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

Battle Count: 52

Highly relevant to quantitative trading. The paper directly addresses non-Markovian environments with jump-diffusions and structural breaks - characteristics of real financial markets. The signature-augmented state space provides a principled way to handle path-dependence in trading strategies. The Anticipatory TD-Error and Single-Pass evaluation offer computational advantages for real-time decision-making. The Signature Greeks enable proactive risk management and policy rectification against anticipated volatility shifts. The framework is explicitly motivated by high-frequency finance applications. However, the lack of empirical validation limits immediate practical applicability.

Extremely high implementation complexity. Requires: (1) Marcus-integral Neural CDE solvers with jump handling, (2) Signature computation up to degree 4 in multi-dimensional spaces, (3) Nyström kernel approximation with landmark selection, (4) Self-Consistent Field optimization with joint parameter updates, (5) Anticipatory TD-error computation via Chen's Identity algebraic operations, (6) AVNSG spectral whitening, (7) Adjoint sensitivity methods for gradient computation, (8) C1-boundary consistency enforcement at temporal junctions. The mathematical prerequisites (Rough Path Theory, tensor algebras, distributional RL) are substantial. No reference implementation is provided.

This is a purely theoretical working paper with no empirical experiments, no code repository, no datasets, and no benchmark results. All proofs are provided in the appendix but no implementation or numerical validation is included. The mathematical framework is highly specialized, requiring expertise in Rough Path Theory, Marcus integration, and distributional RL. Reproduction would require implementing the entire ARL architecture from scratch without reference code.