Reinforcement Learning with Pairwise Preferences in Long-Term Decision Problems
This work provides a theoretically grounded and computationally efficient framework for reinforcement learning with pairwise preferences, addressing inefficiencies and lack of guarantees in long-term decision problems.
The paper introduces the Markov decision contest (MDC) as a new model for reinforcement learning with pairwise preferences, proving that stationary Markov policies are optimal among history-dependent policies, that solving MDCs exactly is in P, and that a simple iterative algorithm converges sublinearly. In high-dimensional long-horizon problems, the proposed approximate algorithm significantly outperforms prior methods in learning efficiency.
Reinforcement learning problems typically define the goal as maximizing the expected value of a scalar reward function. But, pairwise preferences are often easier to specify than scalar rewards, and they express certain goals that scalar rewards cannot. Methods for reinforcement learning with pairwise preferences have thus received growing interest. Unfortunately, these methods are inefficient in problems with long time horizons, and they lack guarantees on the performance of Markov policies relative to history-dependent policies, which bridge the theory and practice of reinforcement learning. We therefore propose the \textit{Markov decision contest} as a new problem model for reinforcement learning with pairwise preferences. We prove that stationary Markov policies are optimal among all history-dependent policies, that solving a Markov decision contest exactly is in P, and that a simple iterative algorithm converges to an optimal policy at a sublinear rate. Lastly, in a set of high-dimensional decision problems with long time horizons, we show that our approximate algorithm is significantly more learning-efficient than prior work.