[Paper Review] Multi-channel Autobidding with Budget and ROI Constraints

Yuan Deng, Negin Golrezaei+3 more|arXiv (Cornell University)|Feb 3, 2023

Auction Theory and Applications9 citations

TL;DR

This paper models multi-channel autobidding where advertisers set per-channel budgets and ROIs to maximize total conversions under global ROI and budget constraints. It shows budgets suffice for global optimality and proposes a bandit-based SGD-UCB algorithm to learn per-channel budgets under limited feedback.

ABSTRACT

In digital online advertising, advertisers procure ad impressions simultaneously on multiple platforms, or so-called channels, such as Google Ads, Meta Ads Manager, etc., each of which consists of numerous ad auctions. We study how an advertiser maximizes total conversion (e.g. ad clicks) while satisfying aggregate return-on-investment (ROI) and budget constraints across all channels. In practice, an advertiser does not have control over, and thus cannot globally optimize, which individual ad auctions she participates in for each channel, and instead authorizes a channel to procure impressions on her behalf: the advertiser can only utilize two levers on each channel, namely setting a per-channel budget and per-channel target ROI. In this work, we first analyze the effectiveness of each of these levers for solving the advertiser's global multi-channel problem. We show that when an advertiser only optimizes over per-channel ROIs, her total conversion can be arbitrarily worse than what she could have obtained in the global problem. Further, we show that the advertiser can achieve the global optimal conversion when she only optimizes over per-channel budgets. In light of this finding, under a bandit feedback setting that mimics real-world scenarios where advertisers have limited information on ad auctions in each channels and how channels procure ads, we present an efficient learning algorithm that produces per-channel budgets whose resulting conversion approximates that of the global optimal problem. Finally, we argue that all our results hold for both single-item and multi-item auctions from which channels procure impressions on advertisers' behalf.

Motivation & Objective

• Motivate the practical problem of optimizing ad campaigns across multiple channels with limited control over individual auctions.
• Formally model two advertiser levers—per-channel budgets and per-channel ROIs—and analyze their effectiveness for achieving a global optimum.
• Show that per-channel budgets (and not ROIs) can achieve global optimal conversion under global ROI and budget constraints.
• Develop and analyze a learning algorithm that finds near-optimal per-channel budgets under bandit feedback.
• Provide numerical studies validating the proposed approach and exploring extensions to general objectives.

Proposed method

• Define GL-OPT as the advertiser’s global optimization problem over all channels with a global ROI constraint and a total budget constraint.
• Show that per-channel ROI optimization can yield arbitrarily worse conversion than GL-OPT, while per-channel budgets can achieve GL-OPT (Theorem 3.2 and Theorem 3.3).
• Conclude that per-channel ROIs are redundant once budgets are optimized (Corollary 3.4).
• Formulate CH-OPT with budget-only levers and analyze the bandit-feedback learning problem.
• Develop an SGD-UCB based algorithm that, over T periods, outputs per-channel budgets achieving an O(T^{-1/3}) approximation to the budget-optimal conversion.
• Provide assumptions and discuss extensions to general objectives and multi-impression auctions.

Experimental results

Research questions

• RQ1 Do per-channel budgets and per-channel ROIs suffice to achieve the global optimal conversion under ROI and budget constraints?
• RQ2 Can optimizing only per-channel budgets achieve GL-OPT, while per-channel ROIs may fail?
• RQ3 How can advertisers learn near-optimal per-channel budgets under bandit feedback?
• RQ4 What extensions are viable for general advertiser objectives and multi-impression auctions?

Key findings

• Per-channel budgets suffice to achieve the global optimum (GL-OPT) for any target ROI and budget, even with finite budgets.
• Per-channel ROI-only optimization can lead to arbitrarily poor conversion compared to GL-OPT under the same global constraints.
• Per-channel ROIs become redundant when budgets are optimized (redundancy result).
• An SGD-UCB based algorithm under bandit feedback achieves an O(T^{-1/3}) approximation to the optimal per-channel budget solution within T periods.
• Numerical studies show the proposed algorithm accurately approximates optimal per-channel budgets in practical setups.