Law-Strength Frontiers and a No-Free-Lunch Result for Law-Seeking Reinforcement Learning on Volatility Law Manifolds

Battle Count: 75

Highly relevant to quantitative trading as it directly addresses the interaction between RL agents and no-arbitrage constraints in volatility modeling. The paper demonstrates that naive and law-penalized RL on learned world models systematically exploit ghost arbitrage rather than discovering genuine law-consistent edges. The finding that simple structural baselines (Zero-Hedge, Vol-Trend) dominate RL on the joint P&L-law-tail frontier has direct implications for trading system design. The Goodhart decomposition and law-strength frontier framework provides practical tools for evaluating RL-based trading strategies. However, the paper is primarily a negative result / diagnostic study rather than proposing a new trading system.

The theoretical framework involves convex optimization, projection operators onto polyhedral sets, and multi-objective Pareto analysis. The empirical pipeline requires: (1) a synthetic IV-surface generator with stochastic volatility dynamics, (2) a GRU/LSTM world model trained on surface trajectories, (3) PPO-based RL with law-penalty shaping, (4) convex QP for projection onto the law manifold, (5) multi-regime evaluation with shock scenarios, and (6) frontier construction across multiple metrics. The code is described as Gym-style with standard deep learning frameworks, but the full pipeline with all diagnostics and frontier plots is non-trivial to reproduce.

The paper provides detailed experimental setup including hyperparameters, grid specifications, and evaluation protocols. However, results are based on single-seed runs (case-study evidence), no GitHub repository is mentioned, and the synthetic generator parameters are not fully specified. The code is described as organized in configuration files but not publicly linked. The theoretical framework is well-defined with proofs in appendices, but empirical reproducibility is limited by single-seed experiments.