Online Continual Learning (OCL) requires models to learn sequentially from data streams with limited memory. Rehearsal-based methods, particularly Experience Replay (ER), are commonly used in OCL scenarios. This paper revisits ER through the lens of ϵ-constraint optimization, revealing that ER implicitly employs a soft constraint on past task performance, with its weighting parameter post-hoc defining a slack variable. While effective, ER's implicit and fixed slack strategy has limitations: it can inadvertently lead to updates that negatively impact generalization, and its fixed trade-off between plasticity and stability may not optimally balance current streaming with memory retention, potentially overfitting to the memory buffer. To address these shortcomings, we propose the Gradient-Guided Epsilon Constraint (GEC) method for online continual learning. GEC explicitly formulates the OCL update as an ϵ-constraint optimization problem, which minimize the loss on the current task data and transform the stability objective as constraints and propose a gradient-guided method to dynamically adjusts the update direction based on whether the performance on memory samples violates a predefined slack tolerance ε: if forgetting exceeds this tolerance, GEC prioritizes constraint satisfaction; otherwise, it focuses on the current task while controlling the rate of increase in memory loss. Empirical evaluations on standard OCL benchmarks demonstrate GEC's ability to achieve a superior trade-off, leading to improved overall performance.

This appendix is organized as follows: Section A: the detailed dataset statistics and a summary of model properties w.r.t. We present the details on each dataset in Table 4. Under the online continual setting, the tasks are observed following a fixed order and the data from each task is observed as a (one-pass) stream of samples. The batch size is 10 for all the datasets. We do not randomize the order of tasks or optimize the task orders.

Continual learning has primarily focused on the issue of catastrophic forgetting and the associated stability-plasticity tradeoffs. However, little attention has been paid to the efficacy of continually learned representations, as representations are learned alongside classifiers throughout the learning process. Our primary contribution is empirically demonstrating that existing online continually trained deep networks produce inferior representations compared to a simple pre-defined random transforms. Our approach embeds raw pixels using a fixed random transform, approximating an RBF-Kernel initialized before any data is seen. We then train a simple linear classifier on top without storing any exemplars, processing one sample at a time in an online continual learning setting. This method, called RanDumb, significantly outperforms state-of-the-art continually learned representations across all standard online continual learning benchmarks. Our study reveals the significant limitations of representation learning, particularly in low-exemplar and online continual learning scenarios. Extending our investigation to popular exemplar-free scenarios with pretrained models, we find that training only a linear classifier on top of pretrained representations surpasses most continual fine-tuning and prompt-tuning strategies. Overall, our investigation challenges the prevailing assumptions about effective representation learning in the online continual learning.

In this natural setting, it is not common to see the same data sample multiple times, or even twice at times.