Class-Incremental Learning updates a deep classifier with new categories while maintaining the previously observed class accuracy. Regularizing the neural network weights is a common method to prevent forgetting previously learned classes while learning novel ones. However, existing regularizers use a constant magnitude throughout the learning sessions, which may not reflect the varying levels of difficulty of the tasks encountered during incremental learning. This study investigates the necessity of adaptive regularization in Class-Incremental Learning, which dynamically adjusts the regularization strength according to the complexity of the task at hand. We propose a Bayesian Optimization-based approach to automatically determine the optimal regularization magnitude for each learning task. Our experiments on two datasets via two regularizers demonstrate the importance of adaptive regularization for achieving accurate and less forgetful visual incremental learning.