  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.
