Fixed-Horizon Temporal Difference Methods for Stable Reinforcement Learning

TL;DR

This paper introduces fixed-horizon temporal difference methods for reinforcement learning, which predict rewards over a set number of steps and avoid stability issues of traditional off-policy TD methods, with proven convergence.

Contribution

The paper presents a novel fixed-horizon TD approach that is immune to the deadly triad stability problems and demonstrates its effectiveness and convergence.

Findings

Fixed-horizon methods are stable and avoid the deadly triad.

They can be used competitively with Q-learning.

Convergence is proven for linear and general function approximation.

Abstract

We explore fixed-horizon temporal difference (TD) methods, reinforcement learning algorithms for a new kind of value function that predicts the sum of rewards over a $\textit{fixed}$ number of future time steps. To learn the value function for horizon $h$, these algorithms bootstrap from the value function for horizon $h-1$, or some shorter horizon. Because no value function bootstraps from itself, fixed-horizon methods are immune to the stability problems that plague other off-policy TD methods using function approximation (also known as "the deadly triad"). Although fixed-horizon methods require the storage of additional value functions, this gives the agent additional predictive power, while the added complexity can be substantially reduced via parallel updates, shared weights, and $n$-step bootstrapping. We show how to use fixed-horizon value functions to solve reinforcement learning problems competitively with methods such as Q-learning that learn conventional value functions. We also prove convergence of fixed-horizon temporal difference methods with linear and general function approximation. Taken together, our results establish fixed-horizon TD methods as a viable new way of avoiding the stability problems of the deadly triad.