arXiv subjects

Patrick Loiseau

Publications and source records attributed to Patrick Loiseau.

At least 19 recordsLinked to original sources

arXiv2026

Kernel Methods for Refined Prophet Inequalities

The single-selection prophet inequality is a canonical Bayesian online selection problem in which independent nonnegative values arrive sequentially and the decision-maker must irrevocably select at most one. Classical single-threshold guarantees are tight in the worst case, but the hard instances that prove tightness are highly irregular: the prophet's advantage is driven by rare, very large realizations of the maximum. We refine this worst-case picture by imposing a bound on the relative variance of the prophet's value, $\mathrm{Var}(\max_{i\in[n]}X_i)/\mathbb E[\max_{i\in[n]}X_i]^2$. This yields a nonparametric complexity measure that interpolates between deterministic instances, where the full prophet value can be recovered, and the unrestricted worst-case regime. Our main technical contribution is a general kernel method for single-threshold prophet inequalities. The method represents an instance by the quantile function of the maximum and rewrites the payoff of a threshold as a linear kernel functional of this quantile. This turns the worst-case analysis into an infinite-dimensional convex program, restores strong minimax duality in quantile space, and reduces the bounded-variance adversary's problem to a one-parameter variational family. Applying this framework, we obtain an exact characterization of the IID bounded-variance curve and asymptotically optimal finite-horizon thresholds, a closed-form expression for the fixed-order non-identical model, and a prophet-secretary lower-bound program together with a strict separation from the IID benchmark at every positive finite variance constraint. As a further application of the same kernel viewpoint, we derive an exact formula for IID random horizons under a convexity condition on the horizon pgf, which includes monotone-hazard-rate horizons, highlighting the broad applicability of this new technique for single threshold settings.

cs.GT↗

arXiv2026

An Asymptotic Analysis of the Shapley Value for Dataset Valuation

We propose an asymptotic analysis of the Shapley value in a dataset valuation setting in which utilities are modeled as smooth functionals of empirical distributions via reproducing kernel Hilbert space (RKHS) mean embeddings. We prove that, despite its combinatorial definition, the Shapley value of a data source is asymptotically captured by a simple leading term. This term can be interpreted as the first-order contribution of a dataset relative to the surrounding data population. It also identifies the scale of the Shapley value as the number of data sources grows and provides a framework for analyzing existing Shapley value estimators. Moreover, for practitioners working with large numbers of datasets, the leading term becomes a tractable reference against which Shapley value approximations can be benchmarked.

cs.GT↗

arXiv2026

Complexity of Auctions with Interdependence

We study auction design in the celebrated interdependence model introduced by Milgrom and Weber [1982], where a mechanism designer allocates a good, maximizing the value of the agent who receives it, while inducing truthfulness using payments. In the lesser-studied procurement auctions, one allocates a chore, minimizing the cost incurred by the agent selected to perform it. Most of the past literature in theoretical computer science considers designing truthful mechanisms with constant approximation for the value setting, with restricted domains and monotone valuation functions. In this work, we study the general computational problems of optimizing the approximation ratio of truthful mechanism, for both value and cost, in the deterministic and randomized settings. Unlike most previous works, we remove the domain restriction and the monotonicity assumption imposed on value functions. We provide theoretical explanations for why some previously considered special cases are tractable, reducing them to classical combinatorial problems, and providing efficient algorithms and characterizations. We complement our positive results with hardness results for the general case, providing query complexity lower bounds, and proving the NP-Hardness of the general case.

cs.GT↗

arXiv2025

Shapley-based Data Valuation for LLM Alignment via Sequential Preference Optimization

