arXiv subjects

Eloïse Berthier

Publications and source records attributed to Eloïse Berthier.

13 recordsLinked to original sources

arXiv2026

No-Regret Gaussian Process Optimization of Time-Varying Functions

Sequential optimization of black-box functions from noisy evaluations has been widely studied, with Gaussian Process bandit algorithms such as GP-UCB guaranteeing no-regret in stationary settings. However, for time-varying objectives, no-regret is unattainable under pure bandit feedback unless strong and often unrealistic assumptions are imposed. We propose a novel method for optimizing time-varying rewards in the frequentist setting, where the objective has bounded RKHS norm almost surely. Time variations are captured through uncertainty injection, enabling heteroscedastic Gaussian process regression that adapts past observations to the current time step. As no-regret is unattainable in general in the strict bandit setting, we relax the latter allowing additional queries on previously observed points. Building on sparse inference and the effect of uncertainty injection on regret, we propose W-SparQ-GP-UCB, an online algorithm that achieves no-regret with a vanishing number of additional queries per iteration. To assess the theoretical limits of this approach, we establish a lower bound on the number of additional queries required for no-regret, proving the efficiency of our method. Finally, we provide a comprehensive analysis linking the temporal regime of the function to achievable regret rates, together with upper and lower bounds on the number of additional queries needed in each regime.

stat.ML↗

arXiv2026

No-regret optimization of time-varying bilevel problems

Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear bilevel programs are strongly NP-hard. In this work, we consider bilevel optimization with a known upper-level objective and an unknown, potentially time-varying lower-level response, accessible only through noisy zeroth-order observations. We propose W-SparQ-BL, a Bayesian optimization framework that models the lower-level mapping using multi-output Gaussian processes and enables efficient optimization under uncertainty. Our approach leverages a sparse, observation-based approximation to control the effect of noise and temporal variability, while requiring only limited access to additional information over time. We establish regularity results linking the lower-level response to standard RKHS assumptions for common kernels, including Matérn and squared exponential. We prove that W-SparQ-BL achieves sublinear dynamic regret in both stationary and time-varying settings. Experiments on representative time-varying game-theoretic problems demonstrate the effectiveness of our approach.

math.OC↗

arXiv2026

Convergence Guarantees for Federated SARSA with Local Training and Heterogeneous Agents

We present a novel theoretical analysis of Federated SARSA (FedSARSA) with linear function approximation and local training. We establish convergence guarantees for FedSARSA in the presence of heterogeneity, both in local transitions and rewards, providing the first sample and communication complexity bounds in this setting. At the core of our analysis is a new, exact multi-step error expansion for single-agent SARSA, which is of independent interest. Our analysis precisely quantifies the impact of heterogeneity, demonstrating the convergence of FedSARSA with multiple local updates. Crucially, we show that FedSARSA achieves linear speed-up with respect to the number of agents, up to higher-order terms due to Markovian sampling. Numerical experiments support our theoretical findings.

cs.LG↗

arXiv2025

Time-varying Gaussian Process Bandit Optimization with Experts: no-regret in logarithmically-many side queries

We study a time-varying Bayesian optimization problem with bandit feedback, where the reward function belongs to a Reproducing Kernel Hilbert Space (RKHS). We approach the problem via an upper-confidence bound Gaussian Process algorithm, which has been proven to yield no-regret in the stationary case. The time-varying case is more challenging and no-regret results are out of reach in general in the standard setting. As such, we instead tackle the question of how many additional observations asked to an expert are required to regain a no-regret property. To do so, we formulate the presence of past observation via an uncertainty injection procedure, and we reframe the problem as a heteroscedastic Gaussian Process regression. In addition, to achieve a no-regret result, we discard long outdated observations and replace them with updated (possibly very noisy) ones obtained by asking queries to an external expert. By leveraging and extending sparse inference to the heteroscedastic case, we are able to secure a no-regret result in a challenging time-varying setting with only logarithmically-many side queries per time step. Our method demonstrates that minimal additional information suffices to counteract temporal drift, ensuring efficient optimization despite time variation.

