To behave adaptively, animals must learn to predict future reward, or value. To do this, animals are thought to learn reward predictions using reinforcement learning. However, in contrast to classical models, animals must learn to estimate value using only incomplete state information. Previous work suggests that animals estimate value in partially observable tasks by first forming "beliefs"-optimal Bayesian estimates of the hidden states in the task. Although this is one way to solve the problem of partial observability, it is not the only way, nor is it the most computationally scalable solution in complex, real-world environments. Here we show that a recurrent neural network (RNN) can learn to estimate value directly from observations, generating reward prediction errors that resemble those observed experimentally, without any explicit objective of estimating beliefs. We integrate statistical, functional, and dynamical systems perspectives on beliefs to show that the RNN's learned representation encodes belief information, but only when the RNN's capacity is sufficiently large. These results illustrate how animals can estimate value in tasks without explicitly estimating beliefs, yielding a representation useful for systems with limited capacity.
Author summary: Natural environments are full of uncertainty. For example, just because my fridge had food in it yesterday does not mean it will have food today. Despite such uncertainty, animals can estimate which states and actions are the most valuable. Previous work suggests that animals estimate value using a brain area called the basal ganglia, using a process resembling a reinforcement learning algorithm called TD learning. However, traditional reinforcement learning algorithms cannot accurately estimate value in environments with state uncertainty (e.g., when my fridge's contents are unknown). One way around this problem is if agents form "beliefs," a probabilistic estimate of how likely each state is, given any observations so far. However, estimating beliefs is a demanding process that may not be possible for animals in more complex environments. Here we show that an artificial recurrent neural network (RNN) trained with TD learning can estimate value from observations, without explicitly estimating beliefs. The trained RNN's error signals resembled the neural activity of dopamine neurons measured during the same task. Importantly, the RNN's activity resembled beliefs, but only when the RNN had enough capacity. This work illustrates how animals could estimate value in uncertain environments without needing to first form beliefs, which may be useful in environments where computing the true beliefs is too costly.