The arts are one of the most complex of human endeavours, and so it is fitting that a special issue on Complex Systems in Aesthetics and Arts is being published. As the editors of this special issue, we would like to thank the reviewers of the submitted papers for their hard work in making this issue possible, as well as the authors who submitted their work and were very responsive to the comments of the reviewers and editors.

A theoretical framework for the reinforcement learning of aesthetic biases was recently proposed based on brain circuitries revealed by neuroimaging. A model grounded on that framework accounted for interesting features of human aesthetic biases. These features included individuality, cultural predispositions, stochastic dynamics of learning and aesthetic biases, and the peak-shift effect. However, despite the success in explaining these features, a potential weakness was the linearity of the value function used to predict reward. This linearity meant that the learning process employed (...) a value function that assumed a linear relationship between reward and sensory stimuli. Linearity is common in reinforcement learning in neuroscience. However, linearity can be problematic because neural mechanisms and the dependence of reward on sensory stimuli were typically nonlinear. Here, we analyze the learning performance with models including optimal nonlinear value functions. We also compare updating the free parameters of the value functions with the delta rule, which neuroscience models use frequently, vs. updating with a new Phi rule that considers the structure of the nonlinearities. Our computer simulations showed that optimal nonlinear value functions resulted in improvements of learning errors when the reward models were nonlinear. Similarly, the new Phi rule led to improvements in these errors. These improvements were accompanied by the straightening of the trajectories of the vector of free parameters in its phase space. This straightening meant that the process became more efficient in learning the prediction of reward. Surprisingly, however, this improved efficiency had a complex relationship with the rate of learning. Finally, the stochasticity arising from the probabilistic sampling of sensory stimuli, rewards, and motivations helped the learning process narrow the range of free parameters to nearly optimal outcomes. Therefore, we suggest that value functions and update rules optimized for social and ecological constraints are ideal for learning aesthetic biases. (shrink)