math.OC↗

arXiv2025

Enhancing Concept Localization in CLIP-based Concept Bottleneck Models

This paper addresses explainable AI (XAI) through the lens of Concept Bottleneck Models (CBMs) that do not require explicit concept annotations, relying instead on concepts extracted using CLIP in a zero-shot manner. We show that CLIP, which is central in these techniques, is prone to concept hallucination, incorrectly predicting the presence or absence of concepts within an image in scenarios used in numerous CBMs, hence undermining the faithfulness of explanations. To mitigate this issue, we introduce Concept Hallucination Inhibition via Localized Interpretability (CHILI), a technique that disentangles image embeddings and localizes pixels corresponding to target concepts. Furthermore, our approach supports the generation of saliency-based explanations that are more interpretable.

cs.CV↗

arXiv2025

Benchmarking XAI Explanations with Human-Aligned Evaluations

We introduce PASTA (Perceptual Assessment System for explanaTion of Artificial Intelligence), a novel human-centric framework for evaluating eXplainable AI (XAI) techniques in computer vision. Our first contribution is the creation of the PASTA-dataset, the first large-scale benchmark that spans a diverse set of models and both saliency-based and concept-based explanation methods. This dataset enables robust, comparative analysis of XAI techniques based on human judgment. Our second contribution is an automated, data-driven benchmark that predicts human preferences using the PASTA-dataset. This scoring called PASTA-score method offers scalable, reliable, and consistent evaluation aligned with human perception. Additionally, our benchmark allows for comparisons between explanations across different modalities, an aspect previously unaddressed. We then propose to apply our scoring method to probe the interpretability of existing models and to build more human interpretable XAI methods.

cs.CV↗

arXiv2025

Concept-Based Mechanistic Interpretability Using Structured Knowledge Graphs

While concept-based interpretability methods have traditionally focused on local explanations of neural network predictions, we propose a novel framework and interactive tool that extends these methods into the domain of mechanistic interpretability. Our approach enables a global dissection of model behavior by analyzing how high-level semantic attributes (referred to as concepts) emerge, interact, and propagate through internal model components. Unlike prior work that isolates individual neurons or predictions, our framework systematically quantifies how semantic concepts are represented across layers, revealing latent circuits and information flow that underlie model decision-making. A key innovation is our visualization platform that we named BAGEL (for Bias Analysis with a Graph for global Explanation Layers), which presents these insights in a structured knowledge graph, allowing users to explore concept-class relationships, identify spurious correlations, and enhance model trustworthiness. Our framework is model-agnostic, scalable, and contributes to a deeper understanding of how deep learning models generalize (or fail to) in the presence of dataset biases. The demonstration is available at https://knowledge-graph-ui-4a7cb5.gitlab.io/.

cs.LG↗

arXiv2025

Explainability for Vision Foundation Models: A Survey

As artificial intelligence systems become increasingly integrated into daily life, the field of explainability has gained significant attention. This trend is particularly driven by the complexity of modern AI models and their decision-making processes. The advent of foundation models, characterized by their extensive generalization capabilities and emergent uses, has further complicated this landscape. Foundation models occupy an ambiguous position in the explainability domain: their complexity makes them inherently challenging to interpret, yet they are increasingly leveraged as tools to construct explainable models. In this survey, we explore the intersection of foundation models and eXplainable AI (XAI) in the vision domain. We begin by compiling a comprehensive corpus of papers that bridge these fields. Next, we categorize these works based on their architectural characteristics. We then discuss the challenges faced by current research in integrating XAI within foundation models. Furthermore, we review common evaluation methodologies for these combined approaches. Finally, we present key observations and insights from our survey, offering directions for future research in this rapidly evolving field.

