Large speech emotion recognition datasets are hard to obtain, and small datasets may contain biases. Deep-net-based classifiers, in turn, are prone to exploit those biases and find shortcuts such as speaker characteristics. These shortcuts usually harm a model's ability to generalize. To address this challenge, we propose a gradient-based adversary learning framework that learns a speech emotion recognition task while normalizing speaker characteristics from the feature representation. We demonstrate the efficacy of our method on both speaker-independent and speaker-dependent settings and obtain new state-of-the-art results on the challenging IEMOCAP dataset.