We provide a complete theory of optimal universal rates for binary classification in the agnostic setting. This extends the realizable-case theory of Bousquet, Hanneke, Moran, van Handel, and Yehudayoff (2021) by removing the realizability assumption on the distribution. We identify a fundamental tetrachotomy of optimal rates: for every concept class, the optimal universal rate of convergence of the excess error rate is one of $e^{-n}$, $e^{-o(n)}$, $o(n^{-1/2})$, or arbitrarily slow. We further identify simple combinatorial structures which determine which of these categories any given concept class falls into.

We thank all the Reviewers for their feedback and their service to the community. We summarize it in the following paragraphs. In particular, taking localization to mean "analysis of the variance-constrained star-convex hull", function Instead taking localization to mean "constrain by raw-variance," the above issue is solved, but now the We intend to fully explore this connection in future work.

Cormas is an agent-based simulation platform developed in the late 90s by the Green research at CIRAD unit to support the management of natural resources and understand the interactions between natural and social dynamics. This platform is well-suited for a participatory simulation approach that empowers local stakeholders by including them in all modelling and knowledge-sharing steps. In this short paper, we present the Cormas platform and discuss its unique features and their importance for the participatory simulation approach. We then present the early results of our ongoing study on managing pastoral resources in the Sahel region, identify the problems faced by local stakeholders, and discuss the potential use of Cormas at the next stage of our study to collectively model and understand the effective ways of managing the shared agro-sylvo-pastoral resources.

We analyze a family of supervised learning algorithms based on sample compression schemes that are stable, in the sense that removing points from the training set which were not selected for the compression set does not alter the resulting classifier. We use this technique to derive a variety of novel or improved data-dependent generalization bounds for several learning algorithms. In particular, we prove a new margin bound for SVM, removing a log factor. The new bound is provably optimal.

We derive sharper probabilistic concentration bounds for the Monte Carlo Empirical Rademacher Averages (MCERA), which are proved through recent results on the concentration of self-bounding functions. Our novel bounds allow obtaining sharper bounds to (Local) Rademacher Averages. We also derive novel variance-aware bounds for the special case where only one vector of Rademacher random variables is used to compute the MCERA. Then, we leverage the framework of self-bounding functions to derive novel probabilistic bounds to the supremum deviations, that may be of independent interest.

A robotic system, which draws from both nautical and biological designs, has been developed by engineers from the Massachusetts Institute of Technology (MIT). Their innovative robotic glider can skim along the water's surface. The research team say their robotic device rides the wind like an albatross while also surfing the waves like a sailboat. In high wind conditions the robot is designed to stay aloft, much like its avian counterpart, whereas in calmer winds, the robot has a keel it can dip into the water allowing it to ride in the manner of a highly efficient sailboat. The robotic system is relatively lightweight, weighing about 6 pounds, and can cover a given distance using one-third as much wind as an albatross and traveling 10 times faster than a typical sailboat.

"The oceans remain vastly under-monitored," said Gabriel Bousquet, an MIT postdoc who led the design of a unique robot as part of his graduate thesis. "In particular, it's very important to understand the Southern Ocean and how it is interacting with climate change. But it's very hard to get there." Bousquet and his team designed a hybrid vehicle that can both fly above tumultuous seas and sail on them when things are calmer. The vehicle uses one-third as much wind as an albatross would and travels ten times faster than a typical sailboat, making for a very efficient way to survey the vast areas of the planet's seas.

We show two novel concentration inequalities for suprema of empirical processes when sampling without replacement, which both take the variance of the functions into account. While these inequalities may potentially have broad applications in learning theory in general, we exemplify their significance by studying the transductive setting of learning theory. For which we provide the first excess risk bounds based on the localized complexity of the hypothesis class, which can yield fast rates of convergence also in the transductive learning setting. We give a preliminary analysis of the localized complexities for the prominent case of kernel classes.