A Goal-Set Characterization of Task Composition in the Boolean Task Algebra

Researchers demonstrate that the Boolean Task Algebra (BTA) framework for reinforcement learning can be substantially simplified by eliminating redundant base tasks. Their goal-set-based composition method achieves comparable performance while reducing computational costs for both learning and composition across diverse environments, with experiments showing that additional base tasks provide no performance benefits.

This research addresses a fundamental inefficiency in how reinforcement learning systems compose complex tasks from simpler ones. The Boolean Task Algebra previously required learning a logarithmic set of base tasks to enable zero-shot composition through Boolean operations, but this study reveals that in deterministic environments, all optimal value functions collapse to being fully determined by just two functions: the universal and empty tasks. This theoretical insight has direct practical implications—the researchers demonstrate that their simplified goal-set-based approach preserves policy performance while substantially reducing both the number of tasks requiring training and the time needed to compose new behaviors. The work validates this finding across multiple experimental domains, from tabular and visual environments to continuous control problems, showing consistent evidence that learning beyond these two reference tasks yields no measurable gains.

The broader context involves ongoing efforts to make reinforcement learning more sample-efficient and scalable. Task composition represents an important frontier—the ability to leverage knowledge from existing tasks to quickly solve new problems without retraining. The original BTA framework was conceptually elegant but computationally expensive. By identifying the mathematical redundancy and proposing a method that exploits this collapse, the researchers enable practitioners to achieve equivalent results with substantially fewer computational requirements. This is particularly valuable for robotics and continuous-control applications where training costs remain prohibitive.

The stochastic setting analysis adds important nuance, revealing that this simplification does not universally apply and optimal composition may require exponentially many policies in stochastic environments. This distinction matters for real-world deployment where environments contain uncertainty.

• →Boolean Task Algebra can be simplified to use only universal and empty tasks without performance loss in deterministic environments
• →Goal-set-based composition reduces learning costs and composition time compared to standard BTA approaches
• →Experiments across multiple domains confirm that learning additional base tasks provides no performance benefits
• →Stochastic environments require different approaches, as the collapse property may not hold with environment noise
• →Code availability enables reproducibility and practical adoption of the simplified framework