Robust Decision Aggregation with Adversarial Experts

2024-03-13

arXiv.org

AI Summary

This paper studies robust decision aggregation for inferring a binary ground truth in the presence of a mixture of honest and adversarial experts. Honest experts report private signals truthfully, while adversarial experts may arbitrarily manipulate their reports. The aggregator must minimize worst-case regret—the expected loss relative to an ideal oracle—without knowledge of the underlying information structure or adversarial strategy. The authors establish the first optimal aggregators: a truncated mean (minimax-optimal under L₁ loss) and a randomized truncated decision rule (universally optimal for hard binary outputs). Crucially, their regret depends only on the fraction of adversaries, not their absolute number. Theoretical analysis extends to L₂ loss, where piecewise-linear aggregators are shown to be optimal. Numerical experiments demonstrate substantial gains over baselines in adversarial ensemble learning settings.

Technology Category

• Multiagent Systems: Adversarial Agents
• Machine Learning: Adversarial Learning & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

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. We focus on binary states and reports. Under L1 loss, we show that the truncated mean aggregator is optimal. When there are at most k adversaries, this aggregator discards the k lowest and highest reported values and averages the remaining ones. For L2 loss, the optimal aggregators are piecewise linear functions. All the optimalities hold when the ratio of adversaries is bounded above by a value determined by the experts' priors and posteriors. The regret only depends on the ratio of adversaries, not on their total number. For hard aggregators that output a decision, we prove that a random version of the truncated mean is optimal for both L1 and L2. This aggregator randomly follows a remaining value after discarding the $k$ lowest and highest reported values. We extend the hard aggregator to multi-state setting. We evaluate our aggregators numerically in an ensemble learning task. We also obtain negative results for general adversarial aggregation problems under broader information structures and report spaces.

Problem

• Robust aggregation with truthful and adversarial experts
• Optimal aggregator design under worst-case scenarios
• Regret minimization in decision aggregation with adversaries

Innovation

• Truncated mean optimal for L1 loss
• Piecewise linear functions for L2 loss
• Random truncated mean for hard decisions