arXiv subjects

Flore Sentenac

Publications and source records attributed to Flore Sentenac.

12 recordsLinked to original sources

arXiv2026

On the Average-Case Performance of Greedy for Maximum Coverage

For the classical maximum coverage problem, the greedy algorithm achieves a worst-case $1-1/e$ approximation, which is optimal unless $\text{P} = \text{NP}$. The notion of coverage appears in a wide range of optimization tasks, where empirical evaluations indicate approximation ratios close to $1$ for the greedy algorithm on real data. Random models have provided average-case justifications for the empirical performance of many well-known algorithms, but little is known about the average-case performance of greedy for maximum coverage. We analyze the expected approximation ratio of the greedy algorithm in a random model, which we call the left-regular random model. We first show that, for all parameter settings of this model, the expected approximation ratio of the greedy algorithm improves by a constant over its worst-case $1-1/e$ guarantee. We then identify two simple conditions, either of which ensures that the expected approximation ratio is close to $1$ for sufficiently large graphs. Finally, we show that there is a regime where greedy does not achieve an expected approximation better than $0.94$. To obtain these results, we develop analytical tools, including a novel application of the differential equation method and a connection to maximum matching in Erd\H{o}s-R\'enyi graphs, which may be of independent interest for other random models.

cs.DS↗

arXiv2026

Flexibility allocation in random bipartite matching markets: exact matching rates and dominance regimes

This paper studies how a fixed flexibility budget should be allocated across the two sides of a balanced bipartite matching market. We model compatibilities via a sparse bipartite stochastic block model in which flexible agents are more likely to connect with agents on the opposite side, and derive an exact variational formula for the asymptotic matching rate under any flexibility allocation. The derivation extends the local weak convergence framework of [BLS11] from single-type to multi-type unimodular Galton-Watson trees, reducing the matching rate to an explicit low-dimensional optimization problem. Using this formula, we analytically investigate when the one-sided allocation, which concentrates all flexibility on one side, dominates the two-sided allocation and vice versa, sharpening and extending the comparisons of [FMZ26] which relied on approximate algorithmic bounds rather than an exact characterization of the matching rate.

math.PR↗

arXiv2026

A uniformity principle for spatial matching

Platforms matching spatially distributed supply to demand face a fundamental design choice: given a fixed total budget of service range, how should it be allocated across supply nodes ex ante, i.e. before supply and demand locations are realized, to maximize fulfilled demand? We model this problem using bipartite random geometric graphs where $n$ supply and $m$ demand nodes are uniformly distributed on $[0,1]^k$ ($k \ge 1$), and edges form when demand falls within a supply node's service region, the volume of which is determined by its service range. Since each supply node serves at most one demand, platform performance is determined by the expected size of a maximum matching. We establish a uniformity principle: whenever one service range allocation is more uniform than the other, the more uniform allocation yields a larger expected matching. This principle emerges from diminishing marginal returns to range expanding service range, and limited interference between supply nodes due to bounded ranges naturally fragmenting the graph. For $k=1$, we further characterize the expected matching size through a Markov chain embedding and derive closed-form expressions for special cases. Our results provide theoretical guidance for service-range allocation and incentive design in ride-hailing, on-demand labor markets, and drone delivery platforms, highlighting the benefits of reducing disparities in supply-side flexibility.

math.PR↗

arXiv2025

The Challenger: When Do New Data Sources Justify Switching Machine Learning Models?

Organizations often have an incumbent predictive model in production when new data sources become available. Because historical training data lack the new features, a challenger model must be trained on a small but growing full-feature dataset. We study whether, and when, the organization should switch to the challenger. The decision is statistical and economic: the challenger's predictive performance improves as full-feature data accumulate, but repeated retraining is costly and delays benefits from deployment. We develop a framework linking learning-curve dynamics to model-switching economics. Under a standard power-law learning curve and finite data-collection horizon $T$, the optimal time to train and evaluate the challenger scales as $T^{1/(1+\alpha)}$: learning-curve shape (through its learning speed $\alpha$) is the primary theoretical determinant of when to stop experimenting; costs determine switching profitability. Even without knowing the learning curve, the operational problem is tractable: we show that any algorithm stopping on the $T^{2/3}$ scale and making reliable switch/discard decisions achieves $O(T^{2/3}\sqrt{\log T})$ regret relative to a full-foresight oracle. We propose a sequential evaluation algorithm that uses local learning-curve trends to anticipate improvement, and test it in a real-world credit-scoring study. Even with this local approximation, the algorithm theoretically and empirically achieves near-oracle performance. It is also more stable than greedy sequential evaluation algorithms, where noisy early estimates trigger premature discarding, or simple one-shot evaluation algorithms, which work only when their fixed evaluation time matches the (unknown in practice) theoretical timing scale. Our framework offers a step toward principled model governance when new data sources require costly collection, validation, and deployment.

