Ito-Adam Optimizer for Training LSTM Networks: Application to Stock Price Forecasting

This study introduces ItoAdam, an enhanced optimizer that incorporates Itô’s lemma and Brownian noise into Adam to improve convergence in complex, non-convex settings. By perturbing gradient updates with stochastic noise, ItoAdam enables better exploration of the loss surface and avoids poor local minima. We apply ItoAdam to train Long Short-Term Memory (LSTM) networks for stock price forecasting across 13 major companies sourced from Yahoo Finance. Experiments show that ItoAdam-LSTM consistently outperforms Adam-LSTM across RMSE, MAE, and R², with sensitivity analysis indicating that optimal performance occurs when noise standard deviation lies between 2.1 × 10⁻⁴ and 2.9 × 10⁻⁴. Overall, results demonstrate the effectiveness of combining Itô-driven stochastic optimization, evolutionary hyperparameter tuning, and recurrent architectures for reliable financial time series forecasting in noisy and nonstationary environments.