Data valuation is a natural framework for understanding which preference datasets matter most when aligning a Large Language Model (LLM) using multiple sources. The standard game-theoretic approach assigns each dataset a contribution score via the Shapley value. In practice, however, Shapley-based valuation is computationally prohibitive because it requires fine-tuning a separate model for every possible coalition of preference datasets, i.e., an exponential number of alignments. We address this challenge for a broad family of preference-optimization objectives, including DPO and IPO, that learn directly from log-policy ratios with respect to a reference policy. We introduce Sequential Preference Optimization, an offline procedure that applies existing preference optimization methods sequentially, source by source, updating the current policy after each dataset. Under exact optimization, this procedure yields an additive composition rule in reward space and an equivalent arithmetic composition rule in policy space. This observation enables an efficient approximation of the Shapley value: we train one model per preference dataset and reconstruct coalition policies at inference time from the singleton models, reducing the required alignments from exponential to linear in the number of sources. Leveraging this property, we compute Shapley values for several real-world preference datasets and reveal how each source drives model alignment.

cs.LG↗

arXiv2025

Correlation of Rankings in Matching Markets

We study the role of correlation in matching markets, where multiple decision-makers simultaneously face selection problems from the same pool of candidates. We propose a model in which a candidate's priority scores across different decision-makers exhibit varying levels of correlation dependent on the candidate's sociodemographic group. Such differential correlation can arise in school choice due to the varying prevalence of selection criteria, in college admissions due to test-optional policies, or due to algorithmic monoculture, that is, when decision-makers rely on the same algorithms and data sets to evaluate candidates. We show that higher correlation for one of the groups generally improves the outcome for all groups, leading to higher efficiency. However, students from a given group are more likely to remain unmatched as their own correlation level increases. This implies that it is advantageous to belong to a low-correlation group. Finally, we extend the tie-breaking literature to multiple priority classes and intermediate levels of correlation. Overall, our results point to differential correlation as a previously overlooked systemic source of group inequalities in school, university, and job admissions.

cs.GT↗

arXiv2025

Two-Sided Matching with Resource-Regional Caps

We study two-sided many-to-one matching problems under a novel type of distributional constraints, resource-regional caps. In the context of college admissions, under resource-regional caps, an admitted student may be provided with a unit of some resource through a college, which belongs to a region possessing some amount of this resource. A student may be admitted to a college with at most one unit of any resource, i.e., all resources are close substitutes, e.g., dorms on the campus, dorms outside the campus, subsidies for renting a room, etc. The core feature of our model is that students are allowed to be admitted without any resource, which breaks heredity property of previously studied models with regions. It is well known that a stable matching may not exist under markets with regional constraints. Thus, we focus on three weakened versions of stability that restore existence under resource-regional caps: envyfreeness plus resource-efficiency, non-wastefulness, and novel direct-envy stability. For each version of stability we design corresponding matching mechanism(s). Finally, we compare stability performances of constructed mechanisms on an exhaustive collection of synthetic markets, and conclude that the most sophisticated direct-envy stable mechanism is the go-to mechanism for maximal stability of the resulting matching under resource-regional caps.

cs.GT↗

arXiv2025

On the Impact of the Utility in Semivalue-based Data Valuation

Semivalue-based data valuation uses cooperative-game theory intuitions to assign each data point a value reflecting its contribution to a downstream task. Still, those values depend on the practitioner's choice of utility, raising the question: How robust is semivalue-based data valuation to changes in the utility? This issue is critical when the utility is set as a trade-off between several criteria and when practitioners must select among multiple equally valid utilities. We address this by introducing the notion of a dataset's spatial signature: given a semivalue, we embed each data point into a lower-dimensional space in which any utility becomes a linear functional, making the data valuation framework amenable to a simpler geometric picture. Building on this, we propose a practical methodology centered on an explicit robustness metric that informs practitioners whether and by how much their data valuation results will shift as the utility changes. We validate this approach across diverse datasets and semivalues, demonstrating strong agreement with rank-correlation analyses and offering analytical insight into how choosing a semivalue can amplify or diminish robustness.

