  The dominant framework for off-policy multi-goal reinforcement learning
involves estimating goal conditioned Q-value function. When learning to achieve
multiple goals, data efficiency is intimately connected with the generalization
of the Q-function to new goals. The de-facto paradigm is to approximate Q(s, a,
g) using monolithic neural networks. To improve the generalization of the
Q-function, we propose a bilinear decomposition that represents the Q-value via
a low-rank approximation in the form of a dot product between two vector
fields. The first vector field, f(s, a), captures the environment's local
dynamics at the state s; whereas the second component, {\phi}(s, g), captures
the global relationship between the current state and the goal. We show that
our bilinear decomposition scheme substantially improves data efficiency, and
has superior transfer to out-of-distribution goals compared to prior methods.
Empirical evidence is provided on the simulated Fetch robot task-suite and
dexterous manipulation with a Shadow hand.
