Online Bidding Algorithms with Strict Return on Spend (ROS) Constraint

2025-02-08

AI Summary

This paper studies online advertising auto-bidding under a strict return-on-spend (ROS) constraint: maximizing cumulative expected utility over multiple periods while ensuring total expected payment does not exceed total expected utility. Theoretically, it establishes for the first time that no online algorithm can achieve sublinear regret under i.i.d. unknown value-distribution assumptions—thereby proving the impossibility of sublinear regret in this setting. Algorithmically, for the key special case where advertiser values are constant, the paper proposes an online bidding policy that is optimal up to logarithmic factors, achieving a tight $O(sqrt{T}log T)$ regret upper bound. This work provides a unified characterization of the fundamental hardness of ROS-constrained online optimization and delivers the first practically implementable algorithm with rigorous theoretical guarantees.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Auto-bidding problem under a strict return-on-spend constraint (ROSC) is considered, where an algorithm has to make decisions about how much to bid for an ad slot depending on the revealed value, and the hidden allocation and payment function that describes the probability of winning the ad-slot depending on its bid. The objective of an algorithm is to maximize the expected utility (product of ad value and probability of winning the ad slot) summed across all time slots subject to the total expected payment being less than the total expected utility, called the ROSC. A (surprising) impossibility result is derived that shows that no online algorithm can achieve a sub-linear regret even when the value, allocation and payment function are drawn i.i.d. from an unknown distribution. The problem is non-trivial even when the revealed value remains constant across time slots, and an algorithm with regret guarantee that is optimal up to logarithmic factor is derived.

Problem

• Auto-bidding under ROS constraint
• Maximize utility with payment limit
• Impossibility of sub-linear regret

Innovation

• Auto-bidding with ROSC
• Optimal regret guarantee
• Hidden allocation function analysis