cs.AI↗

arXiv2024

Prophet Inequalities: Competing with the Top $\ell$ Items is Easy

We explore a prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that $\mathrm{CR}_{\ell}$ the worst-case competitive ratio between the expected optimal performance of an online decision maker compared to that of a prophet who uses the average of the top $\ell$ items is exactly the solution to an integral equation. This quantity $\mathrm{CR}_{\ell}$ is larger than $1-e^{-\ell}$. This implies that the bound converges exponentially fast to $1$ as $\ell$ grows. In particular for $\ell=2$, $\mathrm{CR}_{2} \approx 0.966$ which is much closer to $1$ than the classical bound of $0.745$ for $\ell=1$. Additionally, we prove asymptotic lower bounds for the competitive ratio of a more general scenario, where the decision maker is permitted to select $k$ items. This subsumes the $k$ multi-unit i.i.d. prophet problem and provides the current best asymptotic guarantees, as well as enables broader understanding in the more general framework. Finally, we prove a tight asymptotic competitive ratio when only static threshold policies are allowed.

cs.DS↗

arXiv2024

Equitable Auctions

We initiate the study of how auction design affects the division of surplus among buyers. We propose a parsimonious measure for equity and apply it to the family of standard auctions for homogeneous goods. Our surplus-equitable mechanism is efficient, Bayesian-Nash incentive compatible, and achieves surplus parity among winners ex-post. The uniform-price auction is equity-optimal if and only if buyers have a pure common value. Against intuition, the pay-as-bid auction is not always preferred in terms of equity if buyers have pure private values. In auctions with price mixing between pay-as-bid and uniform prices, we provide prior-free bounds on the equity-preferred pricing rule under a common regularity condition on signals.

econ.TH↗

arXiv2024

The Price of Opportunity Fairness in Matroid Allocation Problems

We consider matroid allocation problems under opportunity fairness constraints: resources need to be allocated to a set of agents under matroid constraints (which include classical problems such as bipartite matching). Agents are divided into $C$ groups according to a sensitive attribute, and an allocation is opportunity-fair if each group receives the same share proportional to the maximum feasible allocation it could achieve in isolation. We study the Price of Fairness (PoF), i.e., the ratio between maximum size allocations and maximum size opportunity-fair allocations. We first provide a characterization of the PoF leveraging the underlying polymatroid structure of the allocation problem. Based on this characterization, we prove bounds on the PoF in various settings from fully adversarial (worst-case) to fully random. Notably, one of our main results considers an arbitrary matroid structure with agents randomly divided into groups. In this setting, we prove a PoF bound as a function of the (relative) size of the largest group. Our result implies that, as long as there is no dominant group (i.e., the largest group is not too large), opportunity fairness constraints do not induce any loss of social welfare (defined as the allocation size). Overall, our results give insights into which aspects of the problem's structure affect the trade-off between opportunity fairness and social welfare.

cs.GT↗

arXiv2023

Trading-off price for data quality to achieve fair online allocation

We consider the problem of online allocation subject to a long-term fairness penalty. Contrary to existing works, however, we do not assume that the decision-maker observes the protected attributes -- which is often unrealistic in practice. Instead they can purchase data that help estimate them from sources of different quality; and hence reduce the fairness penalty at some cost. We model this problem as a multi-armed bandit problem where each arm corresponds to the choice of a data source, coupled with the online allocation problem. We propose an algorithm that jointly solves both problems and show that it has a regret bounded by $\mathcal{O}(\sqrt{T})$. A key difficulty is that the rewards received by selecting a source are correlated by the fairness penalty, which leads to a need for randomization (despite a stochastic setting). Our algorithm takes into account contextual information available before the source selection, and can adapt to many different fairness notions. We also show that in some instances, the estimates used can be learned on the fly.

cs.LG↗

arXiv2023

DU-Shapley: A Shapley Value Proxy for Efficient Dataset Valuation

We consider the dataset valuation problem, that is, the problem of quantifying the incremental gain, to some relevant pre-defined utility of a machine learning task, of aggregating an individual dataset to others. The Shapley value is a natural tool to perform dataset valuation due to its formal axiomatic justification, which can be combined with Monte Carlo integration to overcome the computational tractability challenges. Such generic approximation methods, however, remain expensive in some cases. In this paper, we exploit the knowledge about the structure of the dataset valuation problem to devise more efficient Shapley value estimators. We propose a novel approximation, referred to as discrete uniform Shapley, which is expressed as an expectation under a discrete uniform distribution with support of reasonable size. We justify the relevancy of the proposed framework via asymptotic and non-asymptotic theoretical guarantees and illustrate its benefits via an extensive set of numerical experiments.

