Both target-specific and domain-invariant features can facilitate Open Set Domain Adaptation (OSDA). To exploit these features, we propose a Knowledge Exchange (KnowEx) model which jointly trains two complementary constituent networks: (1) a Domain-Adversarial Network (DAdvNet) learning the domain-invariant representation, through which the supervision in source domain can be exploited to infer the class information of unlabeled target data; (2) a Private Network (PrivNet) exclusive for target domain, which is beneficial for discriminating between instances from known and unknown classes. The two constituent networks exchange training experience in the learning process. Toward this end, we exploit an adversarial perturbation process against DAdvNet to regularize PrivNet. This enhances the complementarity between the two networks. At the same time, we incorporate an adaptation layer into DAdvNet to address the unreliability of the PrivNet's experience. Therefore, DAdvNet and PrivNet are able to mutually reinforce each other during training. We have conducted thorough experiments on multiple standard benchmarks to verify the effectiveness and superiority of KnowEx in OSDA.