Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process

Abstract

Abstraction is a critical technique in general problem-solving, allowing complex tasks to be decomposed into smaller, manageable sub-tasks. While traditional symbolic planning relies on predefined primitive symbols to construct structured abstractions, its reliance on formal representations limits applicability to real-world tasks. On the other hand, reinforcement learning excels at learning end-to-end policies directly from sensory inputs in unstructured environments but struggles with compositional generalization in complex tasks with delayed rewards. In this paper, we propose Abductive Abstract Reinforcement Learning (A2RL), a novel neuro-symbolic RL framework bridging the two paradigms based on Abductive Learning (ABL), enabling RL agents to learn abstractions directly from raw sensory inputs without predefined symbols. A2RL induces a finite state machine to represent high-level, step-by-step procedures, where each abstract state corresponds to a sub-algebra of the original Markov Decision Process (MDP). This approach not only bridges the gap between symbolic abstraction and sub-symbolic learning but also provides a natural mechanism for the emergence of new symbols. Experiments show that A2RL can mitigate the delayed reward problem and improve the generalization capability compared to traditional end-to-end RL methods.