Is Online Linear Optimization Sufficient for Strategic Robustness?

2026-02-12

AI Summary

This work addresses the challenge of designing bidding algorithms in repeated Bayesian first-price auctions that simultaneously achieve low regret and strategic robustness against seller manipulation. The authors propose a black-box reduction that transforms any online linear optimization (OLO) algorithm into a bidding strategy that is both no-regret and robust, applicable in both known and unknown value distribution settings. A key contribution is the first proof that sublinear linearized regret suffices to guarantee strategic robustness, yielding an exponential improvement in dependence on the number of bidders $K$ and eliminating the need for prior assumptions on bounded density. Under known distributions, the algorithm achieves $O(\sqrt{T \log K})$ regret; under unknown distributions, it attains $O(\sqrt{T(\log K + \log(T/\delta))})$ regret with high probability, while preserving strategic robustness.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We consider bidding in repeated Bayesian first-price auctions. Bidding algorithms that achieve optimal regret have been extensively studied, but their strategic robustness to the seller's manipulation remains relatively underexplored. Bidding algorithms based on no-swap-regret algorithms achieve both desirable properties, but are suboptimal in terms of statistical and computational efficiency. In contrast, online gradient ascent is the only algorithm that achieves $O(\sqrt{TK})$ regret and strategic robustness [KSS24], where $T$ denotes the number of auctions and $K$ the number of bids. In this paper, we explore whether simple online linear optimization (OLO) algorithms suffice for bidding algorithms with both desirable properties. Our main result shows that sublinear linearized regret is sufficient for strategic robustness. Specifically, we construct simple black-box reductions that convert any OLO algorithm into a strategically robust no-regret bidding algorithm, in both known and unknown value distribution settings. For the known value distribution case, our reduction yields a bidding algorithm that achieves $O(\sqrt{T \log K})$ regret and strategic robustness (with exponential improvement on the $K$-dependence compared to [KSS24]). For the unknown value distribution case, our reduction gives a bidding algorithm with high-probability $O(\sqrt{T (\log K+\log(T/\delta)})$ regret and strategic robustness, while removing the bounded density assumption made in [KSS24].

Problem

• Online Linear Optimization
• Strategic Robustness
• First-Price Auctions
• No-Regret Bidding
• Bayesian Auctions

Innovation

• online linear optimization
• strategic robustness
• no-regret bidding
• black-box reduction
• first-price auctions