The Dually Flat Geometry of Planning as Inference

2026-09-03

AI Summary

本文通过将规划标准嵌入动力学中，重新定义了强化学习的占用度量，并利用对偶平坦几何结构解决非线性奖励函数下的规划问题。

Abstract

We present an alternative characterization of the occupancy measure of reinforcement learning, obtained by embedding the planning criterion into the dynamics through a resetting planning process. Its stationary measure, which we term visitation measure, is the object on which the information geometry of decision making is most naturally expressed. The achievable visitation measures form a dually flat statistical manifold whose two affine charts are the visitation probabilities and the log-policies, dual under the conditional entropy. This structure makes planning-as-inference generalize from linear rewards to nonlinear functionals of the visitation, each iterate solved by one natural-gradient step, and gives the temporal-difference error the interpretation of a marginal-utility estimate. We develop the geometry and its consequences for reinforcement learning and theoretical neuroscience.

Problem

• reinforcement learning
• information geometry
• planning as inference
• visitation measure
• dually flat statistical manifold

Innovation

• dually flat geometry
• visitation measure
• natural-gradient step
• planning-as-inference
• temporal-difference error