The first year of the OCEAN project has been highly productive. The consortium has made significant progress in all work packages, and we are generally on track with our planned research agenda.
First, Ocean produced several results regarding "optimization core" work package. Michael I. Jordan's team carried out a work to improve the optimization methods to derive Nash equilibria in quantum zero-sum games, and three more projects studying respectively extra-gradient methods for separable stochastic variational inequalities, for general variational inequalities with general constraints and for monotone equations in continuous time.
Second, Ocean made significant progress in the "Bayesian inference and sampling core" work package. The Warwick team and associated partners published several studies designing novel MCMC-related methods such as the Divide-and-conquer approach. A particular emphasis has been put on Bayesian methods for heterogenous and distributed inference such as the Bayesian fusion.
Likewise, advances were made for the "Federated Learning" package in the year 2024. Eric Moulines supervised a project aimed at understanding and quantifying a heterogeneity bias that arises in federated procedures. An algorithm, SCAFFLSA, was also proposed to correct this bias in the context of linear stochastic approximation and TD learning. Likewise, Pr. Dieuleveut contributed to the work package through studying compression schemes for federated learning which produce a specific error distribution. Additionally, Gareth Roberts carried out two projects related to Bayesian fusion, an approach particularly well suited for decentralized learning.
Significant results have also been obtained for the "Privacy" work package. Warwick and associated Universities' teams published a study which incorporates privacy in posterior sampling. They relied on Huber contamination with heavy-tailed distributions and showed that their method enjoys desirable asymptotic properties. Christian Robert focused with his team on laying the foundation of a novel decision-theoretic framework for privacy, as an alternative to the differential privacy paradigm. Moreover, Finally, the UC Berkeley node also got involved in this work package, with one study establishing that privacy may arise endogenously in strategic environments and another one characterizing the impact of privacy on market segmentation.
Similarly, Ocean's efforts in the "Data market and economic value of data" work package proved succesful. A study co-supervised by Eric Moulines and Michael Jordan characterizes the effect of adverse selection on collaborative learning and shows that it may fall victim to unravelling. Similarly, the UC Berkeley team produced several projects addressing participation incentives for collaborative learning, in particular when participants have divergent strategic interests.
Additionally, the "Strategic experimentation" work package has also been addressed during this first year. For instance, a project carried out by two PhD students at Polytechnique studies the case of a principal-agent problem in a bandit environment. An explicit algorithm, along with theoretical guarantees, has been designed to solve the principal’s problem. Another follow-up paper generalizes this idea to a multi-agent setting with externalities and adapts the former algorithm to recover the celebrated Coase theorem.
Finally, we will start working on WP7 from the year 2026 on, as planned per our prospective research agenda.
