arXiv subjects

Eric Moulines

Publications and source records attributed to Eric Moulines.

At least 55 records · Page 3Linked to original sources

arXiv2025

Online Decision-Making in Tree-Like Multi-Agent Games with Transfers

The widespread deployment of Machine Learning systems everywhere raises challenges, such as dealing with interactions or competition between multiple learners. In that goal, we study multi-agent sequential decision-making by considering principal-agent interactions in a tree structure. In this problem, the reward of a player is influenced by the actions of her children, who are all self-interested and non-cooperative, hence the complexity of making good decisions. Our main finding is that it is possible to steer all the players towards the globally optimal set of actions by simply allowing single-step transfers between them. A transfer is established between a principal and one of her agents: the principal actually offers the proposed payment if the agent picks the recommended action. The analysis poses specific challenges due to the intricate interactions between the nodes of the tree and the propagation of the regret within this tree. Considering a bandit setup, we propose algorithmic solutions for the players to end up being no-regret with respect to the optimal pair of actions and incentives. In the long run, allowing transfers between players makes them act as if they were collaborating together, although they remain self-interested non-cooperative: transfers restore efficiency.

cs.GT↗

arXiv2025

Briding Diffusion Posterior Sampling and Monte Carlo methods: a survey

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage \emph{pre-trained} diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a \emph{twisting} mechanism for the intermediate distributions within the diffusion process, guiding the simulations toward the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.

cs.LG↗

arXiv2025

Improved Central Limit Theorem and Bootstrap Approximations for Linear Stochastic Approximation

In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the normal approximation by the Gaussian distribution with covariance matrix predicted by the Polyak-Juditsky central limit theorem and establish the rate up to order $n^{-1/3}$ in convex distance, where $n$ is the number of samples used in the algorithm. We also prove a non-asymptotic validity of the multiplier bootstrap procedure for approximating the distribution of the rescaled error of the averaged LSA estimator. We establish approximation rates of order up to $1/\sqrt{n}$ for the latter distribution, which significantly improves upon the previous results obtained by Samsonov et al. (2024).

stat.ML↗

arXiv2025

Curriculum-Augmented GFlowNets For mRNA Sequence Generation

Designing mRNA sequences is a major challenge in developing next-generation therapeutics, since it involves exploring a vast space of possible nucleotide combinations while optimizing sequence properties like stability, translation efficiency, and protein expression. While Generative Flow Networks are promising for this task, their training is hindered by sparse, long-horizon rewards and multi-objective trade-offs. We propose Curriculum-Augmented GFlowNets (CAGFN), which integrate curriculum learning with multi-objective GFlowNets to generate de novo mRNA sequences. CAGFN integrates a length-based curriculum that progressively adapts the maximum sequence length guiding exploration from easier to harder subproblems. We also provide a new mRNA design environment for GFlowNets which, given a target protein sequence and a combination of biological objectives, allows for the training of models that generate plausible mRNA candidates. This provides a biologically motivated setting for applying and advancing GFlowNets in therapeutic sequence design. On different mRNA design tasks, CAGFN improves Pareto performance and biological plausibility, while maintaining diversity. Moreover, CAGFN reaches higher-quality solutions faster than a GFlowNet trained with random sequence sampling (no curriculum), and enables generalization to out-of-distribution sequences.

cs.LG↗

arXiv2025

Neural Optimal Transport Meets Multivariate Conformal Prediction

We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of joint distributions. Our method parametrizes the conditional vector quantile function as the gradient of a convex potential implemented by an input-convex neural network, ensuring monotonicity and uniform ranks. To reduce the cost of solving high-dimensional variational problems, we introduced amortized optimization of the dual potentials, yielding efficient training and faster inference. We then exploit the induced multivariate ranks for conformal prediction, constructing distribution-free predictive regions with finite-sample validity. Unlike coordinatewise methods, our approach adapts to the geometry of the conditional distribution, producing tighter and more informative regions. Experiments on benchmark datasets show improved coverage-efficiency trade-offs compared to baselines, highlighting the benefits of integrating neural optimal transport with conformal prediction.

