Agile quadrotor flight relies on rapidly planning and accurately tracking time-optimal trajectories, a technology critical to their application in the wild. However, the computational burden of computing time-optimal trajectories based on the full quadrotor dynamics (typically on the order of minutes or even hours) can hinder its ability to respond quickly to changing scenarios. Additionally, modeling errors and external disturbances can lead to deviations from the desired trajectory during tracking in real time. This letter proposes a novel approach to computing time-optimal trajectories, by fixing the nodes with waypoint constraints and adopting separate sampling intervals for trajectories between waypoints, which significantly accelerates trajectory planning. Furthermore, the planned paths are tracked via a time-adaptive model predictive control scheme whose allocated tracking time can be adaptively adjusted on-the-fly, therefore enhancing the tracking accuracy and robustness. We evaluate our approach through simulations and experimentally validate its performance in dynamic waypoint scenarios for time-optimal trajectory replanning and trajectory tracking.

Vertical federated learning (FL) is a collaborative machine learning framework that enables devices to learn a global model from the feature-partition datasets without sharing local raw data. However, as the number of the local intermediate outputs is proportional to the training samples, it is critical to develop communication-efficient techniques for wireless vertical FL to support high-dimensional model aggregation with full device participation. In this paper, we propose a novel cloud radio access network (Cloud-RAN) based vertical FL system to enable fast and accurate model aggregation by leveraging over-the-air computation (AirComp) and alleviating communication straggler issue with cooperative model aggregation among geographically distributed edge servers. However, the model aggregation error caused by AirComp and quantization errors caused by the limited fronthaul capacity degrade the learning performance for vertical FL. To address these issues, we characterize the convergence behavior of the vertical FL algorithm considering both uplink and downlink transmissions. To improve the learning performance, we establish a system optimization framework by joint transceiver and fronthaul quantization design, for which successive convex approximation and alternate convex search based system optimization algorithms are developed. We conduct extensive simulations to demonstrate the effectiveness of the proposed system architecture and optimization framework for vertical FL.

Federated learning is an important framework in modern machine learning that seeks to integrate the training of learning models from multiple users, each user having their own local data set, in a way that is sensitive to data privacy and to communication loss constraints. In clustered federated learning, one assumes an additional unknown group structure among users, and the goal is to train models that are useful for each group, rather than simply training a single global model for all users. In this paper, we propose a novel solution to the problem of clustered federated learning that is inspired by ideas in consensus-based optimization (CBO). Our new CBO-type method is based on a system of interacting particles that is oblivious to group memberships. Our model is motivated by rigorous mathematical reasoning, including a mean field analysis describing the large number of particles limit of our particle system, as well as convergence guarantees for the simultaneous global optimization of general non-convex objective functions (corresponding to the loss functions of each cluster of users) in the mean-field regime. Experimental results demonstrate the efficacy of our FedCBO algorithm compared to other state-of-the-art methods and help validate our methodological and theoretical work.

Laplacian regularized stratified models (LRSM) are models that utilize the explicit or implicit network structure of the sub-problems as defined by the categorical features called strata (e.g., age, region, time, forecast horizon, etc.), and draw upon data from neighboring strata to enhance the parameter learning of each sub-problem. They have been widely applied in machine learning and signal processing problems, including but not limited to time series forecasting, representation learning, graph clustering, max-margin classification, and general few-shot learning. Nevertheless, existing works on LRSM have either assumed a known graph or are restricted to specific applications. In this paper, we start by showing the importance and sensitivity of graph weights in LRSM, and provably show that the sensitivity can be arbitrarily large when the parameter scales and sample sizes are heavily imbalanced across nodes. We then propose a generic approach to jointly learn the graph while fitting the model parameters by solving a single optimization problem. We interpret the proposed formulation from both a graph connectivity viewpoint and an end-to-end Bayesian perspective, and propose an efficient algorithm to solve the problem. Convergence guarantees of the proposed optimization algorithm is also provided despite the lack of global strongly smoothness of the Laplacian regularization term typically required in the existing literature, which may be of independent interest. Finally, we illustrate the efficiency of our approach compared to existing methods by various real-world numerical examples.

In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.

