Federated Learning (FL) is a promising privacy-preserving distributed learning framework where a server aggregates models updated by multiple devices without accessing their private datasets. Hierarchical FL (HFL), as a device-edge-cloud aggregation hierarchy, can enjoy both the cloud server's access to more datasets and the edge servers' efficient communications with devices. However, the learning latency increases with the HFL network scale due to the increasing number of edge servers and devices with limited local computation capability and communication bandwidth. To address this issue, in this paper, we introduce model pruning for HFL in wireless networks to reduce the neural network scale. We present the convergence analysis of an upper on the l2 norm of gradients for HFL with model pruning, analyze the computation and communication latency of the proposed model pruning scheme, and formulate an optimization problem to maximize the convergence rate under a given latency threshold by jointly optimizing the pruning ratio and wireless resource allocation. By decoupling the optimization problem and using Karush Kuhn Tucker (KKT) conditions, closed-form solutions of pruning ratio and wireless resource allocation are derived. Simulation results show that our proposed HFL with model pruning achieves similar learning accuracy compared with the HFL without model pruning and reduces about 50 percent communication cost.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Hyperparameter optimization is crucial to achieving high performance in deep learning. On top of the performance, other criteria such as inference time or memory requirement often need to be optimized due to some practical reasons. This motivates research on multi-objective optimization (MOO). However, Pareto fronts of MOO methods are often shown without considering the variability caused by random seeds and this makes the performance stability evaluation difficult. Although there is a concept named empirical attainment surface to enable the visualization with uncertainty over multiple runs, there is no major Python package for empirical attainment surface. We, therefore, develop a Python package for this purpose and describe the usage. The package is available at https://github.com/nabenabe0928/empirical-attainment-func.

Submodular functions have many real-world applications, such as document summarization, sensor placement, and image segmentation. For all these applications, the key building block is how to compute the maximum value of a submodular function efficiently. We consider both the online and offline versions of the problem: in each iteration, the data set changes incrementally or is not changed, and a user can issue a query to maximize the function on a given subset of the data. The user can be malicious, issuing queries based on previous query results to break the competitive ratio for the online algorithm. Today, the best-known algorithm for online submodular function maximization has a running time of $O(n k d^2)$ where $n$ is the total number of elements, $d$ is the feature dimension and $k$ is the number of elements to be selected. We propose a new method based on a novel search tree data structure. Our algorithm only takes $\widetilde{O}(nk + kd^2 + nd)$ time.

Controller tuning is a vital step to ensure the controller delivers its designed performance. DiffTune has been proposed as an automatic tuning method that unrolls the dynamical system and controller into a computational graph and uses auto-differentiation to obtain the gradient for the controller's parameter update. However, DiffTune uses the vanilla gradient descent to iteratively update the parameter, in which the performance largely depends on the choice of the learning rate (as a hyperparameter). In this paper, we propose to use hyperparameter-free methods to update the controller parameters. We find the optimal parameter update by maximizing the loss reduction, where a predicted loss based on the approximated state and control is used for the maximization. Two methods are proposed to optimally update the parameters and are compared with related variants in simulations on a Dubin's car and a quadrotor. Simulation experiments show that the proposed first-order method outperforms the hyperparameter-based methods and is more robust than the second-order hyperparameter-free methods.

We propose a new iteration scheme, the Cauchy-Simplex, to optimize convex problems over the probability simplex $\{w\in\mathbb{R}^n\ |\ \sum_i w_i=1\ \textrm{and}\ w_i\geq0\}$. Other works have taken steps to enforce positivity or unit normalization automatically but never simultaneously within a unified setting. This paper presents a natural framework for manifestly requiring the probability condition. Specifically, we map the simplex to the positive quadrant of a unit sphere, envisage gradient descent in latent variables, and map the result back in a way that only depends on the simplex variable. Moreover, proving rigorous convergence results in this formulation leads inherently to tools from information theory (e.g. cross entropy and KL divergence). Each iteration of the Cauchy-Simplex consists of simple operations, making it well-suited for high-dimensional problems. We prove that it has a convergence rate of ${O}(1/T)$ for convex functions, and numerical experiments of projection onto convex hulls show faster convergence than similar algorithms. Finally, we apply our algorithm to online learning problems and prove the convergence of the average regret for (1) Prediction with expert advice and (2) Universal Portfolios.

