Robust Online Learning with Private Information

2025-05-08

AI Summary

This paper investigates the robustness of online learning algorithms against adaptive adversaries when learners possess private information: existing no-external-regret algorithms are vulnerable to strategic manipulation, leading to complete extraction of surplus—even in stationary environments. We model the interaction as a repeated two-player game between the learner and the environment, propose the “partial safety” design principle, and introduce the Explore-Exploit-Punish (EEP) algorithm. EEP provably satisfies partial safety: it achieves the optimal $O(sqrt{T})$ external regret bound in stationary settings while resisting full exploitation by adaptive adversaries. We further derive welfare-enhancing variants. Our analysis exposes a fundamental vulnerability of standard regret-minimization algorithms under adverse selection, revealing that low external regret alone does not guarantee robustness or surplus preservation. This work establishes a new paradigm for robust online mechanism design, bridging learning theory and incentive-aware optimization.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Online Learning & Bandits
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper investigates the robustness of online learning algorithms when learners possess private information. No-external-regret algorithms, prevalent in machine learning, are vulnerable to strategic manipulation, allowing an adaptive opponent to extract full surplus. Even standard no-weak-external-regret algorithms, designed for optimal learning in stationary environments, exhibit similar vulnerabilities. This raises a fundamental question: can a learner simultaneously prevent full surplus extraction by adaptive opponents while maintaining optimal performance in well-behaved environments? To address this, we model the problem as a two-player repeated game, where the learner with private information plays against the environment, facing ambiguity about the environment's types: stationary or adaptive. We introduce emph{partial safety} as a key design criterion for online learning algorithms to prevent full surplus extraction. We then propose the emph{Explore-Exploit-Punish} ( extsf{EEP}) algorithm and prove that it satisfies partial safety while achieving optimal learning in stationary environments, and has a variant that delivers improved welfare performance. Our findings highlight the risks of applying standard online learning algorithms in strategic settings with adverse selection. We advocate for a shift toward online learning algorithms that explicitly incorporate safeguards against strategic manipulation while ensuring strong learning performance.

Problem

• Robustness of online learning with private information
• Preventing surplus extraction by adaptive opponents
• Balancing safety and performance in strategic settings

Innovation

• Introduces partial safety design criterion
• Proposes Explore-Exploit-Punish algorithm
• Ensures optimal learning with safeguards