Online learning is crucial for handling complex data streams in big data applications. Recent research has begun to focus on dynamic scenarios, i.e., non-stationary environments. However, a crucial yet often overlooked aspect is label latency, where new data may not receive labels in time due to the slow and expensive labeling process, thus hindering rapid adaptation to dynamic environments. To resolve this impasse, we propose Dual-Track Geometry Online Learning (DT-GOL), a novel framework that shifts from temporal compensation to spatial reasoning to bridge the supervised latency gap. By modeling the delay challenge as a semi-supervised task, we leverage real-time topological evolution of features as a reliable geometric surrogate for unobservable conceptual changes to achieve proactive supervised adaptation within the delay window. Unlike rigid self-training, we introduce a dynamic evidence calibration mechanism that distills geometric information into soft labels that perceive uncertainty, effectively mitigating the confirmation bias inherent in hard pseudo-labels. Furthermore, to resolve the stability-plasticity dilemma, we design a decoupled dual-track architecture in which a master learner serves as a stable anchor, updated strictly from delayed ground truth, while a transient branch leverages soft geometric knowledge for low-risk forward adaptation. Extensive experiments on real and synthetic datasets demonstrate that DT-GOL significantly outperforms existing state-of-the-art baseline methods, especially in scenarios with concept drift.

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