Safe Online Bid Optimization with Return on Investment and Budget Constraints
Matteo Castiglioni, Alessandro Nuara, Giulia Romano, Giorgio Spadaro, Francesco Trovò, Nicola Gatti
TL;DR
Addresses the challenge of online bid optimization under uncertain ROI and budget constraints in internet advertising. Proposes GP-based estimation integrated with a dynamic-programming optimizer to produce GCB and safe variants, and proves fundamental limits showing a tradeoff between sublinear regret and constraint violations. The paper provides sublinear regret guarantees for GCB, safety guarantees for GCB_safe, and a tunable tolerance version GCB_safe(ψ,φ) that achieves both goals with controlled relaxation. Empirical results on synthetic AdTech-like settings illustrate the safety/regret tradeoffs and practical viability of tolerance-based safety in dynamic bidding.
Abstract
In online marketing, the advertisers aim to balance achieving high volumes and high profitability. The companies' business units address this tradeoff by maximizing the volumes while guaranteeing a minimum Return On Investment (ROI) level. Such a task can be naturally modeled as a combinatorial optimization problem subject to ROI and budget constraints that can be solved online. In this picture, the learner's uncertainty over the constraints' parameters plays a crucial role since the algorithms' exploration choices might lead to their violation during the entire learning process. Such violations represent a major obstacle to adopting online techniques in real-world applications. Thus, controlling the algorithms' exploration during learning is paramount to making humans trust online learning tools. This paper studies the nature of both optimization and learning problems. In particular, we show that the learning problem is inapproximable within any factor (unless P = NP) and provide a pseudo-polynomial-time algorithm to solve its discretized version. Subsequently, we prove that no online learning algorithm can violate the (ROI or budget) constraints a sublinear number of times during the learning process while guaranteeing a sublinear regret. We provide the $GCB$ algorithm that guarantees sublinear regret at the cost of a linear number of constraint violations and $GCB_{safe}$ that guarantees w.h.p. a constant upper bound on the number of constraint violations at the cost of a linear regret. Moreover, we designed $GCB_{safe}(ψ,φ)$, which guarantees both sublinear regret and safety w.h.p. at the cost of accepting tolerances $ψ$ and $φ$ in the satisfaction of the ROI and budget constraints, respectively. Finally, we provide experimental results to compare the regret and constraint violations of $GCB$, $GCB_{safe}$, and $GCB_{safe}(ψ,φ)$.