Reinforcement Learning for Long-Horizon Unordered Tasks: From Boolean to Coupled Reward Machines

Researchers introduce coupled reward machines (CRMs) and the QCoRM algorithm to improve reinforcement learning efficiency for long-horizon tasks with unordered subtasks. The approach scales exponentially better than existing methods by using compact reward representations and task decomposition, with validation across discrete and continuous environments.

This research addresses a fundamental scalability challenge in reinforcement learning where traditional reward machines become computationally intractable for problems involving multiple independent subtasks. The core innovation lies in recognizing that unordered subtasks create exponential complexity in standard RM formulations—a problem that compounds as task quantities increase. By introducing coupled reward machines that track remaining subtasks through agendas, the authors decouple task representations, reducing information growth from exponential to polynomial. The QCoRM algorithm combines this structural innovation with Q-learning-based task decomposition while maintaining optimality guarantees in tabular settings, demonstrating practical advantages across four distinct domains.

The work emerges from growing recognition within the RL community that real-world problems rarely present perfectly sequential task structures. Manufacturing workflows, robotics pipelines, and autonomous systems frequently permit flexible task ordering. Prior reward machine research struggled with such flexibility because state-space representations exploded combinatorially. Coupled RMs solve this by associating reward machine states with specific subtask agendas rather than global task sequences.

For practitioners developing RL systems, this research offers immediately applicable techniques for hierarchical task decomposition. The algorithm's preservation of global optimality guarantees in tabular settings provides theoretical confidence for implementation. The cross-domain validation—including both discrete and continuous action/state spaces—indicates broad applicability beyond academic benchmarks. As RL moves toward industrial deployment in robotics and autonomous systems, efficient handling of unordered task structures becomes increasingly critical. Future work will likely focus on scaling these methods to deep RL settings and handling more complex task dependencies.

• →Coupled reward machines eliminate exponential state-space growth by tracking task agendas rather than global orderings
• →QCoRM algorithm preserves optimality guarantees while decomposing long-horizon problems with unordered subtasks
• →Method scales effectively across both discrete and continuous action/state environments
• →Research addresses practical bottleneck limiting RL deployment in real-world flexible-task scenarios
• →Numeric and agenda-based RM generalizations provide compact task representation frameworks