cs.CV↗

arXiv2024

CLIP-QDA: An Explainable Concept Bottleneck Model

In this paper, we introduce an explainable algorithm designed from a multi-modal foundation model, that performs fast and explainable image classification. Drawing inspiration from CLIP-based Concept Bottleneck Models (CBMs), our method creates a latent space where each neuron is linked to a specific word. Observing that this latent space can be modeled with simple distributions, we use a Mixture of Gaussians (MoG) formalism to enhance the interpretability of this latent space. Then, we introduce CLIP-QDA, a classifier that only uses statistical values to infer labels from the concepts. In addition, this formalism allows for both local and global explanations. These explanations come from the inner design of our architecture, our work is part of a new family of greybox models, combining performances of opaque foundation models and the interpretability of transparent models. Our empirical findings show that in instances where the MoG assumption holds, CLIP-QDA achieves similar accuracy with state-of-the-art methods CBMs. Our explanations compete with existing XAI methods while being faster to compute.

cs.CV↗

arXiv2024

On Double Descent in Reinforcement Learning with LSTD and Random Features

Temporal Difference (TD) algorithms are widely used in Deep Reinforcement Learning (RL). Their performance is heavily influenced by the size of the neural network. While in supervised learning, the regime of over-parameterization and its benefits are well understood, the situation in RL is much less clear. In this paper, we present a theoretical analysis of the influence of network size and $l_2$-regularization on performance. We identify the ratio between the number of parameters and the number of visited states as a crucial factor and define over-parameterization as the regime when it is larger than one. Furthermore, we observe a double descent phenomenon, i.e., a sudden drop in performance around the parameter/state ratio of one. Leveraging random features and the lazy training regime, we study the regularized Least-Square Temporal Difference (LSTD) algorithm in an asymptotic regime, as both the number of parameters and states go to infinity, maintaining a constant ratio. We derive deterministic limits of both the empirical and the true Mean-Squared Bellman Error (MSBE) that feature correction terms responsible for the double descent. Correction terms vanish when the $l_2$-regularization is increased or the number of unvisited states goes to zero. Numerical experiments with synthetic and small real-world environments closely match the theoretical predictions.

cs.LG↗

arXiv2022

A Non-asymptotic Analysis of Non-parametric Temporal-Difference Learning

Temporal-difference learning is a popular algorithm for policy evaluation. In this paper, we study the convergence of the regularized non-parametric TD(0) algorithm, in both the independent and Markovian observation settings. In particular, when TD is performed in a universal reproducing kernel Hilbert space (RKHS), we prove convergence of the averaged iterates to the optimal value function, even when it does not belong to the RKHS. We provide explicit convergence rates that depend on a source condition relating the regularity of the optimal value function to the RKHS. We illustrate this convergence numerically on a simple continuous-state Markov reward process.

math.OC↗

arXiv2021

Infinite-Dimensional Sums-of-Squares for Optimal Control

We introduce an approximation method to solve an optimal control problem via the Lagrange dual of its weak formulation. It is based on a sum-of-squares representation of the Hamiltonian, and extends a previous method from polynomial optimization to the generic case of smooth problems. Such a representation is infinite-dimensional and relies on a particular space of functions-a reproducing kernel Hilbert space-chosen to fit the structure of the control problem. After subsampling, it leads to a practical method that amounts to solving a semi-definite program. We illustrate our approach by a numerical application on a simple low-dimensional control problem.

math.OC↗

arXiv2020

Amplifying Rényi Differential Privacy via Shuffling

Differential privacy is a useful tool to build machine learning models which do not release too much information about the training data. We study the Rényi differential privacy of stochastic gradient descent when each training example is sampled without replacement (also known as cyclic SGD). Cyclic SGD is typically faster than traditional SGD and is the algorithm of choice in large-scale implementations. We recover privacy guarantees for cyclic SGD which are competitive with those known for sampling with replacement. Our proof techniques make no assumptions on the model or on the data and are hence widely applicable.

cs.LG↗