Competitive Auctions with Imperfect Predictions
Pinyan Lu, Zongqi Wan, Jialin Zhang
TL;DR
This work investigates revenue-maximizing auctions under the competitive framework when bidders' private values are available as imperfect predictions. By introducing a learning-augmented framework with 1-consistency against the OPT benchmark and constant-robustness against traditional benchmarks, the authors design mechanisms for digital goods, limited-supply, and downward-closed permutation environments, including online variants. The core techniques include a Bid-Independent Combination approach, Benchmark Decomposition, and the Discard-and-Limit Weakest Competitor VCG mechanism, along with an error-tolerant design that adapts to prediction error through confidence parameters. A key result is that 1-consistency with OPT is achievable across environments while maintaining constant robustness against benchmarks like $\mathcal{F}^{(2)}$, $\textsc{maxV}$, and $EFO^{(2)}$, though a fundamental lower bound shows perfect consistency precludes achieving the absolute optimal worst-case ratio. The work also provides OSAP for online settings and rigorous lower bounds, illustrating a nuanced trade-off between consistency and robustness in learning-augmented auction design with practical error tolerance.
Abstract
The competitive auction was first proposed by Goldberg, Hartline, and Wright. In their paper, they introduce the competitive analysis framework of online algorithm designing into the traditional revenue-maximizing auction design problem. While the competitive analysis framework only cares about the worst-case bound, a growing body of work in the online algorithm community studies the learning-augmented framework. In this framework, designers are allowed to leverage imperfect machine-learned predictions of unknown information and pursue better theoretical guarantees when the prediction is accurate(consistency). Meanwhile, designers also need to maintain a nearly-optimal worst-case ratio(robustness). In this work, we revisit the competitive auctions in the learning-augmented setting. We leverage the imperfect predictions of the private value of the bidders and design the learning-augmented mechanisms for several competitive auctions with different constraints, including digital good auctions, limited-supply auctions, and general downward-closed permutation environments. For all these auction environments, our mechanisms enjoy $1$-consistency against the strongest benchmark $OPT$, which is impossible to achieve $O(1)$-competitive without predictions. At the same time, our mechanisms also maintain the $O(1)$-robustness against all benchmarks considered in the traditional competitive analysis. Considering the possible inaccuracy of the predictions, we provide a reduction that transforms our learning-augmented mechanisms into an error-tolerant version, which enables the learning-augmented mechanism to ensure satisfactory revenue in scenarios where the prediction error is moderate.