cs.LG↗

arXiv2025

Balancing optimism and pessimism in offline-to-online learning

We consider what we call the offline-to-online learning setting, focusing on stochastic finite-armed bandit problems. In offline-to-online learning, a learner starts with offline data collected from interactions with an unknown environment in a way that is not under the learner's control. Given this data, the learner begins interacting with the environment, gradually improving its initial strategy as it collects more data to maximize its total reward. The learner in this setting faces a fundamental dilemma: if the policy is deployed for only a short period, a suitable strategy (in a number of senses) is the Lower Confidence Bound (LCB) algorithm, which is based on pessimism. LCB can effectively compete with any policy that is sufficiently "covered" by the offline data. However, for longer time horizons, a preferred strategy is the Upper Confidence Bound (UCB) algorithm, which is based on optimism. Over time, UCB converges to the performance of the optimal policy at a rate that is nearly the best possible among all online algorithms. In offline-to-online learning, however, UCB initially explores excessively, leading to worse short-term performance compared to LCB. This suggests that a learner not in control of how long its policy will be in use should start with LCB for short horizons and gradually transition to a UCB-like strategy as more rounds are played. This article explores how and why this transition should occur. Our main result shows that our new algorithm performs nearly as well as the better of LCB and UCB at any point in time. The core idea behind our algorithm is broadly applicable, and we anticipate that our results will extend beyond the multi-armed bandit setting.

cs.LG↗

arXiv2024

Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits

We prove that single-parameter natural exponential families with subexponential tails are self-concordant with polynomial-sized parameters. For subgaussian natural exponential families we establish an exact characterization of the growth rate of the self-concordance parameter. Applying these findings to bandits allows us to fill gaps in the literature: We show that optimistic algorithms for generalized linear bandits enjoy regret bounds that are both second-order (scale with the variance of the optimal arm's reward distribution) and free of an exponential dependence on the bound of the problem parameter in the leading term. To the best of our knowledge, ours is the first regret bound for generalized linear bandits with subexponential tails, broadening the class of problems to include Poisson, exponential and gamma bandits.

cs.LG↗

arXiv2023

Online Matching in Geometric Random Graphs

We investigate online maximum cardinality matching, a central problem in ad allocation. In this problem, users are revealed sequentially, and each new user can be paired with any previously unmatched campaign that it is compatible with. Despite the limited theoretical guarantees, the greedy algorithm, which matches incoming users with any available campaign, exhibits outstanding performance in practice. Some theoretical support for this practical success was established in specific classes of graphs, where the connections between different vertices lack strong correlations - an assumption not always valid. To bridge this gap, we focus on the following model: both users and campaigns are represented as points uniformly distributed in the interval $[0,1]$, and a user is eligible to be paired with a campaign if they are similar enough, i.e. the distance between their respective points is less than $c/N$, with $c>0$ a model parameter. As a benchmark, we determine the size of the optimal offline matching in these bipartite random geometric graphs. In the online setting and investigate the number of matches made by the online algorithm closest, which greedily pairs incoming points with their nearest available neighbors. We demonstrate that the algorithm's performance can be compared to its fluid limit, which is characterized as the solution to a specific partial differential equation (PDE). From this PDE solution, we can compute the competitive ratio of closest, and our computations reveal that it remains significantly better than its worst-case guarantee. This model turns out to be related to the online minimum cost matching problem, and we can extend the results to refine certain findings in that area of research. Specifically, we determine the exact asymptotic cost of closest in the $\epsilon$-excess regime, providing a more accurate estimate than the previously known loose upper bound.

