  Automated bidding, an emerging intelligent decision making paradigm powered
by machine learning, has become popular in online advertising. Advertisers in
automated bidding evaluate the cumulative utilities and have private financial
constraints over multiple ad auctions in a long-term period. Based on these
distinct features, we consider a new ad auction model for automated bidding:
the values of advertisers are public while the financial constraints, such as
budget and return on investment (ROI) rate, are private types. We derive the
truthfulness conditions with respect to private constraints for this
multi-dimensional setting, and demonstrate any feasible allocation rule could
be equivalently reduced to a series of non-decreasing functions on budget.
However, the resulted allocation mapped from these non-decreasing functions
generally follows an irregular shape, making it difficult to obtain a
closed-form expression for the auction objective. To overcome this design
difficulty, we propose a family of truthful automated bidding auction with
personalized rank scores, similar to the Generalized Second-Price (GSP)
auction. The intuition behind our design is to leverage personalized rank
scores as the criteria to allocate items, and compute a critical ROI to
transform the constraints on budget to the same dimension as ROI. The
experimental results demonstrate that the proposed auction mechanism
outperforms the widely used ad auctions, such as first-price auction and
second-price auction, in various automated bidding environments.
