Collective preference learning in the best-of- n problem

Decentralised autonomous systems rely on distributed learning to make decisions and to collaborate in pursuit of a shared objective. For example, in swarm robotics the best-of- n problem is a well-known collective decision-making problem in which agents attempt to learn the best option out of n possible alternatives based on local feedback from the environment. This typically involves gathering information about all n alternatives while then systematically discarding information about all but the best option. However, for applications such as search and rescue in which learning the ranking of options is useful or crucial, best-of- n decision-making can be wasteful and costly. Instead, we investigate a more general distributed learning process in which agents learn a preference ordering over all of the n options. More specifically, we introduce a distributed rank learning algorithm based on three-valued logic. We then use agent-based simulation experiments to demonstrate the effectiveness of this model. In this context, we show that a population of agents are able to learn a total ordering over the n options and furthermore the learning process is robust to evidential noise. To demonstrate the practicality of our model, we restrict the communication bandwidth between the agents and show that this model is also robust to limited communications whilst outperforming a comparable probabilistic model under the same communication conditions.