Non-intrusive load monitoring (NILM) is a cost-effective energy disaggregation means to estimate the energy consumption of individual appliances from a central load reading. Learning-based methods are the new trends in NILM implementations but require large labeled data to work properly at end-user premises. We first formulate an unsupervised multi-source domain adaptation problem to address this challenge by leveraging rich public datasets for building the NILM model. Then, we prove a new generalization bound for the target domain under multi-source settings. A hybrid loss-driven multi-source domain adversarial network (HLD-MDAN) is developed by approximating and optimizing the bound to tackle the domain shift between source and target domains. We conduct extensive experiments on three real-world residential energy datasets to evaluate the effectiveness of HLD-MDAN, showing that it is superior to other methods in single-source and multi-source learning scenarios.