# Learning to Bid in Contextual First Price Auctions

arXiv: https://arxiv.org/abs/2109.03173 · HTML: https://mlsanity.com/paper/2109.03173/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 7 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Online learning in repeated auctions](https://mlsanity.com/paper/1511.05720/) (2015)
- [Learning to Bid Without Knowing your Value](https://mlsanity.com/paper/1711.01333/) (2017)
- [Optimal No-regret Learning in Repeated First-price Auctions](https://mlsanity.com/paper/2003.09795/) (2020)
- [Learning to Bid Optimally and Efficiently in Adversarial First-price Auctions](https://mlsanity.com/paper/2007.04568/) (2020)
- [Contextual Bandits with Cross-learning](https://mlsanity.com/paper/1809.09582/) (2018)
- [Contextual Search via Intrinsic Volumes](https://mlsanity.com/paper/1804.03195/) (2018)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Learning in repeated auctions](https://mlsanity.com/paper/2011.09365/) (2020)
- [Bid Prediction in Repeated Auctions with Learning](https://mlsanity.com/paper/2007.13193/) (2020)
- [Incentive-aware Contextual Pricing with Non-parametric Market Noise](https://mlsanity.com/paper/1911.03508/) (2019)
- [Bayesian Nash Equilibrium in First-Price Auction with Discrete Value Distributions](https://mlsanity.com/paper/1906.09403/) (2019)
- [Reserve Price Optimization for First Price Auctions](https://mlsanity.com/paper/2006.06519/) (2020)

## Built on by (most cited first, 19 of 19)

- [Online Bidding Algorithms for Return-on-Spend Constrained Advertisers](https://mlsanity.com/paper/2208.13713/) (2022)
- [The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations](https://mlsanity.com/paper/2307.09478/) (2023)
- [Leveraging the Hints: Adaptive Bidding in Repeated First-Price Auctions](https://mlsanity.com/paper/2211.06358/) (2022)
- [No-regret Learning in Repeated First-Price Auctions with Budget Constraints](https://mlsanity.com/paper/2205.14572/) (2022)
- [Nash Convergence of Mean-Based Learning Algorithms in First-Price Auctions](https://mlsanity.com/paper/2110.03906/) (2021)
- [Strategizing against No-Regret Learners in First-Price Auctions](https://mlsanity.com/paper/2402.08637/) (2024)
- [Optimal cross-learning for contextual bandits with unknown context distributions](https://mlsanity.com/paper/2401.01857/) (2024)
- [Joint Value Estimation and Bidding in Repeated First-Price Auctions](https://mlsanity.com/paper/2502.17292/) (2025)
- [Incrementality Bidding via Reinforcement Learning under Mixed and Delayed Rewards](https://mlsanity.com/paper/2206.01293/) (2022)
- [Best of Many Worlds Guarantees for Online Learning with Knapsacks](https://mlsanity.com/paper/2202.13710/) (2022)
- [A Parametric Contextual Online Learning Theory of Brokerage](https://mlsanity.com/paper/2407.01566/) (2024)
- [Learning in Repeated Multi-Unit Pay-As-Bid Auctions](https://mlsanity.com/paper/2307.15193/) (2023)
- [Online Bidding under RoS Constraints without Knowing the Value](https://mlsanity.com/paper/2503.03195/) (2025)
- [From No-Regret to Strategically Robust Learning in Repeated Auctions](https://mlsanity.com/paper/2601.03853/) (2026)
- [The (Marginal) Value of a Search Ad: An Online Causal Framework for Repeated Second-price Auctions](https://mlsanity.com/paper/2605.01756/) (2026)
- [Learning to Bid with Unknown Private Values in Budget-Constrained First-Price Auctions](https://mlsanity.com/paper/2605.09448/) (2026)
- [Minimax PAC Bounds for Learning in Exogenous Contextual MDPs](https://mlsanity.com/paper/2606.25170/) (2026)
- [Learning Personalized Ad Impact via Contextual Reinforcement Learning under Delayed Rewards](https://mlsanity.com/paper/2510.20055/) (2025)
- [Is Online Linear Optimization Sufficient for Strategic Robustness?](https://mlsanity.com/paper/2602.12253/) (2026)

## Abstract (arXiv)

In this paper, we investigate the problem about how to bid in repeated contextual first price auctions. We consider a single bidder (learner) who repeatedly bids in the first price auctions: at each time t, the learner observes a context xt∈ ℝd and decides the bid based on historical information and xt. We assume a structured linear model of the maximum bid of all the others mt = α0· xt + zt, where α0∈ ℝd is unknown to the learner and zt is randomly sampled from a noise distribution F with log-concave density function f. We consider both binary feedback (the learner can only observe whether she wins or not) and full information feedback (the learner can observe mt) at the end of each time t. For binary feedback, when the noise distribution F is known, we propose a bidding algorithm, by using maximum likelihood estimation (MLE) method to achieve at most widetildeO(√log(d) T) regret. Moreover, we generalize this algorithm to the setting with binary feedback and the noise distribution is unknown but belongs to a parametrized family of distributions. For the full information feedback with unknown noise distribution, we provide an algorithm that achieves regret at most widetildeO(√dT). Our approach combines an estimator for log-concave density functions and then MLE method to learn the noise distribution F and linear weight α0 simultaneously. We also provide a lower bound result such that any bidding policy in a broad class must achieve regret at least Omega(√T), even when the learner receives the full information feedback and F is known.