We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional $L^p$ geometry, Orlicz-Wasserstein (OW) and generalized Sobolev transport (GST) employ \emph{Orlicz geometric structure}, leveraging convex functions to capture nuanced geometric relationships and remarkably contribute to advance certain machine learning approaches. However, both OW and GST are restricted to measures with equal total mass, limiting their applicability to real-world scenarios where mass variation is common, and input measures may have noisy supports, or outliers. To address unbalanced measures, OW can either incorporate mass constraints or marginal discrepancy penalization, but this leads to a more complex two-level optimization problem. Additionally, GST provides a scalable yet rigid framework, which poses significant challenges to extend GST to accommodate nonnegative measures.

In distributed machine learning (DML), the network performance between machines significantly impacts the speed of iterative training. In this paper we propose BML, a new gradient synchronization algorithm with higher network performance and lower network cost than the current practice. BML runs on BCube network, instead of using the traditional Fat-Tree topology.

We introduce the best order score search (BOSS) and grow-shrink trees (GSTs) for learning directed acyclic graphs (DAGs) in this paradigm.

Learning to predict properties of a large graph is challenging because each prediction requires the knowledge of an entire graph, while the amount of memory available during training is bounded.

We introduce the best order score search (BOSS) and grow-shrink trees (GSTs) for learning directed acyclic graphs (DAGs) in this paradigm.

Data stemming from networks, however, does not exhibit a regular inherent structure that can be effectively exploited by convolutions.

We thank all the reviewers and the AC for their time, effort and constructive feedback. First, we will include an explicit comparison with the GST of [W1]. This is required to control the impact that topology changes have on the eigenvectors. Likewise, since Prop. 2 shows stability of the graph The formal assumption in Prop. 3 indicates that all involved graph filters in the multirresolution wavelet bank have to The hypothesis in Prop. 3 will be changed to reflect this. Theorem 1 states that it does not depend on the spectral norm of the graph.

Mobile robots navigating in crowds trained using reinforcement learning are known to suffer performance degradation when faced with out-of-distribution scenarios. We propose that by properly accounting for the uncertainties of pedestrians, a robot can learn safe navigation policies that are robust to distribution shifts. Our method augments agent observations with prediction uncertainty estimates generated by adaptive conformal inference, and it uses these estimates to guide the agent's behavior through constrained reinforcement learning. The system helps regulate the agent's actions and enables it to adapt to distribution shifts. In the in-distribution setting, our approach achieves a 96.93% success rate, which is over 8.80% higher than the previous state-of-the-art baselines with over 3.72 times fewer collisions and 2.43 times fewer intrusions into ground-truth human future trajectories. In three out-of-distribution scenarios, our method shows much stronger robustness when facing distribution shifts in velocity variations, policy changes, and transitions from individual to group dynamics. We deploy our method on a real robot, and experiments show that the robot makes safe and robust decisions when interacting with both sparse and dense crowds. Our code and videos are available on https://gen-safe-nav.github.io/.