Learning invariant representations is a critical first step in a number of machine learning tasks. A common approach is given by the so-called information bottleneck principle in which an application dependent function of mutual information is carefully chosen and optimized. Unfortunately, in practice, these functions are not suitable for optimization purposes since these losses are agnostic of the metric structure of the parameters of the model. In our paper, we introduce a class of losses for learning representations that are invariant to some extraneous variable of interest by inverting the class of contrastive losses, i.e., inverse contrastive loss (ICL). We show that if the extraneous variable is binary, then optimizing ICL is equivalent to optimizing a regularized MMD divergence. More generally, we also show that if we are provided a metric on the sample space, our formulation of ICL can be decomposed into a sum of convex functions of the given distance metric. Our experimental results indicate that models obtained by optimizing ICL achieve significantly better invariance to the extraneous variable for a fixed desired level of accuracy. In a variety of experimental settings, we show applicability of ICL for learning invariant representations for both continuous and discrete protected/extraneous variables. The project page with code is available at https://github.com/adityakumarakash/ICL

We present and analyze methods for patrolling and surveillance in an environment with a distributed swarm of robots with limited capabilities. Our approach is based on a distributed triangulation of the work space, in which a set of p stationary sensors provides coverage control; in addition, there are r mobile robots that can move between the sensors. Building on our prior work on structured exploration of unknown spaces with multi-robot systems, we can make use of a triangulation that is constructed in a distributed fashion and guarantees good local navigation properties, even when sensors and robots have very limited capabilities.