Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functions

• URL: http://arxiv.org/abs/2604.04662v1
• Date: Mon, 06 Apr 2026 13:15:44 GMT
• Title: Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functions
• Abstract summary: This paper introduces Anticipatory Reinforcement Learning (ARL), a novel framework designed to bridge the gap between non-Markovian decision processes and classical reinforcement learning architectures.<n>In environments characterised by jump-diffusions and structural breaks, traditional state-based methods often fail to capture the essential path-dependent geometry required for accurate foresight.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces Anticipatory Reinforcement Learning (ARL), a novel framework designed to bridge the gap between non-Markovian decision processes and classical reinforcement learning architectures, specifically under the constraint of a single observed trajectory. In environments characterised by jump-diffusions and structural breaks, traditional state-based methods often fail to capture the essential path-dependent geometry required for accurate foresight. We resolve this by lifting the state space into a signature-augmented manifold, where the history of the process is embedded as a dynamical coordinate. By utilising a self-consistent field approach, the agent maintains an anticipated proxy of the future path-law, allowing for a deterministic evaluation of expected returns. This transition from stochastic branching to a single-pass linear evaluation significantly reduces computational complexity and variance. We prove that this framework preserves fundamental contraction properties and ensures stable generalisation even in the presence of heavy-tailed noise. Our results demonstrate that by grounding reinforcement learning in the topological features of path-space, agents can achieve proactive risk management and superior policy stability in highly volatile, continuous-time environments.

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