We study fairness through the lens of cooperative multi-agent learning. Our work is motivated by empirical evidence that naive maximization of team reward yields unfair outcomes for individual team members. To address fairness in multi-agent contexts, we introduce team fairness, a group-based fairness measure for multi-agent learning. We then prove that it is possible to enforce team fairness during policy optimization by transforming the team's joint policy into an equivariant map. We refer to our multi-agent learning strategy as Fairness through Equivariance (Fair-E) and demonstrate its effectiveness empirically. We then introduce Fairness through Equivariance Regularization (Fair-ER) as a soft-constraint version of Fair-E and show that it reaches higher levels of utility than Fair-E and fairer outcomes than non-equivariant policies. Finally, we present novel findings regarding the fairness-utility trade-off in multi-agent settings; showing that the magnitude of the trade-off is dependent on agent skill.

Robotic tasks such as manipulation with visual inputs require image features that capture the physical properties of the scene, e.g., the position and configuration of objects. Recently, it has been suggested to learn such features in an unsupervised manner from simulated, self-supervised, robot interaction; the idea being that high-level physical properties are well captured by modern physical simulators, and their representation from visual inputs may transfer well to the real world. In particular, learning methods based on noise contrastive estimation have shown promising results. To robustify the simulation-to-real transfer, domain randomization (DR) was suggested for learning features that are invariant to irrelevant visual properties such as textures or lighting. In this work, however, we show that a naive application of DR to unsupervised learning based on contrastive estimation does not promote invariance, as the loss function maximizes mutual information between the features and both the relevant and irrelevant visual properties. We propose a simple modification of the contrastive loss to fix this, exploiting the fact that we can control the simulated randomization of visual properties. Our approach learns physical features that are significantly more robust to visual domain variation, as we demonstrate using both rigid and non-rigid objects.