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This paper investigates whether online linear optimization (OLO) algorithms are sufficient for achieving strategic robustness in repeated Bayesian first-price auctions. The authors demonstrate that sublinear linearized regret in OLO is sufficient for strategic robustness, enabling the construction of strategically robust no-regret bidding algorithms via black-box reductions. Their reductions yield improved regret bounds compared to prior work, achieving $O(\sqrt{T \log K})$ regret in the known value distribution case and $O(\sqrt{T (\log K+\log(T/\delta)})$ regret in the unknown case, while also removing a bounded density assumption.
Simple online linear optimization can be surprisingly effective for designing bidding algorithms that are both regret-optimal and strategically robust against seller manipulation, outperforming prior approaches.
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].