Probabilistic Successor Representations with Kalman Temporal Differences

The effectiveness of Reinforcement Learning (RL) depends on an animal's ability to assign credit for rewards to the appropriate preceding stimuli. One aspect of understanding the neural underpinnings of this process involves understanding what sorts of stimulus representations support generalisation. The Successor Representation (SR), which enforces generalisation over states that predict similar outcomes, has become an increasingly popular model in this space of inquiries. Another dimension of credit assignment involves understanding how animals handle uncertainty about learned associations, using probabilistic methods such as Kalman Temporal Differences (KTD). Combining these approaches, we propose using KTD to estimate a distribution over the SR. KTD-SR captures uncertainty about the estimated SR as well as covariances between different long-term predictions. We show that because of this, KTD-SR exhibits partial transition revaluation as humans do in this experiment without additional replay, unlike the standard TD-SR algorithm. We conclude by discussing future applications of the KTD-SR as a model of the interaction between predictive and probabilistic animal reasoning.