  The goal of Continual Learning (CL) is to continuously learn from new data
streams and accomplish the corresponding tasks. Previously studied CL assumes
that data are given in sequence nose-to-tail for different tasks, thus indeed
belonging to Serial Continual Learning (SCL). This paper studies the novel
paradigm of Parallel Continual Learning (PCL) in dynamic multi-task scenarios,
where a diverse set of tasks is encountered at different time points. PCL
presents challenges due to the training of an unspecified number of tasks with
varying learning progress, leading to the difficulty of guaranteeing effective
model updates for all encountered tasks. In our previous conference work, we
focused on measuring and reducing the discrepancy among gradients in a
multi-objective optimization problem, which, however, may still contain
negative transfers in every model update. To address this issue, in the dynamic
multi-objective optimization problem, we introduce task-specific elastic
factors to adjust the descent direction towards the Pareto front. The proposed
method, called Elastic Multi-Gradient Descent (EMGD), ensures that each update
follows an appropriate Pareto descent direction, minimizing any negative impact
on previously learned tasks. To balance the training between old and new tasks,
we also propose a memory editing mechanism guided by the gradient computed
using EMGD. This editing process updates the stored data points, reducing
interference in the Pareto descent direction from previous tasks. Experiments
on public datasets validate the effectiveness of our EMGD in the PCL setting.