We study landmark-based SLAM with unknown data association: our robot navigates in a completely unknown environment and has to simultaneously reason over its own trajectory, the positions of an unknown number of landmarks in the environment, and potential data associations between measurements and landmarks. This setup is interesting since: (i) it arises when recovering from data association failures or from SLAM with information-poor sensors, (ii) it sheds light on fundamental limits (and hardness) of landmark-based SLAM problems irrespective of the front-end data association method, and (iii) it generalizes existing approaches where data association is assumed to be known or partially known. We approach the problem by splitting it into an inner problem of estimating the trajectory, landmark positions and data associations and an outer problem of estimating the number of landmarks. Our approach creates useful and novel connections with existing techniques from discrete-continuous optimization (e.g., k-means clustering), which has the potential to trigger novel research. We demonstrate the proposed approaches in extensive simulations and on real datasets and show that the proposed techniques outperform typical data association baselines and are even competitive against an "oracle" baseline which has access to the number of landmarks and an initial guess for each landmark.

This work introduces interpretable regional descriptors, or IRDs, for local, model-agnostic interpretations. IRDs are hyperboxes that describe how an observation's feature values can be changed without affecting its prediction. They justify a prediction by providing a set of "even if" arguments (semi-factual explanations), and they indicate which features affect a prediction and whether pointwise biases or implausibilities exist. A concrete use case shows that this is valuable for both machine learning modelers and persons subject to a decision. We formalize the search for IRDs as an optimization problem and introduce a unifying framework for computing IRDs that covers desiderata, initialization techniques, and a post-processing method. We show how existing hyperbox methods can be adapted to fit into this unified framework. A benchmark study compares the methods based on several quality measures and identifies two strategies to improve IRDs.

We study the computational scalability of a Gaussian process (GP) framework for solving general nonlinear partial differential equations (PDEs). This framework transforms solving PDEs to solving quadratic optimization problem with nonlinear constraints. Its complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel of the GP and its partial derivatives at collocation points. We present a sparse Cholesky factorization algorithm for such kernel matrices based on the near-sparsity of the Cholesky factor under a new ordering of Diracs and derivative measurements. We rigorously identify the sparsity pattern and quantify the exponentially convergent accuracy of the corresponding Vecchia approximation of the GP, which is optimal in the Kullback-Leibler divergence. This enables us to compute $\epsilon$-approximate inverse Cholesky factors of the kernel matrices with complexity $O(N\log^d(N/\epsilon))$ in space and $O(N\log^{2d}(N/\epsilon))$ in time. With the sparse factors, gradient-based optimization methods become scalable. Furthermore, we can use the oftentimes more efficient Gauss-Newton method, for which we apply the conjugate gradient algorithm with the sparse factor of a reduced kernel matrix as a preconditioner to solve the linear system. We numerically illustrate our algorithm's near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Amp\`ere equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs.

We propose an extension of the input-output feedback linearization for a class of multivariate systems that are not input-output linearizable in a classical manner. The key observation is that the usual input-output linearization problem can be interpreted as the problem of solving simultaneous linear equations associated with the input gain matrix: thus, even at points where the input gain matrix becomes singular, it is still possible to solve a part of linear equations, by which a subset of input-output relations is made linear or close to be linear. Based on this observation, we adopt the task priority-based approach in the input-output linearization problem. First, we generalize the classical Byrnes-Isidori normal form to a prioritized normal form having a triangular structure, so that the singularity of a subblock of the input gain matrix related to lower-priority tasks does not directly propagate to higher-priority tasks. Next, we present a prioritized input-output linearization via the multi-objective optimization with the lexicographical ordering, resulting in a prioritized semilinear form that establishes input output relations whose subset with higher priority is linear or close to be linear. Finally, Lyapunov analysis on ultimate boundedness and task achievement is provided, particularly when the proposed prioritized input-output linearization is applied to the output tracking problem. This work introduces a new control framework for complex systems having critical and noncritical control issues, by assigning higher priority to the critical ones.

Precise calibration is the basis for the vision-guided robot system to achieve high-precision operations. Systems with multiple eyes (cameras) and multiple hands (robots) are particularly sensitive to calibration errors, such as micro-assembly systems. Most existing methods focus on the calibration of a single unit of the whole system, such as poses between hand and eye, or between two hands. These methods can be used to determine the relative pose between each unit, but the serialized incremental calibration strategy cannot avoid the problem of error accumulation in a large-scale system. Instead of focusing on a single unit, this paper models the multi-eye and multi-hand system calibration problem as a graph and proposes a method based on the minimum spanning tree and graph optimization. This method can automatically plan the serialized optimal calibration strategy in accordance with the system settings to get coarse calibration results initially. Then, with these initial values, the closed-loop constraints are introduced to carry out global optimization. Simulation experiments demonstrate the performance of the proposed algorithm under different noises and various hand-eye configurations. In addition, experiments on real robot systems are presented to further verify the proposed method.