This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover agents' strategic actions and the environment's configurations from partial and noisy observations of the population of agents and the setup of the environment. Our method is a probabilistic tool to infer the behaviors of agents in MFGs from data in scenarios where the comprehensive dataset is either inaccessible or contaminated by noises.

Global trajectory optimization is a crucial step for localization and mappin systems. Because it is unavoidable that trajectory errors accumulate in online odometry estimation that performs real-time optimization using local observations, it is necessary to correct estimation drift by considering the global consistency of the map. Global registration error minimization is one of the most accurate approaches to global trajectory optimization [1]. Unlike the conventional pose graph optimization that minimizes the errors in the pose space [2], global registration error minimization directly minimizes the multi-frame point cloud registration errors over the entire map. This approach avoids the Gaussian approximation of the relative pose constraint and enables accurate trajectory optimization by jointly Figure 1: Dense factor graph for global registration error aligning all frames in the map [3]. However, it is known minimization. The proposed algorithm reduces memory consumption to be computationally expensive compared to pose graph by 99% and processing time by 87% for the optimization, as it requires a re-evaluation of registration optimization of the factor graph. error functions that involve residual computations for many points [4].

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics. We propose the first approach for learning neural Lyapunov control in a broad class of discrete-time systems. Three key ingredients enable us to effectively learn provably stable control policies. The first is a novel mixed-integer linear programming approach for verifying the discrete-time Lyapunov stability conditions, leveraging the particular structure of these conditions. The second is a novel approach for computing verified sublevel sets. The third is a heuristic gradient-based method for quickly finding counterexamples to significantly speed up Lyapunov function learning. Our experiments on four standard benchmarks demonstrate that our approach significantly outperforms state-of-the-art baselines. For example, on the path tracking benchmark, we outperform recent neural Lyapunov control baselines by an order of magnitude in both running time and the size of the region of attraction, and on two of the four benchmarks (cartpole and PVTOL), ours is the first automated approach to return a provably stable controller. Our code is available at: https://github.com/jlwu002/nlc_discrete.

In this work, we propose a collision-free source-seeking control framework for unicycle robots traversing an unknown cluttered environment. In this framework, obstacle avoidance is guided by the control barrier functions (CBF) embedded in quadratic programming and the source seeking control relies solely on the use of on-board sensors that measure the signal strength of the source. To tackle the mixed relative degree of the CBF, we proposed three different CBFs, namely the zeroing control barrier functions (ZCBF), exponential control barrier functions (ECBF), and reciprocal control barrier functions (RCBF) that can directly be integrated with our recent gradient-ascent source-seeking control law. We provide rigorous analysis of the three different methods and show the efficacy of the approaches in simulations using Matlab, as well as, using a realistic dynamic environment with moving obstacles in Gazebo/ROS.

Lowering the memory requirement in full-parameter training on large models has become a hot research area. MeZO fine-tunes the large language models (LLMs) by just forward passes in a zeroth-order SGD optimizer (ZO-SGD), demonstrating excellent performance with the same GPU memory usage as inference. However, the simulated perturbation stochastic approximation for gradient estimate in MeZO leads to severe oscillations and incurs a substantial time overhead. Moreover, without momentum regularization, MeZO shows severe over-fitting problems. Lastly, the perturbation-irrelevant momentum on ZO-SGD does not improve the convergence rate. This study proposes ZO-AdaMU to resolve the above problems by adapting the simulated perturbation with momentum in its stochastic approximation. Unlike existing adaptive momentum methods, we relocate momentum on simulated perturbation in stochastic gradient approximation. Our convergence analysis and experiments prove this is a better way to improve convergence stability and rate in ZO-SGD. Extensive experiments demonstrate that ZO-AdaMU yields better generalization for LLMs fine-tuning across various NLP tasks than MeZO and its momentum variants.

