Low-Complexity Policy Tessellations in Structured Markov Decision Processes

Researchers propose a novel approach to reinforcement learning that approximates optimal policies through geometric tessellations rather than high-dimensional value functions. The method demonstrates superior performance in structured decision problems like inventory control and queue admission, with faster error decay and greater stability compared to traditional RL baselines.

This research represents a meaningful theoretical advance in how machine learning systems can approach decision-making problems. Rather than following the conventional path of approximating complex value functions in high-dimensional spaces, the authors identify that optimal policies exhibit simpler geometric structures that can be directly modeled as decision boundaries or tessellations. This geometric insight has practical implications for algorithm design and computational efficiency.

The work builds on established understanding of Markov decision processes while introducing a fresh perspective on policy representation. By decomposing policy loss into components related to action margins and indifference boundaries, the researchers provide interpretable explanations for where approximation errors concentrate. This analytical framework helps explain why traditional approaches often struggle near decision boundaries where the agent is uncertain between actions.

The experimental validation on inventory control and queue admission problems demonstrates tangible benefits: lower policy error rates, smaller value gaps, faster convergence, and improved stability. These aren't theoretical advantages but practical improvements that matter for real-world applications. Inventory optimization and queue management represent significant operational challenges across industries, making this validation particularly relevant.

The implications extend beyond these specific domains. Any structured decision problem with geometric properties—including resource allocation, network routing, and financial trading—could potentially benefit from boundary-based policy approximation. The approach may be especially valuable in settings where computational resources are constrained or where interpretability matters, since policy regions are inherently more interpretable than opaque value functions.

• →Optimal policies in structured MDPs exhibit simpler geometric tessellation structures than the value functions they induce, enabling more direct approximation methods.
• →Policy-loss decomposition identifies that approximation errors concentrate near indifference boundaries where action margins are small, explaining RL baseline shortcomings.
• →Boundary-based policy learning outperforms traditional RL on inventory control and queue admission tasks with faster convergence and greater stability.
• →The geometric policy representation provides interpretability advantages over value-function approaches by directly modeling decision regions.
• →The framework potentially extends to diverse structured decision problems including resource allocation, routing, and financial optimization.