Event cameras are bio-inspired, motion-activated sensors that demonstrate substantial potential in handling challenging situations, such as motion blur and high-dynamic range. In this paper, we proposed EVI-SAM to tackle the problem of 6 DoF pose tracking and 3D reconstruction using monocular event camera. A novel event-based hybrid tracking framework is designed to estimate the pose, leveraging the robustness of feature matching and the precision of direct alignment. Specifically, we develop an event-based 2D-2D alignment to construct the photometric constraint, and tightly integrate it with the event-based reprojection constraint. The mapping module recovers the dense and colorful depth of the scene through the image-guided event-based mapping method. Subsequently, the appearance, texture, and surface mesh of the 3D scene can be reconstructed by fusing the dense depth map from multiple viewpoints using truncated signed distance function (TSDF) fusion. To the best of our knowledge, this is the first non-learning work to realize event-based dense mapping. Numerical evaluations are performed on both publicly available and self-collected datasets, which qualitatively and quantitatively demonstrate the superior performance of our method. Our EVI-SAM effectively balances accuracy and robustness while maintaining computational efficiency, showcasing superior pose tracking and dense mapping performance in challenging scenarios. Video Demo: https://youtu.be/Nn40U4e5Si8.

Distributed optimization methods with probabilistic local updates have recently gained attention for their provable ability to communication acceleration. Nevertheless, this capability is effective only when the loss function is smooth and the network is sufficiently well-connected. In this paper, we propose the first linear convergent method MG-Skip with probabilistic local updates for nonsmooth distributed optimization. Without any extra condition for the network connectivity, MG-Skip allows for the multiple-round gossip communication to be skipped in most iterations, while its iteration complexity is $\mathcal{O}\left(\kappa \log \frac{1}{\epsilon}\right)$ and communication complexity is only $\mathcal{O}\left(\sqrt{\frac{\kappa}{(1-\rho)}} \log \frac{1}{\epsilon}\right)$, where $\kappa$ is the condition number of the loss function and $\rho$ reflects the connectivity of the network topology. To the best of our knowledge, MG-Skip achieves the best communication complexity when the loss function has the smooth (strongly convex)+nonsmooth (convex) composite form.

In today's data-driven landscape, time series forecasting is pivotal in decision-making across various sectors. Yet, the proliferation of more diverse time series data, coupled with the expanding landscape of available forecasting methods, poses significant challenges for forecasters. To meet the growing demand for efficient forecasting, we introduce auto-sktime, a novel framework for automated time series forecasting. The proposed framework uses the power of automated machine learning (AutoML) techniques to automate the creation of the entire forecasting pipeline. The framework employs Bayesian optimization, to automatically construct pipelines from statistical, machine learning (ML) and deep neural network (DNN) models. Furthermore, we propose three essential improvements to adapt AutoML to time series data: First, pipeline templates to account for the different supported forecasting models. Second, a novel warm-starting technique to start the optimization from prior optimization runs. Third, we adapt multi-fidelity optimizations to make them applicable to a search space containing statistical, ML and DNN models. Experimental results on 64 diverse real-world time series datasets demonstrate the effectiveness and efficiency of the framework, outperforming traditional methods while requiring minimal human involvement.

The design of Wireless Networked Control System (WNCS) requires addressing critical interactions between control and communication systems with minimal complexity and communication overhead while providing ultra-high reliability. This paper introduces a novel optimization theory based deep reinforcement learning (DRL) framework for the joint design of controller and communication systems. The objective of minimum power consumption is targeted while satisfying the schedulability and rate constraints of the communication system in the finite blocklength regime and stability constraint of the control system. Decision variables include the sampling period in the control system, and blocklength and packet error probability in the communication system. The proposed framework contains two stages: optimization theory and DRL. In the optimization theory stage, following the formulation of the joint optimization problem, optimality conditions are derived to find the mathematical relations between the optimal values of the decision variables. These relations allow the decomposition of the problem into multiple building blocks. In the DRL stage, the blocks that are simplified but not tractable are replaced by DRL. Via extensive simulations, the proposed optimization theory based DRL approach is demonstrated to outperform the optimization theory and pure DRL based approaches, with close to optimal performance and much lower complexity.

There has been substantial progress on finding game-theoretic equilibria. Most of that work has focused on games with finite, discrete action spaces. However, many games involving space, time, money, and other fine-grained quantities have continuous action spaces (or are best modeled as such). We study the problem of finding an approximate Nash equilibrium of games with continuous action sets. The standard measure of closeness to Nash equilibrium is exploitability, which measures how much players can benefit from unilaterally changing their strategy. We propose two new methods that minimize an approximation of the exploitability with respect to the strategy profile. The first method uses a learned best-response function, which takes the current strategy profile as input and returns candidate best responses for each player. The strategy profile and best-response functions are trained simultaneously, with the former trying to minimize exploitability while the latter tries to maximize it. The second method maintains an ensemble of candidate best responses for each player. In each iteration, the best-performing elements of each ensemble are used to update the current strategy profile. The strategy profile and best-response ensembles are simultaneously trained to minimize and maximize the approximate exploitability, respectively. We evaluate our methods on various continuous games, showing that they outperform prior methods.

