons

TL;DR

This paper explores hyperbolic discounting in reinforcement learning, proposing a simple method to incorporate it and discovering that learning over multiple horizons enhances RL performance.

Contribution

It introduces a straightforward approach to implement hyperbolic discounting in RL and reveals the benefits of multi-horizon value learning as an auxiliary task.

Findings

Hyperbolic discounting can be approximated with simple modifications in RL.

Learning value functions over multiple horizons improves RL performance.

Multi-horizon learning often outperforms standard RL agents.

Abstract

Reinforcement learning (RL) typically defines a discount factor as part of the Markov Decision Process. The discount factor values future rewards by an exponential scheme that leads to theoretical convergence guarantees of the Bellman equation. However, evidence from psychology, economics and neuroscience suggests that humans and animals instead have hyperbolic time-preferences. In this work we revisit the fundamentals of discounting in RL and bridge this disconnect by implementing an RL agent that acts via hyperbolic discounting. We demonstrate that a simple approach approximates hyperbolic discount functions while still using familiar temporal-difference learning techniques in RL. Additionally, and independent of hyperbolic discounting, we make a surprising discovery that simultaneously learning value functions over multiple time-horizons is an effective auxiliary task which often improves over a strong value-based RL agent, Rainbow.