In this paper, we introduce a novel form of value function, $Q(s, s)$, that expresses the utility of transitioning from a state $s$ to a neighboring state $s$ and then acting optimally thereafter. In order to derive an optimal policy, we develop a forward dynamics model that learns to make next-state predictions that maximize this value. This formulation decouples actions from values while still learning off-policy. We highlight the benefits of this approach in terms of value function transfer, learning within redundant action spaces, and learning off-policy from state observations generated by sub-optimal or completely random policies. Code and videos are available at http://sites.google.com/view/qss-paper.
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