stat.ML↗

arXiv2025

Multidimensional Uncertainty Quantification via Optimal Transport

Most uncertainty quantification (UQ) approaches provide a single scalar value as a measure of model reliability. However, different uncertainty measures could provide complementary information on the prediction confidence. Even measures targeting the same type of uncertainty (e.g., ensemble-based and density-based measures of epistemic uncertainty) may capture different failure modes. We take a multidimensional view on UQ by stacking complementary UQ measures into a vector. Such vectors are assigned with Monge-Kantorovich ranks produced by an optimal-transport-based ordering method. The prediction is then deemed more uncertain than the other if it has a higher rank. The resulting VecUQ-OT algorithm uses entropy-regularized optimal transport. The transport map is learned on vectors of scores from in-distribution data and, by design, applies to unseen inputs, including out-of-distribution cases, without retraining. Our framework supports flexible non-additive uncertainty fusion (including aleatoric and epistemic components). It yields a robust ordering for downstream tasks such as selective prediction, misclassification detection, out-of-distribution detection, and selective generation. Across synthetic, image, and text data, VecUQ-OT shows high efficiency even when individual measures fail. The code for the method is available at: https://github.com/stat-ml/multidimensional_uncertainty.

stat.ML↗

arXiv2025

Rosenthal-type inequalities for linear statistics of Markov chains

In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the dependence of our bounds on the mixing time of the corresponding chain. Precisely, we establish explicit bounds that are linked to the constants from the martingale version of the Rosenthal inequality, as well as the constants that characterize the mixing properties of the underlying Markov kernel. Finally, our proof technique is, up to our knowledge, new and is based on a recurrent application of the Poisson decomposition.

math.PR↗

arXiv2025

Improving French Synthetic Speech Quality via SSML Prosody Control

Despite recent advances, synthetic voices often lack expressiveness due to limited prosody control in commercial text-to-speech (TTS) systems. We introduce the first end-to-end pipeline that inserts Speech Synthesis Markup Language (SSML) tags into French text to control pitch, speaking rate, volume, and pause duration. We employ a cascaded architecture with two QLoRA-fine-tuned Qwen 2.5-7B models: one predicts phrase-break positions and the other performs regression on prosodic targets, generating commercial TTS-compatible SSML markup. Evaluated on a 14-hour French podcast corpus, our method achieves 99.2% F1 for break placement and reduces mean absolute error on pitch, rate, and volume by 25-40% compared with prompting-only large language models (LLMs) and a BiLSTM baseline. In perceptual evaluation involving 18 participants across over 9 hours of synthesized audio, SSML-enhanced speech generated by our pipeline significantly improves naturalness, with the mean opinion score increasing from 3.20 to 3.87 (p < 0.005). Additionally, 15 of 18 listeners preferred our enhanced synthesis. These results demonstrate substantial progress in bridging the expressiveness gap between synthetic and natural French speech. Our code is publicly available at https://github.com/hi-paris/Prosody-Control-French-TTS.

cs.CL↗

arXiv2025

Rectifying Conformity Scores for Better Conditional Coverage

We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage. The transformation is based on an estimate of the conditional quantile of conformity scores. The resulting method is particularly beneficial for constructing adaptive confidence sets in multi-output problems where standard conformal quantile regression approaches have limited applicability. We develop a theoretical bound that captures the influence of the accuracy of the quantile estimate on the approximate conditional validity, unlike classical bounds for conformal prediction methods that only offer marginal coverage. We experimentally show that our method is highly adaptive to the local data structure and outperforms existing methods in terms of conditional coverage, improving the reliability of statistical inference in various applications.

