The recent developments in the research area covered by the provided papers indicate a strong focus on enhancing computational methods and theoretical frameworks in machine learning, particularly in the areas of optimal transport, bandit optimization, and online learning. A significant trend is the exploration of more efficient and scalable algorithms for complex problems, such as the computation of Wasserstein barycentres and the optimization of bandit algorithms under various conditions. Innovations include the generalization of fixed-point methods for computing barycentres with diverse transport costs, the introduction of new models of misspecification in linear bandits that allow for more nuanced regret analysis, and the integration of pre-trained neural networks into contextual bandit optimization to improve learning efficiency. Additionally, there is a notable emphasis on bridging theoretical advancements with practical applications, as seen in the development of novel similarity measures for functions and the application of optimal transport in time series data analysis. These advancements not only push the boundaries of current methodologies but also open new avenues for applying these techniques across a wide range of domains.

Noteworthy Papers

• Computing Barycentres of Measures for Generic Transport Costs: Extends fixed-point methods for Wasserstein barycentres to accommodate diverse transport costs and measures, demonstrating convergence and numerical efficiency.
• No-Regret Linear Bandits under Gap-Adjusted Misspecification: Introduces a novel model of misspecification for linear bandits, showing that the LinUCB algorithm is robust against such misspecification and achieves near-optimal regret.
• Contextual Bandit Optimization with Pre-Trained Neural Networks: Proposes a novel algorithm, E2TC, that leverages pre-trained neural networks for efficient learning in contextual bandits, demonstrating sublinear regret under certain conditions.