Optimization methods are essential in solving complex problems across various domains. In this research paper, we introduce a novel optimization method called Gaussian Crunching Search (GCS). Inspired by the behaviour of particles in a Gaussian distribution, GCS aims to efficiently explore the solution space and converge towards the global optimum. We present a comprehensive analysis of GCS, including its working mechanism, and potential applications. Through experimental evaluations and comparisons with existing optimization methods, we highlight the advantages and strengths of GCS. This research paper serves as a valuable resource for researchers, practitioners, and students interested in optimization, providing insights into the development and potential of Gaussian Crunching Search as a new and promising approach.

Autonomous robots have real-world applications in diverse fields, such as mobile manipulation and environmental exploration, and many such tasks benefit from a hands-off approach in terms of human user involvement over a long task horizon. However, the level of autonomy achievable by a deployment is limited in part by the problem definition or task specification required by the system. Task specifications often require technical, low-level information that is unintuitive to describe and may result in generic solutions, burdening the user technically both before and after task completion. In this thesis, we aim to advance task specification abstraction toward the goal of increasing robot autonomy in real-world scenarios. We do so by tackling problems that address several different angles of this goal. First, we develop a way for the automatic discovery of optimal transition points between subtasks in the context of constrained mobile manipulation, removing the need for the human to hand-specify these in the task specification. We further propose a way to automatically describe constraints on robot motion by using demonstrated data as opposed to manually-defined constraints. Then, within the context of environmental exploration, we propose a flexible task specification framework, requiring just a set of quantiles of interest from the user that allows the robot to directly suggest locations in the environment for the user to study. We next systematically study the effect of including a robot team in the task specification and show that multirobot teams have the ability to improve performance under certain specification conditions, including enabling inter-robot communication. Finally, we propose methods for a communication protocol that autonomously selects useful but limited information to share with the other robots.

Model-based reinforcement learning (RL) has demonstrated remarkable successes on a range of continuous control tasks due to its high sample efficiency. To save the computation cost of conducting planning online, recent practices tend to distill optimized action sequences into an RL policy during the training phase. Although the distillation can incorporate both the foresight of planning and the exploration ability of RL policies, the theoretical understanding of these methods is yet unclear. In this paper, we extend the policy improvement step of Soft Actor-Critic (SAC) by developing an approach to distill from model-based planning to the policy. We then demonstrate that such an approach of policy improvement has a theoretical guarantee of monotonic improvement and convergence to the maximum value defined in SAC. We discuss effective design choices and implement our theory as a practical algorithm -- Model-based Planning Distilled to Policy (MPDP) -- that updates the policy jointly over multiple future time steps. Extensive experiments show that MPDP achieves better sample efficiency and asymptotic performance than both model-free and model-based planning algorithms on six continuous control benchmark tasks in MuJoCo.

Differential Dynamic Programming (DDP) is a popular technique used to generate motion for dynamic-legged robots in the recent past. However, in most cases, only the first-order partial derivatives of the underlying dynamics are used, resulting in the iLQR approach. Neglecting the second-order terms often slows down the convergence rate compared to full DDP. Multi-Shooting is another popular technique to improve robustness, especially if the dynamics are highly non-linear. In this work, we consider Multi-Shooting DDP for trajectory optimization of a bounding gait for a simplified quadruped model. As the main contribution, we develop Second-Order analytical partial derivatives of the rigid-body contact dynamics, extending our previous results for fixed/floating base models with multi-DoF joints. Finally, we show the benefits of a novel Quasi-Newton method for approximating second-order derivatives of the dynamics, leading to order-of-magnitude speedups in the convergence compared to the full DDP method.

We investigate adversarial robustness of unsupervised Graph Contrastive Learning (GCL) against structural attacks. First, we provide a comprehensive empirical and theoretical analysis of existing attacks, revealing how and why they downgrade the performance of GCL. Inspired by our analytic results, we present a robust GCL framework that integrates a homophily-driven sanitation view, which can be learned jointly with contrastive learning. A key challenge this poses, however, is the non-differentiable nature of the sanitation objective. To address this challenge, we propose a series of techniques to enable gradient-based end-to-end robust GCL. Moreover, we develop a fully unsupervised hyperparameter tuning method which, unlike prior approaches, does not require knowledge of node labels. We conduct extensive experiments to evaluate the performance of our proposed model, GCHS (Graph Contrastive Learning with Homophily-driven Sanitation View), against two state of the art structural attacks on GCL. Our results demonstrate that GCHS consistently outperforms all state of the art baselines in terms of the quality of generated node embeddings as well as performance on two important downstream tasks.