stat.ML↗

arXiv2025

Prediction-Aware Learning in Multi-Agent Systems

The framework of uncoupled online learning in multiplayer games has made significant progress in recent years. In particular, the development of time-varying games has considerably expanded its modeling capabilities. However, current regret bounds quickly become vacuous when the game undergoes significant variations over time, even when these variations are easy to predict. Intuitively, the ability of players to forecast future payoffs should lead to tighter guarantees, yet existing approaches fail to incorporate this aspect. This work aims to fill this gap by introducing a novel prediction-aware framework for time-varying games, where agents can forecast future payoffs and adapt their strategies accordingly. In this framework, payoffs depend on an underlying state of nature that agents predict in an online manner. To leverage these predictions, we propose the POWMU algorithm, a contextual extension of the optimistic Multiplicative Weight Update algorithm, for which we establish theoretical guarantees on social welfare and convergence to equilibrium. Our results demonstrate that, under bounded prediction errors, the proposed framework achieves performance comparable to the static setting. Finally, we empirically demonstrate the effectiveness of POWMU in a traffic routing experiment.

cs.GT↗

arXiv2025

Nonasymptotic Analysis of Stochastic Gradient Descent with the Richardson-Romberg Extrapolation

We address the problem of solving strongly convex and smooth minimization problems using stochastic gradient descent (SGD) algorithm with a constant step size. Previous works suggested to combine the Polyak-Ruppert averaging procedure with the Richardson-Romberg extrapolation to reduce the asymptotic bias of SGD at the expense of a mild increase of the variance. We significantly extend previous results by providing an expansion of the mean-squared error of the resulting estimator with respect to the number of iterations $n$. We show that the root mean-squared error can be decomposed into the sum of two terms: a leading one of order $\mathcal{O}(n^{-1/2})$ with explicit dependence on a minimax-optimal asymptotic covariance matrix, and a second-order term of order $\mathcal{O}(n^{-3/4})$, where the power $3/4$ is best known. We also extend this result to the higher-order moment bounds. Our analysis relies on the properties of the SGD iterates viewed as a time-homogeneous Markov chain. In particular, we establish that this chain is geometrically ergodic with respect to a suitably defined weighted Wasserstein semimetric.

math.OC↗

arXiv2025

Model-free Posterior Sampling via Learning Rate Randomization

In this paper, we introduce Randomized Q-learning (RandQL), a novel randomized model-free algorithm for regret minimization in episodic Markov Decision Processes (MDPs). To the best of our knowledge, RandQL is the first tractable model-free posterior sampling-based algorithm. We analyze the performance of RandQL in both tabular and non-tabular metric space settings. In tabular MDPs, RandQL achieves a regret bound of order $\widetilde{O}(\sqrt{H^{5}SAT})$, where $H$ is the planning horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the number of episodes. For a metric state-action space, RandQL enjoys a regret bound of order $\widetilde{O}(H^{5/2} T^{(d_z+1)/(d_z+2)})$, where $d_z$ denotes the zooming dimension. Notably, RandQL achieves optimistic exploration without using bonuses, relying instead on a novel idea of learning rate randomization. Our empirical study shows that RandQL outperforms existing approaches on baseline exploration environments.

stat.ML↗

arXiv2025

Smoothness Estimation for Whittle-Matérn Processes on Closed Riemannian Manifolds

The family of Matérn kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for example, optimal error bounds for kriging and posterior contraction rates in Gaussian process regression. On closed Riemannian manifolds, we show that the smoothness parameter can be consistently estimated from the maximizer(s) of the Gaussian likelihood when the underlying data are from point evaluations of a Gaussian process and, perhaps surprisingly, even when the data comprise evaluations of a non-Gaussian process. The points at which the process is observed need not have any particular spatial structure beyond quasi-uniformity. Our methods are based on results from approximation theory for the Sobolev scale of Hilbert spaces. Moreover, we generalize a well-known equivalence of measures phenomenon related to Matérn kernels to the non-Gaussian case by using Kakutani's theorem.

