MePoly: Max Entropy Polynomial Policy Optimization
arXiv:2602.17832v1 Announce Type: new Abstract: Stochastic Optimal Control provides a unified mathematical framework for solving complex decision-making problems, encompassing paradigms such as maximum entropy reinforcement learning(RL) and imitation learning(IL). However, conventional parametric policies often struggle to represent the multi-modality of the solutions. Though diffusion-based policies are aimed at recovering the multi-modality, they lack an explicit probability density, which complicates policy-gradient optimization. To bridge this gap, we propose MePoly, a novel policy parameterization based on polynomial energy-based models. MePoly provides an explicit, tractable probability density, enabling exact entropy maximization. Theoretically, we ground our method in the classical moment problem, leveraging the universal approximation capabilities for arbitrary distributions. Empirically, we demonstrate that MePoly effectively captures complex non-convex manifolds and outperf
arXiv:2602.17832v1 Announce Type: new Abstract: Stochastic Optimal Control provides a unified mathematical framework for solving complex decision-making problems, encompassing paradigms such as maximum entropy reinforcement learning(RL) and imitation learning(IL). However, conventional parametric policies often struggle to represent the multi-modality of the solutions. Though diffusion-based policies are aimed at recovering the multi-modality, they lack an explicit probability density, which complicates policy-gradient optimization. To bridge this gap, we propose MePoly, a novel policy parameterization based on polynomial energy-based models. MePoly provides an explicit, tractable probability density, enabling exact entropy maximization. Theoretically, we ground our method in the classical moment problem, leveraging the universal approximation capabilities for arbitrary distributions. Empirically, we demonstrate that MePoly effectively captures complex non-convex manifolds and outperforms baselines in performance across diverse benchmarks.
Executive Summary
This article proposes MePoly, a novel policy parameterization for stochastic optimal control problems, leveraging polynomial energy-based models to bridge the gap between conventional parametric policies and diffusion-based policies. MePoly provides an explicit, tractable probability density, enabling exact entropy maximization. Theoretically, the method is grounded in the classical moment problem, and empirically, it outperforms baselines in diverse benchmarks. This work has significant implications for maximum entropy reinforcement learning and imitation learning, as it enables more effective representation of complex decision-making problems.
Key Points
- ▸ MePoly uses polynomial energy-based models to parameterize policies
- ▸ MePoly provides an explicit, tractable probability density for exact entropy maximization
- ▸ The method is grounded in the classical moment problem and has universal approximation capabilities
Merits
Strength in Representation
MePoly's use of polynomial energy-based models enables more effective representation of complex decision-making problems, particularly in cases where conventional parametric policies struggle to capture multi-modality.
Improved Optimization
MePoly's tractable probability density enables exact entropy maximization, which can lead to more efficient and effective policy-gradient optimization.
Theoretical Foundation
MePoly's grounding in the classical moment problem provides a strong theoretical foundation for its universal approximation capabilities.
Demerits
Computational Complexity
MePoly may require significant computational resources, particularly in high-dimensional spaces, which could limit its practical applicability.
Limited Experimental Evaluation
While the article provides some empirical results, further experimental evaluation is needed to fully understand MePoly's performance in a wider range of scenarios.
Expert Commentary
MePoly is a significant contribution to the field of stochastic optimal control, as it addresses a key limitation of conventional parametric policies. The use of polynomial energy-based models to provide an explicit, tractable probability density for exact entropy maximization is a novel and effective approach. However, further experimental evaluation is needed to fully understand MePoly's performance in a wider range of scenarios. Additionally, the computational complexity of MePoly may limit its practical applicability, particularly in high-dimensional spaces.
Recommendations
- ✓ Further experimental evaluation is needed to fully understand MePoly's performance in a wider range of scenarios.
- ✓ The developers should explore ways to reduce the computational complexity of MePoly, such as using approximation techniques or parallel processing.