Mixture models serve as one fundamental tool with versatile applications. However, their training techniques, like the popular Expectation Maximization (EM) algorithm, are notoriously sensitive to parameter initialization and often suffer from bad local optima that could be arbitrarily worse than the optimal. To address the long-lasting bad-local-optima challenge, we draw inspiration from the recent ground-breaking foundation models and propose to leverage their underlying big learning principle to upgrade the EM. Specifically, we present the Big Learning EM (BigLearn-EM), an EM upgrade that simultaneously performs joint, marginal, and orthogonally transformed marginal matchings between data and model distributions. Through simulated experiments, we empirically show that the BigLearn-EM is capable of delivering the optimal with high probability; comparisons on benchmark clustering datasets further demonstrate its effectiveness and advantages over existing techniques. The code is available at https://github.com/YulaiCong/Big-Learning-Expectation-Maximization.

Model predictive control (MPC) has been applied to many platforms in robotics and autonomous systems for its capability to predict a system's future behavior while incorporating constraints that a system may have. To enhance the performance of a system with an MPC controller, one can manually tune the MPC's cost function. However, it can be challenging due to the possibly high dimension of the parameter space as well as the potential difference between the open-loop cost function in MPC and the overall closed-loop performance metric function. This paper presents DiffTune-MPC, a novel learning method, to learn the cost function of an MPC in a closed-loop manner. The proposed framework is compatible with the scenario where the time interval for performance evaluation and MPC's planning horizon have different lengths. We show the auxiliary problem whose solution admits the analytical gradients of MPC and discuss its variations in different MPC settings. Simulation results demonstrate the capability of DiffTune-MPC and illustrate the influence of constraints (from actuation limits) on learning.

Out-of-distribution (OOD) generalization has long been a challenging problem that remains largely unsolved. Gaussian processes (GP), as popular probabilistic model classes, especially in the small data regime, presume strong OOD generalization abilities. Surprisingly, their OOD generalization abilities have been under-explored before compared with other lines of GP research. In this paper, we identify that GP is not free from the problem and propose a domain invariant learning algorithm for Gaussian processes (DIL-GP) with a min-max optimization on the likelihood. DIL-GP discovers the heterogeneity in the data and forces invariance across partitioned subsets of data. We further extend the DIL-GP to improve Bayesian optimization's adaptability on changing environments. Numerical experiments demonstrate the superiority of DIL-GP for predictions on several synthetic and real-world datasets. We further demonstrate the effectiveness of the DIL-GP Bayesian optimization method on a PID parameters tuning experiment for a quadrotor. The full version and source code are available at: https://github.com/Billzxl/DIL-GP.

While semidefinite programming (SDP) has traditionally been limited to moderate-sized problems, recent algorithms augmented with matrix sketching techniques have enabled solving larger SDPs. However, these methods achieve scalability at the cost of an increase in the number of necessary iterations, resulting in slower convergence as the problem size grows. Furthermore, they require iteration-dependent parameter schedules that prohibit effective utilization of warm-start initializations important in practical applications with incrementally-arriving data or mixed-integer programming. We present SpecBM, a provably correct, fast and scalable algorithm for solving massive SDPs that can leverage a warm-start initialization to further accelerate convergence. Our proposed algorithm is a spectral bundle method for solving general SDPs containing both equality and inequality constraints. Moveover, when augmented with an optional matrix sketching technique, our algorithm achieves the dramatically improved scalability of previous work while sustaining convergence speed. We empirically demonstrate the effectiveness of our method, both with and without warm-starting, across multiple applications with large instances. For example, on a problem with 600 million decision variables, SpecBM achieved a solution of standard accuracy in less than 7 minutes, where the previous state-of-the-art scalable SDP solver requires more than 16 hours. Our method solves an SDP with more than 10^13 decision variables on a single machine with 16 cores and no more than 128GB RAM; the previous state-of-the-art method had not achieved an accurate solution after 72 hours on the same instance. We make our implementation in pure JAX publicly available.

We address the problem of convex optimization with preference feedback, where the goal is to minimize a convex function given a weaker form of comparison queries. Each query consists of two points and the dueling feedback returns a (noisy) single-bit binary comparison of the function values of the two queried points. Here we consider the sign-function-based comparison feedback model and analyze the convergence rates with batched and multiway (argmin of a set queried points) comparisons. Our main goal is to understand the improved convergence rates owing to parallelization in sign-feedback-based optimization problems. Our work is the first to study the problem of convex optimization with multiway preferences and analyze the optimal convergence rates. Our first contribution lies in designing efficient algorithms with a convergence rate of $\smash{\widetilde O}(\frac{d}{\min\{m,d\} \epsilon})$ for $m$-batched preference feedback where the learner can query $m$-pairs in parallel. We next study a $m$-multiway comparison (`battling') feedback, where the learner can get to see the argmin feedback of $m$-subset of queried points and show a convergence rate of $\smash{\widetilde O}(\frac{d}{ \min\{\log m,d\}\epsilon })$. We show further improved convergence rates with an additional assumption of strong convexity. Finally, we also study the convergence lower bounds for batched preferences and multiway feedback optimization showing the optimality of our convergence rates w.r.t. $m$.