  Domain adaptation (DA) attempts to transfer the knowledge from a labeled
source domain to an unlabeled target domain that follows different distribution
from the source. To achieve this, DA methods include a source classification
objective to extract the source knowledge and a domain alignment objective to
diminish the domain shift, ensuring knowledge transfer. Typically, former DA
methods adopt some weight hyper-parameters to linearly combine the training
objectives to form an overall objective. However, the gradient directions of
these objectives may conflict with each other due to domain shift. Under such
circumstances, the linear optimization scheme might decrease the overall
objective value at the expense of damaging one of the training objectives,
leading to restricted solutions. In this paper, we rethink the optimization
scheme for DA from a gradient-based perspective. We propose a Pareto Domain
Adaptation (ParetoDA) approach to control the overall optimization direction,
aiming to cooperatively optimize all training objectives. Specifically, to
reach a desirable solution on the target domain, we design a surrogate loss
mimicking target classification. To improve target-prediction accuracy to
support the mimicking, we propose a target-prediction refining mechanism which
exploits domain labels via Bayes' theorem. On the other hand, since prior
knowledge of weighting schemes for objectives is often unavailable to guide
optimization to approach the optimal solution on the target domain, we propose
a dynamic preference mechanism to dynamically guide our cooperative
optimization by the gradient of the surrogate loss on a held-out unlabeled
target dataset. Extensive experiments on image classification and semantic
segmentation benchmarks demonstrate the effectiveness of ParetoDA
