  Machine learning problems with multiple objective functions appear either in
learning with multiple criteria where learning has to make a trade-off between
multiple performance metrics such as fairness, safety and accuracy; or, in
multi-task learning where multiple tasks are optimized jointly, sharing
inductive bias between them. This problems are often tackled by the
multi-objective optimization framework. However, existing stochastic
multi-objective gradient methods and its variants (e.g., MGDA, PCGrad, CAGrad,
etc.) all adopt a biased noisy gradient direction, which leads to degraded
empirical performance. To this end, we develop a stochastic Multi-objective
gradient Correction (MoCo) method for multi-objective optimization. The unique
feature of our method is that it can guarantee convergence without increasing
the batch size even in the non-convex setting. Simulations on multi-task
supervised and reinforcement learning demonstrate the effectiveness of our
method relative to state-of-the-art methods.
