When and Why Hyperbolic Discounting Matters for Reinforcement Learning Interventions

In settings where an AI agent nudges a human agent toward a goal, the quality of the AI's policy depends on how well it models the human. Despite behavioral evidence that humans hyperbolically discount future rewards, the RL community continues to model humans 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.