Title: Non-Linear Rewards For Successor Features. Abstract: Reinforcement Learning algorithms have reached new heights in performance, often overtaking humans on several challenging tasks such as Atari and Go. However, the resulting models learn fragile policies that are unable to transfer between tasks without full retraining. Successor features aim to improve this situation by decomposing the policy into two components: one capturing environmental dynamics and the other modelling reward. Under this framework, transfer between related tasks requires only training the reward component. However, successor features builds upon the limiting assumption that the current reward can be predicted from a linear combination of state features. This paper proposes a novel improvement to the successor feature framework, where we instead assume that the reward function is a non-linear function of the state features, thereby increasing its representational power. After derivation of the new state-action value function, the decomposition includes a second term that learns the auto-correlation matrix between state features. Experimentally, we show this term explicitly models the environment's stochasticity and can also be used in place of $\epsilon$-greedy exploration methods during transfer. The performance of the proposed improvements to the successor feature framework is validated empirically on navigation tasks and control of a simulated robotic arm.