Successful machine learning involves a complete pipeline of data, model, and downstream applications. Instead of treating them separately, there has been a prominent increase of attention within the constrained optimization (CO) and machine learning (ML) communities towards combining prediction and optimization models. The so-called end-to-end (E2E) learning captures the task-based objective for which they will be used for decision making. Although a large variety of E2E algorithms have been presented, it has not been fully investigated how to systematically address uncertainties involved in such models. Most of the existing work considers the uncertainties of ML in the input space and improves robustness through adversarial training. We extend this idea to E2E learning and prove that there is a robustness certification procedure by solving augmented integer programming. Furthermore, we show that neglecting the uncertainty of COs during training causes a new trigger for generalization errors. To include all these components, we propose a unified framework that covers the uncertainties emerging in both the input feature space of the ML models and the COs. The framework is described as a robust optimization problem and is practically solved via end-to-end adversarial training (E2E-AT). Finally, the performance of E2E-AT is evaluated by a real-world end-to-end power system operation problem, including load forecasting and sequential scheduling tasks.

This surge in energy demand not only places strain on existing resources but also raises critical concerns regarding environmental sustainability, largely due to the predominant utilization of fossil fuels [1]. In light of these complex challenges, the electrification of transportation has emerged as a compelling avenue for resolution [1 3]. Consequently, automotive manufacturers are progressively pivoting away from conventional fossil fuel-powered vehicles, embracing innovative energy alternatives such as battery electric vehicles (BEVs), hybrid electric vehicles (HEVs), and fuel cell electric vehicles (FCEVs) [4 6]. Since such electric vehicles (EVs) stand out for their ability to enhance fuel economy, reduce emissions, and extend mileage range while navigating urban and environmental restrictions, however, the main limitations include a limited range compared to HEVs. HEVs allow them to offer the benefits of electrification without the range and charging constraints of BEVs. And FCEVs boast a longer range and faster refueling times compared to BEVs but are limited by the current scarcity of hydrogen refueling infrastructure. However, in response to these challenges, the effective energy management system (EMS) has emerged as a pivotal solution for optimizing energy usage and enhancing efficiency across various sectors.

We present Constrained Stein Variational Trajectory Optimization (CSVTO), an algorithm for performing trajectory optimization with constraints on a set of trajectories in parallel. We frame constrained trajectory optimization as a novel form of constrained functional minimization over trajectory distributions, which avoids treating the constraints as a penalty in the objective and allows us to generate diverse sets of constraint-satisfying trajectories. Our method uses Stein Variational Gradient Descent (SVGD) to find a set of particles that approximates a distribution over low-cost trajectories while obeying constraints. CSVTO is applicable to problems with arbitrary equality and inequality constraints and includes a novel particle resampling step to escape local minima. By explicitly generating diverse sets of trajectories, CSVTO is better able to avoid poor local minima and is more robust to initialization. We demonstrate that CSVTO outperforms baselines in challenging highly-constrained tasks, such as a 7DoF wrench manipulation task, where CSVTO succeeds in 20/20 trials vs 13/20 for the closest baseline. Our results demonstrate that generating diverse constraint-satisfying trajectories improves robustness to disturbances and initialization over baselines.

While network coverage maps continue to expand, many devices located in remote areas remain unconnected to terrestrial communication infrastructures, preventing them from getting access to the associated data-driven services. In this paper, we propose a ground-to-satellite cooperative federated learning (FL) methodology to facilitate machine learning service management over remote regions. Our methodology orchestrates satellite constellations to provide the following key functions during FL: (i) processing data offloaded from ground devices, (ii) aggregating models within device clusters, and (iii) relaying models/data to other satellites via inter-satellite links (ISLs). Due to the limited coverage time of each satellite over a particular remote area, we facilitate satellite transmission of trained models and acquired data to neighboring satellites via ISL, so that the incoming satellite can continue conducting FL for the region. We theoretically analyze the convergence behavior of our algorithm, and develop a training latency minimizer which optimizes over satellite-specific network resources, including the amount of data to be offloaded from ground devices to satellites and satellites' computation speeds. Through experiments on three datasets, we show that our methodology can significantly speed up the convergence of FL compared with terrestrial-only and other satellite baseline approaches.

The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduces balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose a Gaussian process embedding different likelihoods as the surrogate model for a partially observable constraint. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.