Probabilistic Successor Representations with Kalman Temporal Differences

TL;DR

This paper introduces KTD-SR, a probabilistic successor representation model using Kalman Temporal Differences, which captures uncertainty and covariances in state predictions, aligning with human-like revaluation behaviors.

Contribution

It combines Kalman Temporal Differences with successor representations to model uncertainty and covariance, advancing understanding of probabilistic and predictive reasoning in reinforcement learning.

Findings

KTD-SR captures uncertainty and covariances in state predictions.

KTD-SR exhibits partial transition revaluation without replay.

Standard TD-SR lacks this revaluation capability.

Abstract

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.