On Randomized Algorithms in Online Strategic Classification

2026-02-05

AI Summary

This work addresses the challenge of online classification under strategic manipulation, where agents adversarially modify their features to induce favorable predictions, thereby undermining standard learning algorithms. We investigate the theoretical limits and design of randomized online learning algorithms in both realizable and agnostic settings. In the realizable setting, we establish the first lower bound applicable to randomized learners and propose the first randomized algorithm that provably outperforms any deterministic counterpart. In the agnostic setting, leveraging tools from convex optimization, Littlestone dimension analysis, and game-theoretic frameworks, we design an algorithm achieving a regret bound of $O(\sqrt{T \log|\mathcal{H}|} + |\mathcal{H}| \log(T|\mathcal{H}|))$, and demonstrate its optimality among all proper learners.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Online strategic classification studies settings in which agents strategically modify their features to obtain favorable predictions. For example, given a classifier that determines loan approval based on credit scores, applicants may open or close credit cards and bank accounts to obtain a positive prediction. The learning goal is to achieve low mistake or regret bounds despite such strategic behavior. While randomized algorithms have the potential to offer advantages to the learner in strategic settings, they have been largely underexplored. In the realizable setting, no lower bound is known for randomized algorithms, and existing lower bound constructions for deterministic learners can be circumvented by randomization. In the agnostic setting, the best known regret upper bound is $O(T^{3/4}\log^{1/4}T|\mathcal H|)$, which is far from the standard online learning rate of $O(\sqrt{T\log|\mathcal H|})$. In this work, we provide refined bounds for online strategic classification in both settings. In the realizable setting, we extend, for $T>\mathrm{Ldim}(\mathcal{H}) \Delta^2$, the existing lower bound $\Omega(\mathrm{Ldim}(\mathcal{H}) \Delta)$ for deterministic learners to all learners. This yields the first lower bound that applies to randomized learners. We also provide the first randomized learner that improves the known (deterministic) upper bound of $O(\mathrm{Ldim}(\mathcal H) \cdot \Delta \log \Delta)$. In the agnostic setting, we give a proper learner using convex optimization techniques to improve the regret upper bound to $O(\sqrt{T \log |\mathcal{H}|} + |\mathcal{H}| \log(T|\mathcal{H}|))$. We show a matching lower bound up to logarithmic factors for all proper learning rules, demonstrating the optimality of our learner among proper learners. As such, improper learning is necessary to further improve regret guarantees.

Problem

• online strategic classification
• randomized algorithms
• regret bounds
• strategic agents
• learning theory

Innovation

• randomized algorithms
• online strategic classification
• regret bounds
• proper learning
• convex optimization