The ability of deep learning methods to perform classification and regression tasks relies heavily on their capacity to uncover manifolds in high-dimensional data spaces and project them into low-dimensional representation spaces. In this study, we investigate the structure and character of the manifolds generated by classical variational autoencoder (VAE) approaches and deep kernel learning (DKL). In the former case, the structure of the latent space is determined by the properties of the input data alone, while in the latter, the latent manifold forms as a result of an active learning process that balances the data distribution and target functionalities. We show that DKL with active learning can produce a more compact and smooth latent space which is more conducive to optimization compared to previously reported methods, such as the VAE. We demonstrate this behavior using a simple cards data set and extend it to the optimization of domain-generated trajectories in physical systems. Our findings suggest that latent manifolds constructed through active learning have a more beneficial structure for optimization problems, especially in feature-rich target-poor scenarios that are common in domain sciences, such as materials synthesis, energy storage, and molecular discovery. The jupyter notebooks that encapsulate the complete analysis accompany the article.

This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way to understand system behavior and design control algorithms that account for underlying dynamics and changing parameters. The PVKO builds on a conventional Koopman model by incorporating local time-invariant linear systems through interpolation within the lifted space. This paper outlines a procedure for identifying the PVKO and designing a model predictive control using the identified PVKO model. Simulation results demonstrate that the proposed approach improves model accuracy and enables predictions based on future parameter information. The feasibility and stability of the proposed control approach are analyzed, and their effectiveness is demonstrated through simulation.

A global effort has been initiated to reduce the worldwide greenhouse gas (GHG) emissions, primarily carbon emissions, by half by 2030 and reach net-zero by 2050. The development of 6G must also be compliant with this goal. Unfortunately, developing a sustainable and net-zero emission systems to meet the users' fast growing demands on mobile services, especially smart services and applications, may be much more challenging than expected. Particularly, despite the energy efficiency improvement in both hardware and software designs, the overall energy consumption and carbon emission of mobile networks are still increasing at a tremendous speed. The growing penetration of resource-demanding AI algorithms and solutions further exacerbate this challenge. In this article, we identify the major emission sources and introduce an evaluation framework for analyzing the lifecycle of network AI implementations. A novel joint dynamic energy trading and task allocation optimization framework, called DETA, has been introduced to reduce the overall carbon emissions. We consider a federated edge intelligence-based network AI system as a case study to verify the effectiveness of our proposed solution. Experimental results based on a hardware prototype suggest that our proposed solution can reduce carbon emissions of network AI systems by up to 74.9%. Finally, open problems and future directions are discussed.

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the system state will evolve over time, and the design challenge is to optimize the initial conditions that lead to a target outcome. Recent developments in learned simulation have shown that graph neural networks (GNNs) can be used for accurate, efficient, differentiable estimation of simulator dynamics, and support high-quality design optimization with gradient- or sampling-based optimization procedures. However, optimizing designs from scratch requires many expensive model queries, and these procedures exhibit basic failures on either non-convex or high-dimensional problems. In this work, we show how denoising diffusion models (DDMs) can be used to solve inverse design problems efficiently and propose a particle sampling algorithm for further improving their efficiency. We perform experiments on a number of fluid dynamics design challenges, and find that our approach substantially reduces the number of calls to the simulator compared to standard techniques.

Novel applications such as the Metaverse have highlighted the potential of beyond 5G networks, which necessitate ultra-low latency communications and massive broadband connections. Moreover, the burgeoning demand for such services with ever-fluctuating users has engendered a need for heightened service continuity consideration in B5G. To enable these services, the edge-cloud paradigm is a potential solution to harness cloud capacity and effectively manage users in real time as they move across the network. However, edge-cloud networks confront a multitude of limitations, including networking and computing resources that must be collectively managed to unlock their full potential. This paper addresses the joint problem of service placement and resource allocation in a network-cloud integrated environment while considering capacity constraints, dynamic users, and end-to-end delays. We present a non-linear programming model that formulates the optimization problem with the aiming objective of minimizing overall cost while enhancing latency. Next, to address the problem, we introduce a DDQL-based technique using RNNs to predict user behavior, empowered by a water-filling-based algorithm for service placement. The proposed framework adeptly accommodates the dynamic nature of users, the placement of services that mandate ultra-low latency in B5G, and service continuity when users migrate from one location to another. Simulation results show that our solution provides timely responses that optimize the network's potential, offering a scalable and efficient placement.

Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a speed profile that satisfies kino-dynamic and other constraints. While trajectory retiming is most often formulated with the minimum-time objective (i.e. traverse the path as fast as possible), it is not always the most desirable objective, particularly when we seek to balance multiple objectives or when bang-bang control is unsuitable. In this paper, we present a novel algorithm based on factor graph variable elimination that can solve for the global optimum of the retiming problem with quadratic objectives as well (e.g. minimize control effort or match a nominal speed by minimizing squared error), which may extend to arbitrary objectives with iteration. Our work extends prior works, which find only solutions on the boundary of the feasible region, while maintaining the same linear time complexity from a single forward-backward pass. We experimentally demonstrate that (1) we achieve better real-world robot performance by using quadratic objectives in place of the minimum-time objective, and (2) our implementation is comparable or faster than state-of-the-art retiming algorithms.

This paper introduces a differentiable representation for optimization of boustrophedon path plans in convex polygons, explores an additional parameter of these path plans that can be optimized, discusses the properties of this representation that can be leveraged during the optimization process, and shows that the previously published attempt at optimization of these path plans was too coarse to be practically useful. Experiments were conducted to show that this differentiable representation can reproduce the same scores from transitional discrete representations of boustrophedon path plans with high fidelity. Finally, optimization via gradient descent was attempted, but found to fail because the search space is far more non-convex than was previously considered in the literature. The wide range of applications for boustrophedon path plans means that this work has the potential to improve path planning efficiency in numerous areas of robotics including mapping and search tasks using uncrewed aerial systems, environmental sampling tasks using uncrewed marine vehicles, and agricultural tasks using ground vehicles, among numerous others applications.

This paper presents DFL-TORO, a novel Demonstration Framework for Learning Time-Optimal Robotic tasks via One-shot kinesthetic demonstration. It aims at optimizing the process of Learning from Demonstration (LfD), applied in the manufacturing sector. As the effectiveness of LfD is challenged by the quality and efficiency of human demonstrations, our approach offers a streamlined method to intuitively capture task requirements from human teachers, by reducing the need for multiple demonstrations. Furthermore, we propose an optimization-based smoothing algorithm that ensures time-optimal and jerk-regulated demonstration trajectories, while also adhering to the robot's kinematic constraints. The result is a significant reduction in noise, thereby boosting the robot's operation efficiency. Evaluations using a Franka Emika Research 3 (FR3) robot for a reaching task further substantiate the efficacy of our framework, highlighting its potential to transform kinesthetic demonstrations in contemporary manufacturing environments.

Federated learning is an emerging distributed machine learning method, enables a large number of clients to train a model without exchanging their local data. The time cost of communication is an essential bottleneck in federated learning, especially for training large-scale deep neural networks. Some communication-efficient federated learning methods, such as FedAvg and FedAdam, share the same learning rate across different clients. But they are not efficient when data is heterogeneous. To maximize the performance of optimization methods, the main challenge is how to adjust the learning rate without hurting the convergence. In this paper, we propose a heterogeneous local variant of AMSGrad, named FedLALR, in which each client adjusts its learning rate based on local historical gradient squares and synchronized learning rates. Theoretical analysis shows that our client-specified auto-tuned learning rate scheduling can converge and achieve linear speedup with respect to the number of clients, which enables promising scalability in federated optimization. We also empirically compare our method with several communication-efficient federated optimization methods. Extensive experimental results on Computer Vision (CV) tasks and Natural Language Processing (NLP) task show the efficacy of our proposed FedLALR method and also coincides with our theoretical findings.

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference, these models are used to weigh different blocks of the Jacobian and error vector resulting from linearization and hence, additionally affect the stability and convergence of the non-linear system. We propose a gradient-based method to estimate well-conditioned covariance matrices by formulating the learning process as a constrained bilevel optimization problem over factor graphs. We evaluate our method against baselines across a range of simulated and real-world tasks and demonstrate that our technique converges to model estimates that lead to better solutions as evidenced by the improved tracking accuracy on unseen test trajectories.