cs.DS↗

arXiv2022

On Preemption and Learning in Stochastic Scheduling

We study single-machine scheduling of jobs, each belonging to a job type that determines its duration distribution. We start by analyzing the scenario where the type characteristics are known and then move to two learning scenarios where the types are unknown: non-preemptive problems, where each started job must be completed before moving to another job; and preemptive problems, where job execution can be paused in the favor of moving to a different job. In both cases, we design algorithms that achieve sublinear excess cost, compared to the performance with known types, and prove lower bounds for the non-preemptive case. Notably, we demonstrate, both theoretically and through simulations, how preemptive algorithms can greatly outperform non-preemptive ones when the durations of different job types are far from one another, a phenomenon that does not occur when the type durations are known.

cs.LG↗

arXiv2022

Robust Estimation of Discrete Distributions under Local Differential Privacy

Although robust learning and local differential privacy are both widely studied fields of research, combining the two settings is just starting to be explored. We consider the problem of estimating a discrete distribution in total variation from $n$ contaminated data batches under a local differential privacy constraint. A fraction $1-\epsilon$ of the batches contain $k$ i.i.d. samples drawn from a discrete distribution $p$ over $d$ elements. To protect the users' privacy, each of the samples is privatized using an $\alpha$-locally differentially private mechanism. The remaining $\epsilon n $ batches are an adversarial contamination. The minimax rate of estimation under contamination alone, with no privacy, is known to be $\epsilon/\sqrt{k}+\sqrt{d/kn}$, up to a $\sqrt{\log(1/\epsilon)}$ factor. Under the privacy constraint alone, the minimax rate of estimation is $\sqrt{d^2/\alpha^2 kn}$. We show that combining the two constraints leads to a minimax estimation rate of $\epsilon\sqrt{d/\alpha^2 k}+\sqrt{d^2/\alpha^2 kn}$ up to a $\sqrt{\log(1/\epsilon)}$ factor, larger than the sum of the two separate rates. We provide a polynomial-time algorithm achieving this bound, as well as a matching information theoretic lower bound.

math.ST↗

arXiv2021

Pure Exploration and Regret Minimization in Matching Bandits

Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1 assumption on the adjacency matrix to reduce the sample complexity and the regret of off-the-shelf algorithms up to reaching a linear dependency in the number of vertices (up to poly log terms).

stat.ML↗

arXiv2021

Online Matching in Sparse Random Graphs: Non-Asymptotic Performances of Greedy Algorithm

Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the competitive ratio of the simplest algorithm, GREEDY, by approximating some relevant stochastic discrete processes by their continuous counterparts, that are solutions of an explicit system of partial differential equations. This technique gives precise bounds on the estimation errors, with arbitrarily high probability as the problem size increases. In particular, it allows the formal comparison between different configuration models. We also prove that, quite surprisingly, GREEDY can have better performance guarantees than RANKING, another celebrated algorithm for online matching that usually outperforms the former.

cs.DS↗

arXiv2021

Decentralized Learning in Online Queuing Systems

Motivated by packet routing in computer networks, online queuing systems are composed of queues receiving packets at different rates. Repeatedly, they send packets to servers, each of them treating only at most one packet at a time. In the centralized case, the number of accumulated packets remains bounded (i.e., the system is \textit{stable}) as long as the ratio between service rates and arrival rates is larger than $1$. In the decentralized case, individual no-regret strategies ensures stability when this ratio is larger than $2$. Yet, myopically minimizing regret disregards the long term effects due to the carryover of packets to further rounds. On the other hand, minimizing long term costs leads to stable Nash equilibria as soon as the ratio exceeds $\frac{e}{e-1}$. Stability with decentralized learning strategies with a ratio below $2$ was a major remaining question. We first argue that for ratios up to $2$, cooperation is required for stability of learning strategies, as selfish minimization of policy regret, a \textit{patient} notion of regret, might indeed still be unstable in this case. We therefore consider cooperative queues and propose the first learning decentralized algorithm guaranteeing stability of the system as long as the ratio of rates is larger than $1$, thus reaching performances comparable to centralized strategies.

stat.ML↗