Class incremental learning (CIL) requires an agent to learn distinct tasks consecutively with knowledge retention against forgetting. Problems impeding the practical applications of CIL methods are twofold: (1) non-i.i.d batch streams and no boundary prompts to update, known as the harsher online task-free CIL (OTCIL) scenario; (2) CIL methods suffer from memory loss in learning long task streams, as shown in Fig. 1 (a). To achieve efficient decision-making and decrease cumulative regrets during the OTCIL process, a randomized neural network (Randomized NN) with forward regularization (-F) is proposed to resist forgetting and enhance learning performance. This general framework integrates unsupervised knowledge into recursive convex optimization, has no learning dissipation, and can outperform the canonical ridge style (-R) in OTCIL. Based on this framework, we derive the algorithm of the ensemble deep random vector functional link network (edRVFL) with adjustable forward regularization (-kF), where k mediates the intensity of the intervention. edRVFL-kF generates one-pass closed-form incremental updates and variable learning rates, effectively avoiding past replay and catastrophic forgetting while achieving superior performance. Moreover, to curb unstable penalties caused by non-i.i.d and mitigate intractable tuning of -kF in OTCIL, we improve it to the plug-and-play edRVFL-kF-Bayes, enabling all hard ks in multiple sub-learners to be self-adaptively determined based on Bayesian learning. Experiments were conducted on 2 image datasets including 6 metrics, dynamic performance, ablation tests, and compatibility, which distinctly validates the efficacy of our OTCIL frameworks with -kF-Bayes and -kF styles.
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