Adaptive Benign Overfitting (ABO): Overparameterized RLS for Online Learning in Non-stationary Time-series

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Directly applicable to FX forecasting (EUR/USD demonstrated), which is core to quantitative trading. The online learning nature suits real-time trading systems. However, the paper focuses on point forecasting rather than trading strategy development, risk management, or portfolio optimization. The 20-40% speed improvement over kernel methods is relevant for latency-sensitive applications. The non-stationarity handling via forgetting factors is important for regime changes in markets. No transaction costs, slippage, or trading-specific metrics (Sharpe, drawdown) are evaluated.

Requires careful implementation of Givens rotations for QR updates and downdates, recursive Moore-Penrose pseudoinverse updates (Greville/Cline formulas), sliding window management, and exponentially weighted scaling. The algorithm has 9 distinct steps per update cycle. Handling both classical (D≤N) and overparameterized (D>N) regimes adds branching complexity. Numerical stability considerations (avoiding covariance-form RLS) are critical. However, the O(ND) complexity is favorable compared to O(D²) alternatives, and standard LAPACK/BLAS routines support the underlying operations.

The paper provides detailed algorithmic pseudocode (Algorithm 1), complete mathematical derivations for QR updates, pseudoinverse updates/downdates, and forgetting factor scaling. Hyperparameters are specified (window size, RFF dimension, forgetting factor, lag order). However, no code repository is provided. Data sources are publicly available (Dukascopy for EUR/USD, UCI for Electricity). The evaluation protocol (walk-forward rolling validation with Optuna tuning) is described but implementation details for baselines are limited.