From No-Regret to Strategically Robust Learning in Repeated Auctions

TL;DR

This paper demonstrates that any no-regret learning algorithm, when applied to quantile-based bidding strategies in repeated auctions, guarantees strategic robustness and revenue close to optimal, extending prior results beyond specific algorithms.

Contribution

It generalizes the strategic robustness of online learning in auctions to all no-regret algorithms under certain conditions, not just agile OGD.

Findings

Any no-regret algorithm with gradient feedback is strategically robust in repeated auctions.

The multiplicative weights update algorithm achieves both optimal regret and strategic robustness.

Results connect Myerson's auction theory with standard no-regret learning theory.

Abstract

In Bayesian single-item auctions, a monotone bidding strategy--one that prescribes a higher bid for a higher value type--can be equivalently represented as a partition of the quantile space into consecutive intervals corresponding to increasing bids. Kumar et al. (2024) prove that agile online gradient descent (OGD), when used to update a monotone bidding strategy through its quantile representation, is strategically robust in repeated first-price auctions: when all bidders employ agile OGD in this way, the auctioneer's average revenue per round is at most the revenue of Myerson's optimal auction, regardless of how she adjusts the reserve price over time. In this work, we show that this strategic robustness guarantee is not unique to agile OGD or to the first-price auction: any no-regret learning algorithm, when fed gradient feedback with respect to the quantile representation, is strategically robust, even if the auction format changes every round, provided the format satisfies allocation monotonicity and voluntary participation. In particular, the multiplicative weights update (MWU) algorithm simultaneously achieves the optimal regret guarantee and a strong strategic robustness guarantee in this auction setting. At a technical level, our results are established via a simple relation that bridges Myerson's auction theory and standard no-regret learning theory.