cs.AI↗

arXiv2023

Understanding Blockchain Governance: Analyzing Decentralized Voting to Amend DeFi Smart Contracts

Decentralized Autonomous Organizations (DAOs) have emerged as a novel governance mechanism in blockchain ecosystems, particularly within Decentralized Finance (DeFi). By enabling token holders to propose and vote on protocol changes, these systems promise transparent and equitable decision-making without centralized control. In this paper, we present an in-depth empirical study of the governance protocols of Compound and Uniswap, two of the most widely used DAOs in DeFi. Analyzing over 370 governance proposals and millions of on-chain events from their inception until August 2024, we uncover significant centralization of voting power: as few as 3--5 voters were sufficient to sway the majority of proposals. We also find that the cost of voting disproportionately burdens smaller token holders, and that strategic voting behaviors, such as delayed participation and coalition formation, further distort governance outcomes. Our findings suggest that despite their decentralized ideals, current DAO governance mechanisms fall short in practice.

cs.CR↗

arXiv2023

Dissecting Bitcoin and Ethereum Transactions: On the Lack of Transaction Contention and Prioritization Transparency in Blockchains

In permissionless blockchains, transaction issuers include a fee to incentivize miners to include their transactions. To accurately estimate this prioritization fee for a transaction, transaction issuers (or blockchain participants, more generally) rely on two fundamental notions of transparency, namely contention and prioritization transparency. Contention transparency implies that participants are aware of every pending transaction that will contend with a given transaction for inclusion. Prioritization transparency states that the participants are aware of the transaction or prioritization fees paid by every such contending transaction. Neither of these notions of transparency holds well today. Private relay networks, for instance, allow users to send transactions privately to miners. Besides, users can offer fees to miners via either direct transfers to miners' wallets or off-chain payments -- neither of which are public. In this work, we characterize the lack of contention and prioritization transparency in Bitcoin and Ethereum resulting from such practices. We show that private relay networks are widely used and private transactions are quite prevalent. We show that the lack of transparency facilitates miners to collude and overcharge users who may use these private relay networks despite them offering little to no guarantees on transaction prioritization. The lack of these transparencies in blockchains has crucial implications for transaction issuers as well as the stability of blockchains. Finally, we make our data sets and scripts publicly available.

cs.CR↗

arXiv2022

Bounding and Approximating Intersectional Fairness through Marginal Fairness

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that ensuring \emph{marginal fairness} for every dimension independently is not sufficient in general. Due to the exponential number of subgroups, however, directly measuring intersectional fairness from data is impossible. In this paper, our primary goal is to understand in detail the relationship between marginal and intersectional fairness through statistical analysis. We first identify a set of sufficient conditions under which an exact relationship can be obtained. Then, we prove bounds (easily computable through marginal fairness and other meaningful statistical quantities) in high-probability on intersectional fairness in the general case. Beyond their descriptive value, we show that these theoretical bounds can be leveraged to derive a heuristic improving the approximation and bounds of intersectional fairness by choosing, in a relevant manner, protected attributes for which we describe intersectional subgroups. Finally, we test the performance of our approximations and bounds on real and synthetic data-sets.

