Robust Aggregation with Adversarial Experts

We consider a robust aggregation problem in the presence of both truthful and adversarial experts. The truthful experts will report their private signals truthfully, while the adversarial experts can report arbitrarily. We assume experts are marginally symmetric in the sense that they share the same common prior and marginal posteriors. The rule maker needs to design an aggregator to predict the true world state from these experts' reports, without knowledge of the underlying information structures or adversarial strategies. We aim to find the optimal aggregator that outputs a forecast minimizing regret under the worst information structure and adversarial strategies. The regret is defined by the difference in expected loss between the aggregator and a benchmark who aggregates optimally given the information structure and reports of truthful experts.