arXiv subjects

Sébastien Lahaie

Publications and source records attributed to Sébastien Lahaie.

13 recordsLinked to original sources

arXiv2026

Iterative Vickrey Auctions via Linear Programming

Building on the linear programming approach to competitive equilibrium pricing, we develop a general method for constructing iterative auctions that achieve Vickrey-Clarke-Groves (VCG) outcomes. We show how to transform a linear program characterizing competitive equilibrium prices into one that characterizes universal competitive equilibrium (UCE) prices, which elicit precisely the information needed to compute VCG payments. By applying a primal-dual algorithm to these transformed programs, we derive iterative Vickrey auctions that maintain a single price path, eliminating the overhead and incentive problems associated with multiple price paths used solely for payment calculations. We demonstrate the versatility of our method by developing a novel iterative Vickrey auction for the multi-unit setting and an iterative variant of the Product-Mix auction. The resulting auctions combine the transparency of iterative price discovery with the efficiency and incentive properties of the VCG mechanism.

cs.GT↗

arXiv2025

Bidder Feedback in First-Price Auctions for Video Advertising

In first-price auctions for display advertising, exchanges typically communicate the "minimum-bid-to-win" to bidders after the auction as feedback for their bidding algorithms. For a winner, this is the second-highest bid, while for losing bidders it is the highest bid. In this paper we investigate the generalization of this concept to general combinatorial auctions, motivated by the domain of video advertising. In a video pod auction, ad slots during an advertising break in a video stream are auctioned all at once, under several kinds of allocation constraints such as a constraint on total ad duration. We cast the problem in terms of computing bid updates (discounts and raises) that maintain the optimality of the current allocation. Our main result characterizes the set of joint bid updates with this property as the core of an associated bicooperative game. In the case of the assignment problem--a special case of video pod auctions--we provide a linear programming characterization of this bicooperative core. Our characterization leads to several candidates for a generalized minimum-bid-to-win. Drawing on video pod auction data from a real ad exchange, we perform an empirical analysis to understand the bidding dynamics they induce and their convergence properties.

cs.GT↗

arXiv2025

Ad Auctions for LLMs via Retrieval Augmented Generation

In the field of computational advertising, the integration of ads into the outputs of large language models (LLMs) presents an opportunity to support these services without compromising content integrity. This paper introduces novel auction mechanisms for ad allocation and pricing within the textual outputs of LLMs, leveraging retrieval-augmented generation (RAG). We propose a segment auction where an ad is probabilistically retrieved for each discourse segment (paragraph, section, or entire output) according to its bid and relevance, following the RAG framework, and priced according to competing bids. We show that our auction maximizes logarithmic social welfare, a new notion of welfare that balances allocation efficiency and fairness, and we characterize the associated incentive-compatible pricing rule. These results are extended to multi-ad allocation per segment. An empirical evaluation validates the feasibility and effectiveness of our approach over several ad auction scenarios, and exhibits inherent tradeoffs in metrics as we allow the LLM more flexibility to allocate ads.

cs.GT↗

arXiv2025

Integer Programming for Generalized Causal Bootstrap Designs

In experimental causal inference, we distinguish between two sources of uncertainty: design uncertainty, due to the treatment assignment mechanism, and sampling uncertainty, when the sample is drawn from a super-population. This distinction matters in settings with small fixed samples and heterogeneous treatment effects, as in geographical experiments. The standard bootstrap procedure most often used by practitioners primarily estimates sampling uncertainty, and the causal bootstrap procedure, which accounts for design uncertainty, was developed for the completely randomized design and the difference-in-means estimator, whereas non-standard designs and estimators are often used in these low-power regimes. We address this gap by proposing an integer program which computes numerically the worst-case copula used as an input to the causal bootstrap method, in a wide range of settings. Specifically, we prove the asymptotic validity of our approach for unconfounded, conditionally unconfounded, and and individualistic with bounded confoundedness assignments, as well as generalizing to any linear-in-treatment and quadratic-in-treatment estimators. We demonstrate the refined confidence intervals achieved through simulations of small geographical experiments.

stat.ME↗

arXiv2021

Robust Clearing Price Mechanisms for Reserve Price Optimization

Setting an effective reserve price for strategic bidders in repeated auctions is a central question in online advertising. In this paper, we investigate how to set an anonymous reserve price in repeated auctions based on historical bids in a way that balances revenue and incentives to misreport. We propose two simple and computationally efficient methods to set reserve prices based on the notion of a clearing price and make them robust to bidder misreports. The first approach adds random noise to the reserve price, drawing on techniques from differential privacy. The second method applies a smoothing technique by adding noise to the training bids used to compute the reserve price. We provide theoretical guarantees on the trade-offs between the revenue performance and bid-shading incentives of these two mechanisms. Finally, we empirically evaluate our mechanisms on synthetic data to validate our theoretical findings.

cs.GT↗

arXiv2020

Reserve Price Optimization for First Price Auctions

The display advertising industry has recently transitioned from second- to first-price auctions as its primary mechanism for ad allocation and pricing. In light of this, publishers need to re-evaluate and optimize their auction parameters, notably reserve prices. In this paper, we propose a gradient-based algorithm to adaptively update and optimize reserve prices based on estimates of bidders' responsiveness to experimental shocks in reserves. Our key innovation is to draw on the inherent structure of the revenue objective in order to reduce the variance of gradient estimates and improve convergence rates in both theory and practice. We show that revenue in a first-price auction can be usefully decomposed into a \emph{demand} component and a \emph{bidding} component, and introduce techniques to reduce the variance of each component. We characterize the bias-variance trade-offs of these techniques and validate the performance of our proposed algorithm through experiments on synthetic data and real display ad auctions data from Google ad exchange.