stat.ML↗

arXiv2022

Fairness in Selection Problems with Strategic Candidates

To better understand discriminations and the effect of affirmative actions in selection problems (e.g., college admission or hiring), a recent line of research proposed a model based on differential variance. This model assumes that the decision-maker has a noisy estimate of each candidate's quality and puts forward the difference in the noise variances between different demographic groups as a key factor to explain discrimination. The literature on differential variance, however, does not consider the strategic behavior of candidates who can react to the selection procedure to improve their outcome, which is well-known to happen in many domains. In this paper, we study how the strategic aspect affects fairness in selection problems. We propose to model selection problems with strategic candidates as a contest game: A population of rational candidates compete by choosing an effort level to increase their quality. They incur a cost-of-effort but get a (random) quality whose expectation equals the chosen effort. A Bayesian decision-maker observes a noisy estimate of the quality of each candidate (with differential variance) and selects the fraction $\alpha$ of best candidates based on their posterior expected quality; each selected candidate receives a reward $S$. We characterize the (unique) equilibrium of this game in the different parameters' regimes, both when the decision-maker is unconstrained and when they are constrained to respect the fairness notion of demographic parity. Our results reveal important impacts of the strategic behavior on the discrimination observed at equilibrium and allow us to understand the effect of imposing demographic parity in this context. In particular, we find that, in many cases, the results contrast with the non-strategic setting.

cs.GT↗

arXiv2022

Pareto-Optimal Fairness-Utility Amortizations in Rankings with a DBN Exposure Model

In recent years, it has become clear that rankings delivered in many areas need not only be useful to the users but also respect fairness of exposure for the item producers. We consider the problem of finding ranking policies that achieve a Pareto-optimal tradeoff between these two aspects. Several methods were proposed to solve it; for instance a popular one is to use linear programming with a Birkhoff-von Neumann decomposition. These methods, however, are based on a classical Position Based exposure Model (PBM), which assumes independence between the items (hence the exposure only depends on the rank). In many applications, this assumption is unrealistic and the community increasingly moves towards considering other models that include dependences, such as the Dynamic Bayesian Network (DBN) exposure model. For such models, computing (exact) optimal fair ranking policies remains an open question. We answer this question by leveraging a new geometrical method based on the so-called expohedron proposed recently for the PBM (Kletti et al., WSDM'22). We lay out the structure of a new geometrical object (the DBN-expohedron), and propose for it a Carath\'eodory decomposition algorithm of complexity $O(n^3)$, where $n$ is the number of documents to rank. Such an algorithm enables expressing any feasible expected exposure vector as a distribution over at most $n$ rankings; furthermore we show that we can compute the whole set of Pareto-optimal expected exposure vectors with the same complexity $O(n^3)$. Our work constitutes the first exact algorithm able to efficiently find a Pareto-optimal distribution of rankings. It is applicable to a broad range of fairness notions, including classical notions of meritocratic and demographic fairness. We empirically evaluate our method on the TREC2020 and MSLR datasets and compare it to several baselines in terms of Pareto-optimality and speed.

cs.IR↗

arXiv2022

Introducing the Expohedron for Efficient Pareto-optimal Fairness-Utility Amortizations in Repeated Rankings

We consider the problem of computing a sequence of rankings that maximizes consumer-side utility while minimizing producer-side individual unfairness of exposure. While prior work has addressed this problem using linear or quadratic programs on bistochastic matrices, such approaches, relying on Birkhoff-von Neumann (BvN) decompositions, are too slow to be implemented at large scale. In this paper we introduce a geometrical object, a polytope that we call expohedron, whose points represent all achievable exposures of items for a Position Based Model (PBM). We exhibit some of its properties and lay out a Carath\'eodory decomposition algorithm with complexity $O(n^2\log(n))$ able to express any point inside the expohedron as a convex sum of at most $n$ vertices, where $n$ is the number of items to rank. Such a decomposition makes it possible to express any feasible target exposure as a distribution over at most $n$ rankings. Furthermore we show that we can use this polytope to recover the whole Pareto frontier of the multi-objective fairness-utility optimization problem, using a simple geometrical procedure with complexity $O(n^2\log(n))$. Our approach compares favorably to linear or quadratic programming baselines in terms of algorithmic complexity and empirical runtime and is applicable to any merit that is a non-decreasing function of item relevance. Furthermore our solution can be expressed as a distribution over only $n$ permutations, instead of the $(n-1)^2 + 1$ achieved with BvN decompositions. We perform experiments on synthetic and real-world datasets, confirming our theoretical results.

cs.IR↗