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

Paper: arXiv 2604.04662

Authors: Daniel Bloch

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically sophisticated framework combining rough path theory (rough signatures) and anticipatory reinforcement learning to handle non-Markovian environments. However, the theoretical focus leaves empirical validation, backtesting rigor, and reproducible implementation details underdeveloped in the provided abstract.

Research Flowchart

  flowchart TD
    A["Research Goal: RL in Non-Markovian, Jump-Diffusion Environments (Single Trajectory)"] --> B["Input: Continuous-Time Path History & Heavy-Tailed Noise Data"]
    B --> C["Lift State Space to Signature-Augmented Manifold"]
    C --> D["Apply Self-Consistent Field for Anticipatory Proxy Path-Law"]
    D --> E["Deterministic Single-Pass Linear Evaluation of Returns"]
    E --> F["Outcomes: Reduced Variance, Contraction Preservation & Stable Proactive Policy"]