Title: Contextual Subspace Approximation with Neural Householder Transforms. Abstract: Choosing an appropriate action representation is an integral part of solving robotic manipulation problems. Published approaches include latent action models which compress the control space into a low dimensional manifold. These involve training a conditional autoencoder, where the current observation and a low-dimensional action are passed through a neural network decoder to compute high dimensional actuation commands. Such models can have a large number of parameters, and can be difficult to interpret from a user perspective. In this work, we propose that similar performance gains in robotics tasks can be achieved by restructuring the neural network to map observations to a basis for a context-dependent linear actuation subspace. This results in an action interface wherein a user’s actions determine a linear combination of a state-conditioned actuation basis. We introduce the Neural Householder Transform (NHT) as a method for computing this basis. Our results show that reinforcement learning agents trained with NHT in kinematic manipulation and locomotion environments tend to be more robust to hyperparameter choice and achieve higher final success rates compared to agents trained with alternative action representations. NHT agents outperformed agents trained with joint velocity/torque actions, agents trained with an SVD actuation basis, and agents trained with a LASER action interface in the WAMWipe, WAMGrasp, and HalfCheetah environments.