Adaptive Learning Guided by Bias-Noise-Alignment Diagnostics

Abstract

Learning systems deployed in nonstationary and safety-critical environments often suffer from instability, slow convergence, or brittle adaptation when learning dynamics evolve over time. While modern optimization, reinforcement learning, and meta-learning methods adapt to gradient statistics, they largely ignore the temporal structure of the error signal itself. This paper proposes a diagnostic-driven adaptive learning framework that explicitly models error evolution through a principled decomposition into bias, capturing persistent drift; noise, capturing stochastic variability; and alignment, capturing repeated directional excitation leading to overshoot. These diagnostics are computed online from lightweight statistics of loss or temporal-difference (TD) error trajectories and are independent of model architecture or task domain. We show that the proposed bias-noise-alignment decomposition provides a unifying control backbone for supervised optimization, actor-critic reinforcement learning, and learned optimizers. Within this framework, we introduce three diagnostic-driven instantiations: the Human-inspired Supervised Adaptive Optimizer (HSAO), Hybrid Error-Diagnostic Reinforcement Learning (HED-RL) for actor-critic methods, and the Meta-Learned Learning Policy (MLLP). Under standard smoothness assumptions, we establish bounded effective updates and stability properties for all cases. Representative diagnostic illustrations in actor-critic learning highlight how the proposed signals modulate adaptation in response to TD error structure. Overall, this work elevates error evolution to a first-class object in adaptive learning and provides an interpretable, lightweight foundation for reliable learning in dynamic environments.

This preprint focuses on the theoretical framework and diagnostic behavior. Comprehensive experimental validation in application-specific settings is deferred to a companion experimental study