SDTA-MDP: Symbolic Distributed Time Aggregation for Continuous Control

Existing methods address continuous-state Markov decision processes (MDPs) with continuous actions, but balancing control performance, computational cost, and interpretability remains challenging. We propose Symbolic Distributed Time-Aggregated MDP solving (SDTA-MDP). Building on symbolic state partitioning, the framework combines time aggregation over semantic partitions with local control for finite and bounded continuous actions. The topology groups states by feasible program behavior and summarizes block interiors through absorption cost, duration, and successor probabilities. SDTA-MDP solves a frontier semi-Markov decision process with time aggregation and passes the resulting block actions to local controllers for action selection. We establish path signature preservation and bound the effect of absorption estimation error on the frontier Bellman update. Experiments show that SDTA-MDP achieves higher success rates and lower costs than the evaluated baselines on selected stochastic tasks. For environments supplying executable dynamics and branch predicates, the framework organizes continuous states into interpretable symbolic blocks and summarizes their temporal behavior for control.