In this paper, we introduce two Gromov-Wasserstein-type distances on the set of Gaussian mixture models. The first one takes the form of a Gromov-Wasserstein distance between two discrete distributionson the space of Gaussian measures. This distance can be used as an alternative to Gromov-Wasserstein for applications which only require to evaluate how far the distributions are from each other but does not allow to derive directly an optimal transportation plan between clouds of points. To design a way to define such a transportation plan, we introduce another distance between measures living in incomparable spaces that turns out to be closely related to Gromov-Wasserstein. When restricting the set of admissible transportation couplings to be themselves Gaussian mixture models in this latter, this defines another distance between Gaussian mixture models that can be used as another alternative to Gromov-Wasserstein and which allows to derive an optimal assignment between points. Finally, we design a transportation plan associated with the first distance by analogy with the second, and we illustrate their practical uses on medium-to-large scale problems such as shape matching and hyperspectral image color transfer.

The advent of reconfigurable intelligent surfaces(RISs) brings along significant improvements for wireless technology on the verge of beyond-fifth-generation networks (B5G).The proven flexibility in influencing the propagation environment opens up the possibility of programmatically altering the wireless channel to the advantage of network designers, enabling the exploitation of higher-frequency bands for superior throughput overcoming the challenging electromagnetic (EM) propagation properties at these frequency bands. However, RISs are not magic bullets. Their employment comes with significant complexity, requiring ad-hoc deployments and management operations to come to fruition. In this paper, we tackle the open problem of bringing RISs to the field, focusing on areas with little or no coverage. In fact, we present a first-of-its-kind deep reinforcement learning (DRL) solution, dubbed as D-RISA, which trains a DRL agent and, in turn, obtain san optimal RIS deployment. We validate our framework in the indoor scenario of the Rennes railway station in France, assessing the performance of our algorithm against state-of-the-art (SOA) approaches. Our benchmarks showcase better coverage, i.e., 10-dB increase in minimum signal-to-noise ratio (SNR), at lower computational time (up to -25 percent) while improving scalability towards denser network deployments.

In this paper, we propose a novel data-driven approach for learning and control of quadrotor UAVs based on the Koopman operator and extended dynamic mode decomposition (EDMD). Building observables for EDMD based on conventional methods like Euler angles (to represent orientation) is known to involve singularities. To address this issue, we employ a set of physics-informed observables based on the underlying topology of the nonlinear system. We use rotation matrices to directly represent the orientation dynamics and obtain a lifted linear representation of the nonlinear quadrotor dynamics in the SE(3) manifold. This EDMD model leads to accurate prediction and can be generalized to several validation sets. Further, we design a linear model predictive controller (MPC) based on the proposed EDMD model to track agile reference trajectories. Simulation results show that the proposed MPC controller can run as fast as 100 Hz and is able to track arbitrary reference trajectories with good accuracy. Implementation details can be found in \url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}.

We present a novel learning framework to solve the transport-and-packing (TAP) problem in 3D. It constitutes a full solution pipeline from partial observations of input objects via RGBD sensing and recognition to final box placement, via robotic motion planning, to arrive at a compact packing in a target container. The technical core of our method is a neural network for TAP, trained via reinforcement learning (RL), to solve the NP-hard combinatorial optimization problem. Our network simultaneously selects an object to pack and determines the final packing location, based on a judicious encoding of the continuously evolving states of partially observed source objects and available spaces in the target container, using separate encoders both enabled with attention mechanisms. The encoded feature vectors are employed to compute the matching scores and feasibility masks of different pairings of box selection and available space configuration for packing strategy optimization. Extensive experiments, including ablation studies and physical packing execution by a real robot (Universal Robot UR5e), are conducted to evaluate our method in terms of its design choices, scalability, generalizability, and comparisons to baselines, including the most recent RL-based TAP solution. We also contribute the first benchmark for TAP which covers a variety of input settings and difficulty levels.

The ability to learn good representations of states is essential for solving large reinforcement learning problems, where exploration, generalization, and transfer are particularly challenging. The Laplacian representation is a promising approach to address these problems by inducing intrinsic rewards for temporally-extended action discovery and reward shaping, and informative state encoding. To obtain the Laplacian representation one needs to compute the eigensystem of the graph Laplacian, which is often approximated through optimization objectives compatible with deep learning approaches. These approximations, however, depend on hyperparameters that are impossible to tune efficiently, converge to arbitrary rotations of the desired eigenvectors, and are unable to accurately recover the corresponding eigenvalues. In this paper we introduce a theoretically sound objective and corresponding optimization algorithm for approximating the Laplacian representation. Our approach naturally recovers both the true eigenvectors and eigenvalues while eliminating the hyperparameter dependence of previous approximations. We provide theoretical guarantees for our method and we show that those results translate empirically into robust learning across multiple environments.

Our ultimate goal is to build robust policies for robots that assist people. What makes this hard is that people can behave unexpectedly at test time, potentially interacting with the robot outside its training distribution and leading to failures. Even just measuring robustness is a challenge. Adversarial perturbations are the default, but they can paint the wrong picture: they can correspond to human motions that are unlikely to occur during natural interactions with people. A robot policy might fail under small adversarial perturbations but work under large natural perturbations. We propose that capturing robustness in these interactive settings requires constructing and analyzing the entire natural-adversarial frontier: the Pareto-frontier of human policies that are the best trade-offs between naturalness and low robot performance. We introduce RIGID, a method for constructing this frontier by training adversarial human policies that trade off between minimizing robot reward and acting human-like (as measured by a discriminator). On an Assistive Gym task, we use RIGID to analyze the performance of standard collaborative Reinforcement Learning, as well as the performance of existing methods meant to increase robustness. We also compare the frontier RIGID identifies with the failures identified in expert adversarial interaction, and with naturally-occurring failures during user interaction. Overall, we find evidence that RIGID can provide a meaningful measure of robustness predictive of deployment performance, and uncover failure cases in human-robot interaction that are difficult to find manually. https://ood-human.github.io.

The discovery of therapeutic molecules is fundamentally a multi-objective optimization problem. One formulation of the problem is to identify molecules that simultaneously exhibit strong binding affinity for a target protein, minimal off-target interactions, and suitable pharmacokinetic properties. Inspired by prior work that uses active learning to accelerate the identification of strong binders, we implement multi-objective Bayesian optimization to reduce the computational cost of multi-property virtual screening and apply it to the identification of ligands predicted to be selective based on docking scores to on- and off-targets. We demonstrate the superiority of Pareto optimization over scalarization across three case studies. Further, we use the developed optimization tool to search a virtual library of over 4M molecules for those predicted to be selective dual inhibitors of EGFR and IGF1R, acquiring 100% of the molecules that form the library's Pareto front after exploring only 8% of the library. This workflow and associated open source software can reduce the screening burden of molecular design projects and is complementary to research aiming to improve the accuracy of binding predictions and other molecular properties.

Contact-rich manipulation is common in a wide range of robotic applications, including assembly [1, 2, 3, 4, 5, 6, 7, 8], object pivoting [9, 10, 11], grasping[12, 13, 14], and pushing [15, 16]. To accomplish these tasks, robots need to learn both the manipulation trajectory and the force control parameters. The manipulation trajectory guides the robot toward completing the task while physically engaging with the environment, whereas the force control parameters regulate the contact force. Incorrect control parameters can lead to oscillations and excessive contact forces that may damage the robot or the environment. Past works have tackled the contact-rich skill-learning problem in different ways. First, the majority of previous works [2, 10, 6, 7, 3, 17, 9, 18, 19] focus on learning the manipulation trajectories and rely on human experts to manually tune force control parameters. While this simplification has demonstrated remarkable performance in many applications, letting human labor tune control parameters is still inconvenient. Furthermore, the tuned parameter for one task may not generalize well to other task settings with different kinematic or dynamic properties. For example, assembly tasks with different clearances will require different control parameters.

To date, power electronics parameter design tasks are usually tackled using detailed optimization approaches with detailed simulations or using brute force grid search grid search with very fast simulations. A new method, named "Continuously Adapting Random Sampling" (CARS) is proposed, which provides a continuous method in between. This allows for very fast, and / or large amounts of simulations, but increasingly focuses on the most promising parameter ranges. Inspirations are drawn from multi-armed bandit research and lead to prioritized sampling of sub-domains in one high-dimensional parameter tensor. Performance has been evaluated on three exemplary power electronic use-cases, where resulting designs appear competitive to genetic algorithms, but additionally allow for highly parallelizable simulation, as well as continuous progression between explorative and exploitative settings.

This paper considers federated learning (FL) with constraints, where the central server and all local clients collectively minimize a sum of convex local objective functions subject to global and local convex conic constraints. To train the model without moving local data from clients to the central server, we propose an FL framework in which each local client performs multiple updates using the local objective and local constraint, while the central server handles the global constraint and performs aggregation based on the updated local models. In particular, we develop a proximal augmented Lagrangian (AL) based algorithm for FL with global and local convex conic constraints. The subproblems arising in this algorithm are solved by an inexact alternating direction method of multipliers (ADMM) in a federated fashion. Under a local Lipschitz condition and mild assumptions, we establish the worst-case complexity bounds of the proposed algorithm for finding an approximate KKT solution. To the best of our knowledge, this work proposes the first algorithm for FL with global and local constraints. Our numerical experiments demonstrate the practical advantages of our algorithm in performing Neyman-Pearson classification and enhancing model fairness in the context of FL.