cs.GT↗

arXiv2019

Fast Iterative Combinatorial Auctions via Bayesian Learning

Iterative combinatorial auctions (CAs) are often used in multi-billion dollar domains like spectrum auctions, and speed of convergence is one of the crucial factors behind the choice of a specific design for practical applications. To achieve fast convergence, current CAs require careful tuning of the price update rule to balance convergence speed and allocative efficiency. Brero and Lahaie (2018) recently introduced a Bayesian iterative auction design for settings with single-minded bidders. The Bayesian approach allowed them to incorporate prior knowledge into the price update algorithm, reducing the number of rounds to convergence with minimal parameter tuning. In this paper, we generalize their work to settings with no restrictions on bidder valuations. We introduce a new Bayesian CA design for this general setting which uses Monte Carlo Expectation Maximization to update prices at each round of the auction. We evaluate our approach via simulations on CATS instances. Our results show that our Bayesian CA outperforms even a highly optimized benchmark in terms of clearing percentage and convergence speed.

cs.GT↗

arXiv2019

Learning to Clear the Market

The problem of market clearing is to set a price for an item such that quantity demanded equals quantity supplied. In this work, we cast the problem of predicting clearing prices into a learning framework and use the resulting models to perform revenue optimization in auctions and markets with contextual information. The economic intuition behind market clearing allows us to obtain fine-grained control over the aggressiveness of the resulting pricing policy, grounded in theory. To evaluate our approach, we fit a model of clearing prices over a massive dataset of bids in display ad auctions from a major ad exchange. The learned prices outperform other modeling techniques in the literature in terms of revenue and efficiency trade-offs. Because of the convex nature of the clearing loss function, the convergence rate of our method is as fast as linear regression.

cs.LG↗

arXiv2018

A Bayesian Clearing Mechanism for Combinatorial Auctions

We cast the problem of combinatorial auction design in a Bayesian framework in order to incorporate prior information into the auction process and minimize the number of rounds to convergence. We first develop a generative model of agent valuations and market prices such that clearing prices become maximum a posteriori estimates given observed agent valuations. This generative model then forms the basis of an auction process which alternates between refining estimates of agent valuations and computing candidate clearing prices. We provide an implementation of the auction using assumed density filtering to estimate valuations and expectation maximization to compute prices. An empirical evaluation over a range of valuation domains demonstrates that our Bayesian auction mechanism is highly competitive against the combinatorial clock auction in terms of rounds to convergence, even under the most favorable choices of price increment for this baseline.

cs.GT↗

arXiv2018

A Decomposition of Forecast Error in Prediction Markets

We analyze sources of error in prediction market forecasts in order to bound the difference between a security's price and the ground truth it estimates. We consider cost-function-based prediction markets in which an automated market maker adjusts security prices according to the history of trade. We decompose the forecasting error into three components: sampling error, arising because traders only possess noisy estimates of ground truth; market-maker bias, resulting from the use of a particular market maker (i.e., cost function) to facilitate trade; and convergence error, arising because, at any point in time, market prices may still be in flux. Our goal is to make explicit the tradeoffs between these error components, influenced by design decisions such as the functional form of the cost function and the amount of liquidity in the market. We consider a specific model in which traders have exponential utility and exponential-family beliefs representing noisy estimates of ground truth. In this setting, sampling error vanishes as the number of traders grows, but there is a tradeoff between the other two components. We provide both upper and lower bounds on market-maker bias and convergence error, and demonstrate via numerical simulations that these bounds are tight. Our results yield new insights into the question of how to set the market's liquidity parameter and into the forecasting benefits of enforcing coherent prices across securities.

cs.GT↗

arXiv2016

Arbitrage-Free Combinatorial Market Making via Integer Programming

We present a new combinatorial market maker that operates arbitrage-free combinatorial prediction markets specified by integer programs. Although the problem of arbitrage-free pricing, while maintaining a bound on the subsidy provided by the market maker, is #P-hard in the worst case, we posit that the typical case might be amenable to modern integer programming (IP) solvers. At the crux of our method is the Frank-Wolfe (conditional gradient) algorithm which is used to implement a Bregman projection aligned with the market maker's cost function, using an IP solver as an oracle. We demonstrate the tractability and improved accuracy of our approach on real-world prediction market data from combinatorial bets placed on the 2010 NCAA Men's Division I Basketball Tournament, where the outcome space is of size 2^63. To our knowledge, this is the first implementation and empirical evaluation of an arbitrage-free combinatorial prediction market on this scale.

cs.GT↗

arXiv2016

Rate of Price Discovery in Iterative Combinatorial Auctions

We study a class of iterative combinatorial auctions which can be viewed as subgradient descent methods for the problem of pricing bundles to balance supply and demand. We provide concrete convergence rates for auctions in this class, bounding the number of auction rounds needed to reach clearing prices. Our analysis allows for a variety of pricing schemes, including item, bundle, and polynomial pricing, and the respective convergence rates confirm that more expressive pricing schemes come at the cost of slower convergence. We consider two models of bidder behavior. In the first model, bidders behave stochastically according to a random utility model, which includes standard best-response bidding as a special case. In the second model, bidders behave arbitrarily (even adversarially), and meaningful convergence relies on properly designed activity rules.

cs.GT↗

arXiv2014

Information Aggregation in Exponential Family Markets

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability distribution template used in statistics. We give a full development of this relationship and explore a range of benefits. We draw connections between the information aggregation of market prices and the belief aggregation of learning agents that rely on exponential family distributions. We develop a very natural analysis of the market behavior as well as the price equilibrium under the assumption that the traders exhibit risk aversion according to exponential utility. We also consider similar aspects under alternative models, such as when traders are budget constrained.

cs.AI↗