It has been demonstrated that operant behavior can be controlled by spatial stimuli. In one of our experiment, rats were conditioned to press a lever for reward when a moving object was passing through a particular region of the experimental room (unpublished data). Although the stimulus was changing smoothly, the transitions between rewarded and non-rewarded condition were sudden. Consequently the animals anticipated the arrival to the rewarded zone by responding in its vicinity.
We developed a reinforcement learning model to simulate this anticipatory behavior and to study its spatial and temporal components. An output neuron integrated inputs from four classes of sensory neurons: (1) neurons detecting the position of the object, (2) neurons indicating the time elapsed since the last reward and (3) since the last operant response, and (4) a neuron signaling the presence/absence of the reward. While the output neuron was a leaky-integrator with a binary activation function, a manner for sending a motor signal to press the lever, the sensory neurons were simple nodes lacking the time dynamic component that signaled the presence of a stimulus in their receptive field in a rate-coded manner. The synapses between the sensory neurons and the output neuron were modified according to a rule based on the Rescorla-Wagner rule . The overall model resembles the spectral-timing model of Grossberg and Schmajuk  extended to the spatial domain.
Depending on the set up of learning parameters related to the different classes of sensory neurons, the network can learn the spatial and/or temporal features of the task resulting in spatial and/or temporal anticipation of the reward. The network well approximates data observed in real animals.
This work was supported by grants of MSMT (1M0517, LC554, and MSM0021620838) and research projects AVOZ50110509 and 1ET100300517.
Rescorla RA, Wagner AR: A theory of Pavlovian conditioning: The effectiveness of reinforcement and non-reinforcement. In Classical Conditioning II: Current Research and Theory. New-York: Appleton-Century-Crofts; 1972:64-69.
Neural Networks 1989, 2:79-102. Publisher Full Text