Beyond Gradient Descent: Variational Automata for Reinforcement Learning

How Structured Constraints and Information Geometry Could Redefine Policy Optimization

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What if your reinforcement learning agent could not only explore but reason within constraints, as if guided by the grammar of logic itself?
This post introduces Variational Automata for RL (VAC-RL): a structured, mathematically rigorous approach to aligning agents with rules, safety, and interpretability.

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The Problem We Solve

Classical RL methods (e.g., PPO, SAC) assume policies explore in continuous probability spaces with no built-in knowledge of rules (like grammar, safety constraints, or logical sequences).
This leads to:

• Unsafe behavior in robotics or autonomous driving.

• Grammatically invalid outputs in text generation.

• Slow convergence due to wasted exploration in invalid regions.

We need a way to embed automata-based constraints directly into the optimization landscape.

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The Solution

We design Variational Automata for RL: