Motivated by robust dynamic resource allocation in operations research, we study the Online Learning to Transport (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw connections between online learning, optimal transport, and partial differential equations through an insight called the minimal selection principle, originally studied in the Wasserstein gradient flow setting by Ambrosio et al. (2005). This allows us to extend the standard online learning framework to the infinite-dimensional setting seamlessly. Based on our framework, we derive a novel method called the minimal selection or exploration (MSoE) algorithm to solve OLT problems using mean-field approximation and discretization techniques. In the displacement convex setting, the main theoretical message underpinning our approach is that minimizing transport cost over time (via the minimal selection principle) ensures optimal cumulative regret upper bounds. On the algorithmic side, our MSoE algorithm applies beyond the displacement convex setting, making the mathematical theory of optimal transport practically relevant to non-convex settings common in dynamic resource allocation.

This paper describes the design of HotJava Views, a user environment and suite of applications for a Network Computer.A Network Computer differs from the common Personal Computer in that it has no permanent local storage, but instead obtains its software and data as needed over the network from a central server.We have abandoned some characteristic features of current GUI interfaces, such as the desktop metaphor, file systems, and the distinction between applications and documents.Our design principles are focused on simplicity, efficiency of operation, clarity of the interaction model, and tight integration between applications.