Recently, researchers have utilized neural network-based speaker embedding techniques in speaker-recognition tasks to identify speakers accurately. However, speaker-discriminative embeddings do not always represent speech features such as age group well. In an embedding model that has been highly trained to capture speaker traits, the task of age group classification is closer to speech information leakage. Hence, to improve age group classification performance, we consider the use of speaker-discriminative embeddings derived from adversarial multi-task learning to align features and reduce the domain discrepancy in age subgroups. In addition, we investigated different types of speaker embeddings to learn and generalize the domain-invariant representations for age groups. Experimental results on the VoxCeleb Enrichment dataset verify the effectiveness of our proposed adaptive adversarial network in multi-objective scenarios and leveraging speaker embeddings for the domain adaptation task.