This Research Card aims to formulate an optimal bidding strategy for repeated auctions, considering how a buyer’s utility is affected by the time since their last purchase. It also explores the costs involved in implementing simpler shading policies.
- Title: Repeated Bidding with Dynamic Value
- Short Title: How to optimally account for the user fatigue in the bid
- Authors: Benjamin Heymann, Alexandre Gilotte, Rémi Chan-Renous
- Team : AI for Advertising Research
- Revue : WINE
- Status : Accepted
- Category : Control
Why did we work on this topic (the problem we want to solve)?
Traditional bidding strategies in digital advertising, particularly real-time bidding (RTB), often fail to account for the dynamic nature of bidder valuations, leading to suboptimal outcomes. This paper addresses this issue by exploring the scenario where a bidder’s valuation for an item (e.g., ad opportunity) depends on the time elapsed since their last successful bid. This dynamic value stems from factors such as real-time ad slot auctions, repeated banner displays to users, and the temporary drop in marginal value after a user sees a banner. The goal is to design optimal bidding strategies that consider the impact of winning an auction on the value of future opportunities.
What did we find? What did we achieve?
This paper contributes to the field by developing a realistic minimal model to study the coupling between present and future bidding decisions within a dynamic value environment. It formulates the optimal bidding policy design as a continuous-time optimal control problem over an infinite horizon and introduces an Algorithm which iteratively converges toward the optimal policy. Additional it demonstrates that there exists very simple strategies that, while not optimal, perform very well in many scenarios.
How did we proceed?
The paper models the problem as a continuous Markov process, defining the state by the time since the last won auction. It derives a non-linear differential equation for the Bellman value function, representing the optimal achievable value. A dichotomy-based algorithm is presented for computing the optimal policy by analyzing the asymptotic behavior of solutions to a parametrized differential equation. Through numerical simulations, the optimal policy is compared to the greedy policy, and the effectiveness of shading strategies is demonstrated. The paper also emphasizes the complexity of achieving optimal bidding with non-concave reward.
What is the originality here?
We question the common belief that feature engineering alone can optimize RTB bidding strategies by introducing a deliberately minimalistic model. We hope this research will encourage both researchers and practitioners to look further into this problem.
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