Pooling multiple beliefs and opinions is often crucial in multi-agent systems. Specifically, we consider pooling in the context of multi-hypothesis social learning problems, where agents gather evidence and pool information to determine the true hypothesis. Whilst past research has largely focused on designing probability pooling operators to satisfy certain desirable properties, there has been limited exploration of learning operators directly from data. The conventional method, relying on well-motivated axioms and heuristics for pooling, constrains the solution space for operators and choosing between different operators often requires domain specific knowledge. We introduce a machine learning approach to opinion pooling that derives operators via end-to-end reinforcement learning incorporating DeepSets neural networks. We provide empirical results showing that our approach outperforms existing baselines across a range of social learning contexts and exhibits robust generalisation to the number of agents pooled in a single operation. Furthermore, we provide an analysis of the learned neural network representations, offering insights into optimal opinion pooling strategies.

The evidence available to a multi-agent system can take at least two distinct forms. There can be direct evidence from the environment resulting, for example, from sensor measurements or from running tests or experiments. In addition, agents also gain evidence from other individuals in the population with whom they are interacting. We, therefore, envisage an agent's beliefs as a probability distribution over a set of hypotheses of interest, which are updated either on the basis of direct evidence using Bayesian updating, or by taking account of the probabilities of other agents using opinion pooling. This paper investigates the relationship between these two processes in a multi-agent setting. We consider a possible Bayesian interpretation of probability pooling and then explore properties for pooling operators governing the extent to which direct evidence is diluted, preserved or amplified by the pooling process. We then use simulation experiments to show that pooling operators can provide a mechanism by which a limited amount of direct evidence can be efficiently propagated through a population of agents so that an appropriate consensus is reached. In particular, we explore the convergence properties of a parameterised family of operators with a range of evidence propagation strengths.