This work examines the challenges of training neural networks using vector quantization using straight-through estimation. We find that a primary cause of training instability is the discrepancy between the model embedding and the code-vector distribution. We identify the factors that contribute to this issue, including the codebook gradient sparsity and the asymmetric nature of the commitment loss, which leads to misaligned code-vector assignments. We propose to address this issue via affine re-parameterization of the code vectors. Additionally, we introduce an alternating optimization to reduce the gradient error introduced by the straight-through estimation. Moreover, we propose an improvement to the commitment loss to ensure better alignment between the codebook representation and the model embedding. These optimization methods improve the mathematical approximation of the straight-through estimation and, ultimately, the model performance. We demonstrate the effectiveness of our methods on several common model architectures, such as AlexNet, ResNet, and ViT, across various tasks, including image classification and generative modeling.

Nonlinear model predictive control (NMPC) solves a multivariate optimization problem to estimate the system's optimal control inputs in each control cycle. Such optimization is made more difficult by several factors, such as nonlinearities inherited in the system, highly coupled inputs, and various constraints related to the system's physical limitations. These factors make the optimization to be non-convex and hard to solve traditionally. Genetic algorithm (GA) is typically used extensively to tackle such optimization in several application domains because it does not involve differential calculation or gradient evaluation in its solution estimation. However, the size of the search space in which the GA searches for the optimal control inputs is crucial for the applicability of the GA with systems that require fast response. This paper proposes an approach to accelerate the genetic optimization of NMPC by learning optimal search space size. The proposed approach trains a multivariate regression model to adaptively predict the best smallest search space in every control cycle. The estimated best smallest size of search space is fed to the GA to allow for searching the optimal control inputs within this search space. The proposed approach not only reduces the GA's computational time but also improves the chance of obtaining the optimal control inputs in each cycle. The proposed approach was evaluated on two nonlinear systems and compared with two other genetic-based NMPC approaches implemented on the GPU of a Nvidia Jetson TX2 embedded platform in a processor-in-theloop (PIL) fashion. The results show that the proposed approach provides a 39-53% reduction in computational time. Additionally, it increases the convergence percentage to the optimal control inputs within the cycle's time by 48-56%, resulting in a significant performance enhancement. The source code is available on GitHub. Model predictive control (MPC) is a powerful control method used to control a system while satisfying a set of constraints [1]. It generates the optimal control inputs in each control cycle by minimizing a multivariate optimization problem subject to given constraints.

Robots deployed to the real world must be able to interact with other agents in their environment. Dynamic game theory provides a powerful mathematical framework for modeling scenarios in which agents have individual objectives and interactions evolve over time. However, a key limitation of such techniques is that they require a-priori knowledge of all players' objectives. In this work, we address this issue by proposing a novel method for learning players' objectives in continuous dynamic games from noise-corrupted, partial state observations. Our approach learns objectives by coupling the estimation of unknown cost parameters of each player with inference of unobserved states and inputs through Nash equilibrium constraints. By coupling past state estimates with future state predictions, our approach is amenable to simultaneous online learning and prediction in receding horizon fashion. We demonstrate our method in several simulated traffic scenarios in which we recover players' preferences for, e.g., desired travel speed and collision-avoidance behavior. Results show that our method reliably estimates game-theoretic models from noise-corrupted data that closely matches ground-truth objectives, consistently outperforming state-of-the-art approaches.

This paper presents an optimization approach for generating custom manipulator configurations using a proposed unconventional modular library. An end-to-end solution is presented in which the resulting optimal models of the modular compositions can be integrated directly with the Robot Operating System platform. The approach utilizes an unconventional modular library, which is adaptable to a wide range of parameters for customization including non-parallel and non-perpendicular joint axes, and the unified modeling technique for getting the custom modular configurations. The single objective function optimization problem is formulated based upon the discrete parameters of reconfiguration depending upon the available modular library such as, number of joint modules, skew-twist angle, intersecting-twist angle, connection ports of the module, module size, modular sub-assembly unit and curved links. Two case studies, including an application to the agricultural vertical farms, are presented to validate the results.