Online Continual Learning (OCL) requires models to learn from non-stationary data streams under a strict single-pass constraint, making them highly susceptible to catastrophic forgetting. While existing studies have explored various strategies from data, architecture, and optimization perspectives, the optimizer often directly uses generic approaches such as SGD and AdamW. In this work, we reveal a new link between optimization dynamics and OCL needs by recasting Polyak-Ruppert averaging as the engine of "plasticity" and Primal averaging as the anchor of "stability". This inspires our novel optimizer, SPIN (Stability-Plasticity INterpolation), which explicitly decouples plasticity and stability by interpolating between a fast-moving "plasticity" sequence and an adaptive "stability" sequence. We theoretically demonstrate that SPIN implicitly employs an inverse Hessian approximation, providing crucial Tikhonov regularization to damp noisy, single-sample Hessian estimates and mitigate forgetting. More importantly, SPIN can be seamlessly integrated into existing OCL methods by taking resulted gradients as input and replacing standard optimizers. Extensive experiments show that using SPIN instead of standard optimizers yields consistent and significant performance gains across multiple OCL approaches, including the challenging rehearsal-free setting and under strict memory constraints.

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