In the intricate world of machine learning, the efficacy of algorithms like Online Gradient Descent (OGD) is paramount. These algorithms, which underpin critical applications from stock market analysis to autonomous driving and predictive healthcare, must adeptly navigate the complexities introduced by bias and gradient variance. The challenge of ensuring accurate and reliable decision-making in the presence of these uncertainties is not just theoretical—it’s a practical necessity for ensuring accurate and reliable outcomes. Consider the consequences of unaddressed bias in a stock prediction model, potentially leading to misguided investments, or the impact of gradient variance in autonomous vehicle algorithms, which could compromise safety. The real-world implications are vast and varied, underlining the urgency of our investigation.