math.ST↗

arXiv2025

Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting, we extend its methodology to the MFG framework, leveraging its stability and robustness in policy optimization. Under standard assumptions in the MFG literature, we provide a rigorous analysis of MF-TRPO, establishing theoretical guarantees on its convergence. Our results cover both the exact formulation of the algorithm and its sample-based counterpart, where we derive high-probability guarantees and finite sample complexity. This work advances MFG optimization by bridging RL techniques with mean-field decision-making, offering a theoretically grounded approach to solving complex multi-agent problems.

stat.ML↗

arXiv2025

Conditional Diffusion Models with Classifier-Free Gibbs-like Guidance

Classifier-Free Guidance (CFG) is a widely used technique for improving conditional diffusion models by linearly combining the outputs of conditional and unconditional denoisers. While CFG enhances visual quality and improves alignment with prompts, it often reduces sample diversity, leading to a challenging trade-off between quality and diversity. To address this issue, we make two key contributions. First, CFG generally does not correspond to a well-defined denoising diffusion model (DDM). In particular, contrary to common intuition, CFG does not yield samples from the target distribution associated with the limiting CFG score as the noise level approaches zero -- where the data distribution is tilted by a power $w \gt 1$ of the conditional distribution. We identify the missing component: a Rényi divergence term that acts as a repulsive force and is required to correct CFG and render it consistent with a proper DDM. Our analysis shows that this correction term vanishes in the low-noise limit. Second, motivated by this insight, we propose a Gibbs-like sampling procedure to draw samples from the desired tilted distribution. This method starts with an initial sample from the conditional diffusion model without CFG and iteratively refines it, preserving diversity while progressively enhancing sample quality. We evaluate our approach on both image and text-to-audio generation tasks, demonstrating substantial improvements over CFG across all considered metrics. The code is available at https://github.com/yazidjanati/cfgig

cs.LG↗

arXiv2025

Statistical inference for Linear Stochastic Approximation with Markovian Noise

In this paper we derive non-asymptotic Berry-Esseen bounds for Polyak-Ruppert averaged iterates of the Linear Stochastic Approximation (LSA) algorithm driven by the Markovian noise. Our analysis yields $\mathcal{O}(n^{-1/4})$ convergence rates to the Gaussian limit in the Kolmogorov distance. We further establish the non-asymptotic validity of a multiplier block bootstrap procedure for constructing the confidence intervals, guaranteeing consistent inference under Markovian sampling. Our work provides the first non-asymptotic guarantees on the rate of convergence of bootstrap-based confidence intervals for stochastic approximation with Markov noise. Moreover, we recover the classical rate of order $\mathcal{O}(n^{-1/8})$ up to logarithmic factors for estimating the asymptotic variance of the iterates of the LSA algorithm.

stat.ML↗

arXiv2025

A note on concentration inequalities for the overlapped batch mean variance estimators for Markov chains

In this paper, we study the concentration properties of quadratic forms associated with Markov chains using the martingale decomposition method introduced by Atchadé and Cattaneo (2014). In particular, we derive concentration inequalities for the overlapped batch mean (OBM) estimators of the asymptotic variance for uniformly geometrically ergodic Markov chains. Our main result provides an explicit control of the $p$-th moment of the difference between the OBM estimator and the asymptotic variance of the Markov chain with explicit dependence upon $p$ and mixing time of the underlying Markov chain.

math.PR↗

arXiv2025

Scaffold with Stochastic Gradients: New Analysis with Linear Speed-Up

This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client drift--is well established, the impact of stochastic gradient updates on its performance is less understood. To address this problem, we first show that its global parameters and control variates define a Markov chain that converges to a stationary distribution in the Wasserstein distance. Leveraging this result, we prove that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size. Nevertheless, our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases. This highlights opportunities for developing improved stochastic federated learning algorithms

stat.ML↗