GPT, BERT) that are expected to generalize well on a variety of tasks.

In machine learning, knowing the impact of a given datum on model training is a fundamental task referred to as Data Valuation. Building on previous works from the literature, we have designed a novel canonical decomposition allowing practitioners to analyze any data valuation method as the combination of two parts: a utility function that captures characteristics from a given model and an aggregation procedure that merges such information. We also propose to use Gaussian Processes as a means to easily access the utility function on ``sub-models'', which are models trained on a subset of the training set. The strength of our approach stems from both its theoretical grounding in Bayesian theory, and its practical reach, by enabling fast estimation of valuations thanks to efficient update formulae.

A multi-agent system is a network of autonomous entities called agents that share information and collaborate to solve tasks usually beyond an individual agent's scope [12]. This broad description fits well in the recent research trends like cloud computing [11], or Industry 4.0 [10], and allows multi-agent systems to find applications in many other fields. In robotics, in scenarios including groups of mobile robots or swarms of drones, it is necessary to avoid collisions or obstacles and to navigate collaboratively [9]. The agent-based approach is also used for controlling smart grids, i.e., efficient and robust power systems [6]. We can also find numerous other examples, like analyzing the traffic flow [7] or modelling purchasing decisions [3]. Inspired by these multidisciplinary applications, we formally discuss the general problem of distributed learning, with a particular focus on the modelling of nonlinearities under limited information, cf.

This work studies the problem of transfer learning under the functional linear regression model framework, which aims to improve the estimation and prediction of the target model by leveraging the information from related source models. We measure the relatedness between target and source models using Reproducing Kernel Hilbert Spaces (RKHS) norm, allowing the type of information being transferred to be interpreted by the structural properties of the spaces. Two transfer learning algorithms are proposed: one transfers information from source tasks when we know which sources to use, while the other one aggregates multiple transfer learning results from the first algorithm to achieve robust transfer learning without prior information about the sources. Furthermore, we establish the optimal convergence rates for the prediction risk in the target model, making the statistical gain via transfer learning mathematically provable. The theoretical analysis of the prediction risk also provides insights regarding what factors are affecting the transfer learning effect, i.e. what makes source tasks useful to the target task. We demonstrate the effectiveness of the proposed transfer learning algorithms on extensive synthetic data as well as real financial data application.

In Machine Learning, a benchmark refers to an ensemble of datasets associated with one or multiple metrics together with a way to aggregate different systems performances. They are instrumental in (i) assessing the progress of new methods along different axes and (ii) selecting the best systems for practical use. This is particularly the case for NLP with the development of large pre-trained models (e.g. GPT, BERT) that are expected to generalize well on a variety of tasks. While the community mainly focused on developing new datasets and metrics, there has been little interest in the aggregation procedure, which is often reduced to a simple average over various performance measures. However, this procedure can be problematic when the metrics are on a different scale, which may lead to spurious conclusions. This paper proposes a new procedure to rank systems based on their performance across different tasks. Motivated by the social choice theory, the final system ordering is obtained through aggregating the rankings induced by each task and is theoretically grounded. We conduct extensive numerical experiments (on over 270k scores) to assess the soundness of our approach both on synthetic and real scores (e.g. GLUE, EXTREM, SEVAL, TAC, FLICKR). In particular, we show that our method yields different conclusions on state-of-the-art systems than the mean-aggregation procedure while being both more reliable and robust.

In this article, we aim at improving the prediction of expert aggregation by using the underlying properties of the models that provide expert predictions. We restrict ourselves to the case where expert predictions come from Kalman recursions, fitting state-space models. By using exponential weights, we construct different algorithms of Kalman recursions Aggregated Online (KAO) that compete with the best expert or the best convex combination of experts in a more or less adaptive way. We improve the existing results on expert aggregation literature when the experts are Kalman recursions by taking advantage of the second-order properties of the Kalman recursions. We apply our approach to Kalman recursions and extend it to the general adversarial expert setting by state-space modeling the errors of the experts. We apply these new algorithms to a real dataset of electricity consumption and show how it can improve forecast performances comparing to other exponentially weighted average procedures.

Knowledge can be represented compactly in multiple ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a database modelled as a first-order relational structure. In the presence of integrity constraints, we identify classes of aggregators that respect them in the aggregated database, provided these are satisfied in all individual databases. We also characterise languages for first-order queries on which the answer to a query on the aggregated database coincides with the aggregation of the answers to the query obtained on each individual database. This contribution is meant to be a first step on the application of techniques from social choice theory to knowledge representation in databases.

We introduce a new recursive aggregation procedure called Bernstein Online Aggregation (BOA). The exponential weights include an accuracy term and a second order term that is a proxy of the quadratic variation as in Hazan and Kale (2010). This second term stabilizes the procedure that is optimal in different senses. We first obtain optimal regret bounds in the deterministic context. Then, an adaptive version is the first exponential weights algorithm that exhibits a second order bound with excess losses that appears first in Gaillard et al. (2014). The second order bounds in the deterministic context are extended to a general stochastic context using the cumulative predictive risk. Such conversion provides the main result of the paper, an inequality of a novel type comparing the procedure with any deterministic aggregation procedure for an integrated criteria. Then we obtain an observable estimate of the excess of risk of the BOA procedure. To assert the optimality, we consider finally the iid case for strongly convex and Lipschitz continuous losses and we prove that the optimal rate of aggregation of Tsybakov (2003) is achieved. The batch version of the BOA procedure is then the first adaptive explicit algorithm that satisfies an optimal oracle inequality with high probability.

We introduce an alternative to the notion of `fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot always be attained by a learning procedure (i.e., a procedure that selects a function in the given class), we introduce an aggregation procedure that attains that rate under rather minimal assumptions -- for example, that the $L_q$ and $L_2$ norms are equivalent on the linear span of the class for some $q>2$, and the target random variable is square-integrable.