# Optimal Real-Time Bidding Strategies

arXiv: https://arxiv.org/abs/1511.08409 · HTML: https://mlsanity.com/paper/1511.08409/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2015.

## Built on by (most cited first, 8 of 8)

- [Bidding Agent Design in the LinkedIn Ad Marketplace](https://mlsanity.com/paper/2202.12472/) (2022)
- [Adversarial Constrained Bidding via Minimax Regret Optimization with Causality-Aware Reinforcement Learning](https://mlsanity.com/paper/2306.07106/) (2023)
- [Dynamic Budget Throttling in Repeated Second-Price Auctions](https://mlsanity.com/paper/2207.04690/) (2022)
- [Near-continuous time Reinforcement Learning for continuous state-action spaces](https://mlsanity.com/paper/2309.02815/) (2023)
- [Do not Waste Money on Advertising Spend: Bid Recommendation via Concavity Changes](https://mlsanity.com/paper/2212.13923/) (2022)
- [Risk-Aware Bid Optimization for Online Display Advertisement](https://mlsanity.com/paper/2210.15837/) (2022)
- [RTB Formulation Using Point Process](https://mlsanity.com/paper/2308.09122/) (2023)
- [A Lightweight MPC Bidding Framework for Brand Auction Ads](https://mlsanity.com/paper/2603.07721/) (2026)

## Abstract (arXiv)

The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (KPI). The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the textitprice to beat for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and that almost-closed form solutions can be found by using a fluid limit. Numerical examples are also carried out.