Transitive RL: Value Learning via Divide and Conquer

TL;DR

Transitive Reinforcement Learning (TRL) introduces a divide-and-conquer approach for value learning in offline goal-conditioned RL, reducing bias and variance issues and excelling in long-horizon tasks.

Contribution

The paper proposes TRL, a novel value learning algorithm leveraging triangle inequality structure for improved bias and variance management in offline GCRL.

Findings

TRL outperforms previous algorithms on long-horizon benchmarks.

TRL requires fewer recursive updates than TD methods.

Experimental results demonstrate superior performance in challenging tasks.

Abstract

In this work, we present Transitive Reinforcement Learning (TRL), a new value learning algorithm based on a divide-and-conquer paradigm. TRL is designed for offline goal-conditioned reinforcement learning (GCRL) problems, where the aim is to find a policy that can reach any state from any other state in the smallest number of steps. TRL converts a triangle inequality structure present in GCRL into a practical divide-and-conquer value update rule. This has several advantages compared to alternative value learning paradigms. Compared to temporal difference (TD) methods, TRL suffers less from bias accumulation, as in principle it only requires $O(\log T)$ recursions (as opposed to $O(T)$ in TD learning) to handle a length-$T$ trajectory. Unlike Monte Carlo methods, TRL suffers less from high variance as it performs dynamic programming. Experimentally, we show that TRL achieves the best performance in highly challenging, long-horizon benchmark tasks compared to previous offline GCRL algorithms.