Delve into the Applicability of Advanced Optimizers for Multi-Task Learning

Multi-objective optimization (MOO) has demonstrated significant success in multi-task learning by mitigating task conflicts through gradient manipulation. However, most existing methods flatten model parameters into vectors and perform gradient manipulation under Euclidean geometry, thereby overlooking the matrix structure prevalent in modern architectures such as Transformers. In this paper, we show that gradient manipulation in Euclidean space does not generally yield the steepest descent direction under matrix geometry, potentially limiting optimization efficiency. Drawing from the theory of steepest descent for matrix-valued parameters, we propose MOON (Multi-Objective OrthoNormalized Updates), which performs gradient manipulation under spectral--nuclear norm geometry and uses the orthonormalized manipulated gradient for parameter updates. Theoretically, for smooth non-convex objectives, we establish convergence of the averaged Pareto-stationarity measure at rates of $\mathcal{O}(T^{-1/2})$ in the deterministic setting and $\mathcal{O}(T^{-1/4})$ under stochastic gradients. Empirical results across various benchmarks show that MOON consistently improves both optimization efficiency and final multi-task performance. Our code is available at https://github.com/KunlinLyu/MOON.

A fundamental problem in multi-task learning (MTL) is identifying groups of tasks that should be learned together. Since training MTL models for all possible combinations of tasks is prohibitively expensive for large task sets, a crucial component of efficient and effective task grouping is predicting whether a group of tasks would benefit from learning together, measured as per-task performance gain over single-task learning. In this paper, we propose ETAP (Ensemble Task Affinity Predictor), a scalable framework that integrates principled and data-driven estimators to predict MTL performance gains. First, we consider the gradient-based updates of shared parameters in an MTL model to measure the affinity between a pair of tasks as the similarity between the parameter updates based on these tasks. This linear estimator, which we call affinity score, naturally extends to estimating affinity within a group of tasks. Second, to refine these estimates, we train predictors that apply non-linear transformations and correct residual errors, capturing complex and non-linear task relationships. We train these predictors on a limited number of task groups for which we obtain ground-truth gain values via multi-task learning for each group. We demonstrate on benchmark datasets that ETAP improves MTL gain prediction and enables more effective task grouping, outperforming state-of-the-art baselines across diverse application domains.

When different objectives conflict with each other in multi-task learning, gradients begin to interfere and slow convergence, thereby potentially reducing the final model's performance. To address this, we introduce SON-GOKU, a scheduler that computes gradient interference, constructs an interference graph, and then applies greedy graph-coloring to partition tasks into groups that align well with each other. At each training step, only one group (color class) of tasks are activated, and the grouping partition is constantly recomputed as task relationships evolve throughout training. By ensuring that each mini-batch contains only tasks that pull the model in the same direction, our method improves the effectiveness of any underlying multi-task learning optimizer without additional tuning. Since tasks within these groups will update in compatible directions, multi-task learning will improve model performance rather than impede it. Empirical results on six different datasets show that this interference-aware graph-coloring approach consistently outperforms baselines and state-of-the-art multi-task optimizers. We provide extensive theory showing why grouping and sequential updates improve multi-task learning, with guarantees on descent, convergence, and the ability to accurately identify what tasks conflict or align.