Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version

A team of researchers including Dorival Leão, Alberto Ohashi, and Simone Scotti has published a 74-page paper introducing a new machine learning methodology for solving complex stochastic control problems. Their work focuses on "fully non-Markovian" systems where current states depend on entire historical paths rather than just recent information—common in sophisticated financial models like rough-volatility hedging, path-dependent options, and systems driven by fractional Brownian motion. The core innovation is an "off-model training" architecture that generates a single synthetic dataset under a reference model, then uses importance sampling with explicit Radon-Nikodym weights to adapt the AI to different target models without regenerating training data.

This approach enables what the authors call "adaptive learning under parametric model uncertainty." Instead of requiring expensive retraining when model parameters change (a common occurrence in financial calibration), their method allows the AI to adapt by simply reweighting the existing training sample. The paper establishes non-asymptotic error bounds for neural network approximations and provides quantitative estimates separating Monte Carlo approximation error from model-risk error. Numerical experiments on structured linear-quadratic problems demonstrate both the off-model training mechanism and the adaptive importance-sampling update in action, showing practical viability for computationally intensive financial applications.