When and Why Hyperbolic Discounting Matters for Reinforcement Learning Interventions

Ian M. Moore, Eura Nofshin, Siddharth Swaroop, Susan Murphy, Finale Doshi-Velez, Weiwei Pan

Keywords: Reinforcement learning, Hyperbolic discounting, Markov Decision Process, Human as MDP, Agent-based modeling of humans

Abstract: In settings where an AI agent nudges a human agent toward a goal, the AI can quickly learn a high-quality policy by modeling the human well. Despite behavioral evidence that humans hyperbolically discount future rewards, we model human as Markov Decision Processes (MDPs) with exponential discounting. This is because planning is difficult with non-exponential discounts. In this work, we investigate whether the performance benefits of modeling humans as hyperbolic discounters outweigh the computational costs. We focus on AI interventions that change the human's discounting (i.e. decreases the human's "nearsightedness" to help them toward distant goals). We derive a fixed exponential discount factor that can approximate hyperbolic discounting, and prove that this approximation guarantees the AI will never miss a necessary intervention. We also prove that our approximation causes fewer false positives (unnecessary interventions) than the mean hazard rate, another well-known method for approximating hyperbolic MDPs as exponential ones. Surprisingly, our experiments demonstrate that exponential approximations outperform hyperbolic ones in online learning, even when the ground-truth human MDP is hyperbolically discounted.

Submission Number: 59