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.

In many real-life design problems, there is a requirement to simultaneously balance multiple tasks or objectives in the system that are conflicting in nature, where minimizing one objective causes another to increase in value, thereby resulting in trade-offs between the objectives. For example, in embedded multi-core mobile devices and very large scale data centers, there is a continuous problem of simultaneously balancing interfering goals of maximal power savings and minimal performance delay with varying trade-off values for different application workloads executing on them. Typically, the optimal trade-offs for the executing workloads, lie on a difficult to determine optimal Pareto front. The nature of the problem requires learning over the lifetime of the mobile device or server with continuous evaluation and prediction of the trade-off settings on the system that balances the interfering objectives optimally. Towards this, we propose an on-line learning method, where the weights of experts for addressing the objectives are updated based on a convex combination of their relative performance in addressing all objectives simultaneously. An additional importance vector that assigns relative importance to each objective at every round is used, and is sampled from a convex cone pointed at the origin Our preliminary results show that the convex combination of the importance vector and the gradient of the potential functions of the learner's regret with respect to each objective ensure that in the next round, the drift (instantaneous regret vector), is the Pareto descent direction that enables better convergence to the optimal Pareto front.

In many real-life design problems, there is a requirement to simultaneously balance multiple tasks or objectives in the system that are conflicting in nature, where minimizing one objective causes another to increase in value, thereby resulting in trade-offs between the objectives. For example, in embedded multi-core mobile devices and very large scale data centers, there is a continuous problem of simultaneously balancing interfering goals of maximal power savings and minimal performance delay with varying trade-off values for different application workloads executing on them. Typically, the optimal trade-offs for the executing workloads, lie on a difficult to determine optimal Pareto front. The nature of the problem requires learning over the lifetime of the mobile device or server with continuous evaluation and prediction of the trade-off settings on the system that balances the interfering objectives optimally. Towards this, we propose an on-line learning method, where the weights of experts for addressing the objectives are updated based on a convex combination of their relative performance in addressing all objectives simultaneously. An additional importance vector that assigns relative importance to each objective at every round is used, and is sampled from a convex cone pointed at the origin Our preliminary results show that the convex combination of the importance vector and the gradient of the potential functions of the learner's regret with respect to each objective ensure that in the next round, the drift (instantaneous regret vector), is the Pareto descent direction that enables better convergence to the optimal Pareto front.