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.

Students' decisions on whether to take a class are strongly affected by whether their friends plan to take the class with them. A student may prefer to be assigned to a course they likes less, just to be with their friends, rather than taking a more preferred class alone. It has been shown that taking classes with friends positively affects academic performance. Thus, academic institutes should prioritize friendship relations when assigning course seats. The introduction of friendship relations results in several non-trivial changes to current course allocation methods. This paper explores how course allocation mechanisms can account for friendships between students and provide a unique, distributed solution. In particular, we model the problem as an asymmetric distributed constraint optimization problem and develop a new dedicated algorithm. Our extensive evaluation includes both simulated data and data derived from a user study on 177 students' preferences over courses and friends. The results show that our algorithm obtains high utility for the students while keeping the solution fair and observing courses' seat capacity limitations.

Motivated by the above limitations of prior IPP approaches, Environmental monitoring problems require estimating the we present a method that can efficiently generate current state of phenomena, such as temperature, precipitation, both discrete and continuous sensing paths, accommodate ozone concentration, soil chemistry, ocean salinity, constraints such as a distance budget and velocity limits, and fugitive gas density ([1], [2], [3], [4]). These problems handle point sensors and non-point FoV sensors, and handle are closely related to the informative path planning (IPP) both single and multi-robot IPP problems. Our approach problem ([1], [5]) since it is often the case that we have leverages gradient descent optimizable sparse Gaussian processes limited resources and, therefore, must strategically determine to solve the IPP problem, making it significantly the regions from which to collect data and the order in which faster compared to prior approaches and scalable to large to visit the regions to efficiently and accurately estimate the IPP problems.

Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we shall present a novel deep symbolic learning method called the "finite expression method" (FEX) to discover governing equations within a function space containing a finite set of analytic expressions, based on observed dynamic data. The key concept is to employ FEX to generate analytical expressions of the governing equations by learning the derivatives of partial differential equation (PDE) solutions through convolutions. Our numerical results demonstrate that our FEX surpasses other existing methods (such as PDE-Net, SINDy, GP, and SPL) in terms of numerical performance across a range of problems, including time-dependent PDE problems and nonlinear dynamical systems with time-varying coefficients. Moreover, the results highlight FEX's flexibility and expressive power in accurately approximating symbolic governing equations.

Sketch-and-project is a framework which unifies many known iterative methods for solving linear systems and their variants, as well as further extensions to non-linear optimization problems. It includes popular methods such as randomized Kaczmarz, coordinate descent, variants of the Newton method in convex optimization, and others. In this paper, we develop a theoretical framework for obtaining sharp guarantees on the convergence rate of sketch-and-project methods. Our approach is the first to: (1) show that the convergence rate improves at least linearly with the sketch size, and even faster when the data matrix exhibits certain spectral decays; and (2) allow for sparse sketching matrices, which are more efficient than dense sketches and more robust than sub-sampling methods. In particular, our results explain an observed phenomenon that a radical sparsification of the sketching matrix does not affect the per iteration convergence rate of sketch-and-project. To obtain our results, we develop new non-asymptotic spectral bounds for the expected sketched projection matrix, which are of independent interest; and we establish a connection between the convergence rates of iterative sketch-and-project solvers and the approximation error of randomized singular value decomposition, which is a widely used one-shot sketching algorithm for low-rank approximation. Our experiments support the theory and demonstrate that even extremely sparse sketches exhibit the convergence properties predicted by our framework.

We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing integrals, and (c) variational inference in probabilistic models. These problems are related to one another through convex duality, and for all them, there are many applications throughout data science, and we aim for computationally tractable approximation algorithms that preserve properties of the original problem such as potential convexity or monotonicity. In order to achieve this, we derive a sequence of convex relaxations for computing these divergences from non-centered covariance matrices associated with a given feature vector: starting from the typically non-tractable optimal lower-bound, we consider an additional relaxation based on ``sums-of-squares'', which is is now computable in polynomial time as a semidefinite program. We also provide computationally more efficient relaxations based on spectral information divergences from quantum information theory. For all of the tasks above, beyond proposing new relaxations, we derive tractable convex optimization algorithms, and we present illustrations on multivariate trigonometric polynomials and functions on the Boolean hypercube.

Model predictive control (MPC) is a powerful tool for planning and controlling dynamical systems due to its capacity for handling constraints and taking advantage of preview information. Nevertheless, MPC performance is highly dependent on the choice of cost function tuning parameters. In this work, we demonstrate an approach for online automatic tuning of an MPC controller with an example application to an ecological cruise control system that saves fuel by using a preview of road grade. We solve the global fuel consumption minimization problem offline using dynamic programming and find the corresponding MPC cost function by solving the inverse optimization problem. A neural network fitted to these offline results is used to generate the desired MPC cost function weight during online operation. The effectiveness of the proposed approach is verified in simulation for different road geometries.

The large population of wireless users is a key driver of data-crowdsourced Machine Learning (ML). However, data privacy remains a significant concern. Federated Learning (FL) encourages data sharing in ML without requiring data to leave users' devices but imposes heavy computation and communications overheads on mobile devices. Hierarchical FL (HFL) alleviates this problem by performing partial model aggregation at edge servers. HFL can effectively reduce energy consumption and latency through effective resource allocation and appropriate user assignment. Nevertheless, resource allocation in HFL involves optimizing multiple variables, and the objective function should consider both energy consumption and latency, making the development of resource allocation algorithms very complicated. Moreover, it is challenging to perform user assignment, which is a combinatorial optimization problem in a large search space. This article proposes a spectrum resource optimization algorithm (SROA) and a two-stage iterative algorithm (TSIA) for HFL. Given an arbitrary user assignment pattern, SROA optimizes CPU frequency, transmit power, and bandwidth to minimize system cost. TSIA aims to find a user assignment pattern that considerably reduces the total system cost. Experimental results demonstrate the superiority of the proposed HFL framework over existing studies in energy and latency reduction.