Efficient Continuous Pareto Exploration in Multi-Task Learning
This addresses the need for continuous exploration of trade-offs in multi-task learning, which is incremental as it builds on existing Pareto optimality methods by extending them to continuous analysis.
The paper tackles the problem of generating only finite, sparse, and discrete Pareto optimal solutions in multi-task learning by introducing an efficient method that produces locally continuous Pareto sets and fronts, enabling continuous analysis and revealing primary directions for trade-off balancing. The results show the algorithm finds more solutions with different trade-offs efficiently and scales to tasks with millions of parameters.
Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and directly cast multi-task learning as multi-objective optimization problems, but solutions returned by existing methods are typically finite, sparse, and discrete. We present a novel, efficient method that generates locally continuous Pareto sets and Pareto fronts, which opens up the possibility of continuous analysis of Pareto optimal solutions in machine learning problems. We scale up theoretical results in multi-objective optimization to modern machine learning problems by proposing a sample-based sparse linear system, for which standard Hessian-free solvers in machine learning can be applied. We compare our method to the state-of-the-art algorithms and demonstrate its usage of analyzing local Pareto sets on various multi-task classification and regression problems. The experimental results confirm that our algorithm reveals the primary directions in local Pareto sets for trade-off balancing, finds more solutions with different trade-offs efficiently, and scales well to tasks with millions of parameters.