Formal Guarantees for Dynamic Action Space Pruning: Towards Theoretical Foundations of DynaAct

Research Question: Can we develop formal mathematical models and theoretical guarantees for DynaAct's action space optimization process, providing bounds on reasoning performance and computational efficiency?

Hypothesis: By framing dynamic action space pruning as a submodular maximization problem under resource constraints, we can derive provable guarantees (e.g., approximation ratios, sample complexity) for the resulting reasoning outcomes, informing principled algorithm design.

Experiment Plan: - Formally specify the DynaAct action space selection as a submodular maximization subject to cardinality or cost constraints.

• Derive theoretical bounds (e.g., via greedy approximation guarantees, lower bounds on candidate set expressivity).
• Validate these theoretical insights empirically by comparing DynaAct's performance to theoretical predictions on benchmark tasks.
• Explore extensions (e.g., stochastic or adversarial action spaces) and analyze robustness.

References: ['Zhao, X., Wu, W., Guan, J., Li, Q., & Kong, L. (2025). DynaAct: Large Language Model Reasoning with Dynamic Action Spaces.', 'Noarov, G., Ramalingam, R., Roth, A., & Xie, S. (2023). High-Dimensional Prediction for Sequential Decision Making. arXiv.org.', 'Wang, M., Liu, X., Yi, S., Wu, L., Zhao, H., Pan, F., Cai, Q., & Jiang, P. (2025). Hierarchical Semantic RL: Tackling the Problem of Dynamic Action Space for RL-based Recommendations. arXiv.org.']