Multi-Platform Autobidding with and without Predictions

TL;DR

The paper addresses the problem of finding an optimal bidding strategy for advertisers across multiple platforms when the per-platform value-cost mappings are black-box. It models the setting with $m$ platforms and $n$ bids per platform under a global budget and ROS constraint, introducing the marginal-cost function $MC_j(\mu)$ and a fractional optimization framework. The key contributions are the MedianOfMedians algorithm, achieving $O(m \log (mn) \log n)$ query complexity to compute the exact fractional optimum, and a learning-augmented variant BranchOutMedianOfMedians that leverages a predicted strategy $\hat{\pmb{\mu}}$ to obtain $O(m \log (m\eta) \log \eta)$ queries, with robustness that degrades gracefully to the worst-case bound when the prediction is inaccurate. Together, these results deliver a best-of-both-worlds approach that can attain $O(m)$ queries with accurate predictions while preserving the baseline performance in the absence of reliable predictions, offering practical guidance for scalable, cross-platform autobidding under uncertainty.

Abstract

We study the problem of finding the optimal bidding strategy for an advertiser in a multi-platform auction setting. The competition on a platform is captured by a value and a cost function, mapping bidding strategies to value and cost respectively. We assume a diminishing returns property, whereby the marginal cost is increasing in value. The advertiser uses an autobidder that selects a bidding strategy for each platform, aiming to maximize total value subject to budget and return-on-spend constraint. The advertiser has no prior information and learns about the value and cost functions by querying a platform with a specific bidding strategy. Our goal is to design algorithms that find the optimal bidding strategy with a small number of queries. We first present an algorithm that requires \(O(m \log (mn) \log n)\) queries, where $m$ is the number of platforms and $n$ is the number of possible bidding strategies in each platform. Moreover, we adopt the learning-augmented framework and propose an algorithm that utilizes a (possibly erroneous) prediction of the optimal bidding strategy. We provide a $O(m \log (mη) \log η)$ query-complexity bound on our algorithm as a function of the prediction error $η$. This guarantee gracefully degrades to \(O(m \log (mn) \log n)\). This achieves a ``best-of-both-worlds'' scenario: \(O(m)\) queries when given a correct prediction, and \(O(m \log (mn) \log n)\) even for an arbitrary incorrect prediction.

Figures (1)

• Figure 1: Illustration of one round of MedianOfMedians. Each column represents the current search region of a platform. The vertical arrow indicates the increasing direction of $\mu$ in each platform. The platforms are ranked by the median marginals as described in the algorithm. The grey point represents the queried $k$ value. If $\pmb{\mu}^k$ is infeasible, all strategies in the shaded round rectangle are removed; otherwise, all strategies in the non-shaded one are removed.

Theorems & Definitions (21)

• Lemma 1
• Lemma 2
• proof
• proof : Proof of Lemma \ref{['lem:opt']}
• Definition 1: Almost-Optimal Strategy
• Lemma 3: Optimal Bidding Strategy
• proof
• Example 1
• Lemma 4
• proof