  Multi-task learning (MTL) is a subfield of machine learning with important
applications, but the multi-objective nature of optimization in MTL leads to
difficulties in balancing training between tasks. The best MTL optimization
methods require individually computing the gradient of each task's loss
function, which impedes scalability to a large number of tasks. In this paper,
we propose Scaled Loss Approximate Weighting (SLAW), a method for multi-task
optimization that matches the performance of the best existing methods while
being much more efficient. SLAW balances learning between tasks by estimating
the magnitudes of each task's gradient without performing any extra backward
passes. We provide theoretical and empirical justification for SLAW's
estimation of gradient magnitudes. Experimental results on non-linear
regression, multi-task computer vision, and virtual screening for drug
discovery demonstrate that SLAW is significantly more efficient than strong
baselines without sacrificing performance and applicable to a diverse range of
domains.
