Edoardo Urettini

Edoardo Urettini, Antonio Carta

Online Continual Learning (OCL) models continuously adapt to nonstationary data streams, usually without task information. These settings are complex and many traditional CL methods fail, while online methods (mainly replay-based) suffer from instabilities after the task shift. To address this issue, we formalize replay-based OCL as a second-order online joint optimization with explicit KL-divergence constraints on replay data. We propose Online Curvature-Aware Replay (OCAR) to solve the problem: a method that leverages second-order information of the loss using a K-FAC approximation of the Fisher Information Matrix (FIM) to precondition the gradient. The FIM acts as a stabilizer to prevent forgetting while also accelerating the optimization in non-interfering directions. We show how to adapt the estimation of the FIM to a continual setting stabilizing second-order optimization for non-iid data, uncovering the role of the Tikhonov regularization in the stability-plasticity tradeoff. Empirical results show that OCAR outperforms state-of-the-art methods in continual metrics achieving higher average accuracy throughout the training process in three different benchmarks.

Edoardo Urettini, Daniele Atzeni, Ioanna-Yvonni Tsaknaki et al.

Online continual learning (OCL) methods adapt to changing environments without forgetting past knowledge. Similarly, online time series forecasting (OTSF) is a real-world problem where data evolve in time and success depends on both rapid adaptation and long-term memory. Indeed, time-varying and regime-switching forecasting models have been extensively studied, offering a strong justification for the use of OCL in these settings. Building on recent work that applies OCL to OTSF, this paper aims to strengthen the theoretical and practical connections between time series methods and OCL. First, we reframe neural network optimization as a parameter filtering problem, showing that natural gradient descent is a score-driven method and proving its information-theoretic optimality. Then, we show that using a Student's t likelihood in addition to natural gradient induces a bounded update, which improves robustness to outliers. Finally, we introduce Natural Score-driven Replay (NatSR), which combines our robust optimizer with a replay buffer and a dynamic scale heuristic that improves fast adaptation at regime drifts. Empirical results demonstrate that NatSR achieves stronger forecasting performance than more complex state-of-the-art methods.