A Goal-Set Characterization of Task Composition in the Boolean Task Algebra
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Abstract (arXiv)
The Boolean Task Algebra (BTA) provides a principled framework for zero-shot task composition in reinforcement learning by equipping goal-reaching tasks with Boolean operations. We revisit its structural assumptions and formalize a collapse in the space of optimal extended Q-value functions: in deterministic MDPs, every such function is fully determined by the universal and empty tasks. This makes the logarithmic set of base tasks proposed in the original BTA formulation redundant. Building on this observation, we introduce a goal-set-based composition method that performs logical operations on goal sets and reconstructs composed value functions by selecting slices from the universal and empty value functions. This reduces learning costs for standard BTA and reduces composition time for both BTA and Skill Machines, while preserving policy performance. Experiments across tabular, visual, function-approximation, and continuous-control domains show that learning additional base tasks does not yield better performance. Finally, we study the stochastic setting and provide a counterexample showing that this collapse need not hold, that is, optimal composition may require accounting for exponentially many policies in the number of goals. Code is available at urlhttps://github.com/EduardoTerres/GoalSetBTA.
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References · 12
- 2017Reinforcement Learning with Deep Energy-Based Policiescited by 659
- 2016Successor Features for Transfer in Reinforcement Learningcited by 331
- 2017FeUdal Networks for Hierarchical Reinforcement Learningcited by 328
- 2016Modular Multitask Reinforcement Learning with Policy Sketchescited by 200
- 2020Reward Machines: Exploiting Reward Function Structure in Reinforcement Learningcited by 183
- 2018Universal Successor Features Approximatorscited by 102
- 2017Grounded Language Learning in a Simulated 3D Worldcited by 100
- 2021LTL2Action: Generalizing LTL Instructions for Multi-Task RLcited by 72
- 2018Composable Deep Reinforcement Learning for Robotic Manipulationcited by 70
- 2020A Boolean Task Algebra for Reinforcement Learningcited by 46
- 2021Globally Optimal Hierarchical Reinforcement Learning for Linearly-Solvable Markov Decision Processescited by 6
- 2024Planning with a Learned Policy Basis to Optimally Solve Complex Taskscited by 4
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