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and might lead to a suboptimal solution to the original problem. In addition, the intermediate solutions, often ignored by classic homotopy optimization, could be useful for many real-world applications. In this work, we propose a novel model-based approach to learn the whole continuation path for homotopy optimization, which contains infinite intermediate solutions for any surrogate subproblems. Rather than the classic unidirectional easy-to-hard optimization, our method can simultaneously optimize the original problem and all surrogate subproblems in a collaborative manner. The proposed model also supports real-time generation of any intermediate solution, which could be desirable for many applications. Experimental studies on different problems show that our proposed method can significantly improve the performance of homotopy optimization and provide extra helpful information to support better decision-making.

Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) is a promising passive device that contributes to a full-space coverage via transmitting and reflecting the incident signal simultaneously. As a new paradigm in wireless communications, how to analyze the coverage and capacity performance of STAR-RISs becomes essential but challenging. To solve the coverage and capacity optimization (CCO) problem in STAR-RIS assisted networks, a multi-objective proximal policy optimization (MO-PPO) algorithm is proposed to handle long-term benefits than conventional optimization algorithms. To strike a balance between each objective, the MO-PPO algorithm provides a set of optimal solutions to form a Pareto front (PF), where any solution on the PF is regarded as an optimal result. Moreover, in order to improve the performance of the MO-PPO algorithm, two update strategies, i.e., action-value-based update strategy (AVUS) and loss function-based update strategy (LFUS), are investigated. For the AVUS, the improved point is to integrate the action values of both coverage and capacity and then update the loss function. For the LFUS, the improved point is only to assign dynamic weights for both loss functions of coverage and capacity, while the weights are calculated by a min-norm solver at every update. The numerical results demonstrated that the investigated update strategies outperform the fixed weights MO optimization algorithms in different cases, which includes a different number of sample grids, the number of STAR-RISs, the number of elements in the STAR-RISs, and the size of STAR-RISs. Additionally, the STAR-RIS assisted networks achieve better performance than conventional wireless networks without STAR-RISs. Moreover, with the same bandwidth, millimeter wave is able to provide higher capacity than sub-6 GHz, but at a cost of smaller coverage.

In Federated Learning (FL), a number of clients or devices collaborate to train a model without sharing their data. Models are optimized locally at each client and further communicated to a central hub for aggregation. While FL is an appealing decentralized training paradigm, heterogeneity among data from different clients can cause the local optimization to drift away from the global objective. In order to estimate and therefore remove this drift, variance reduction techniques have been incorporated into FL optimization recently. However, these approaches inaccurately estimate the clients' drift and ultimately fail to remove it properly. In this work, we propose an adaptive algorithm that accurately estimates drift across clients. In comparison to previous works, our approach necessitates less storage and communication bandwidth, as well as lower compute costs. Additionally, our proposed methodology induces stability by constraining the norm of estimates for client drift, making it more practical for large scale FL. Experimental findings demonstrate that the proposed algorithm converges significantly faster and achieves higher accuracy than the baselines across various FL benchmarks.

Explicit model-predictive control (MPC) is a widely used control design method that employs optimization tools to find control policies offline; commonly it is posed as a semi-definite program (SDP) or as a mixed-integer SDP in the case of hybrid systems. However, mixed-integer SDPs are computationally expensive, motivating alternative formulations, such as zonotope-based MPC (zonotopes are a special type of symmetric polytopes). In this paper, we propose a robust explicit MPC method applicable to hybrid systems. More precisely, we extend existing zonotope-based MPC methods to account for multiplicative parametric uncertainty. Additionally, we propose a convex zonotope order reduction method that takes advantage of the iterative structure of the zonotope propagation problem to promote diagonal blocks in the zonotope generators and lower the number of decision variables. Finally, we developed a quasi-time-free policy choice algorithm, allowing the system to start from any point on the trajectory and avoid chattering associated with discrete switching of linear control policies based on the current state's membership in state-space regions. Last but not least, we verify the validity of the proposed methods on two experimental setups, varying physical parameters between experiments.

Annual Meeting of Transportation Research Board ABSTRACT The emerging technology of the Autonomous Truck Mounted Attenuator (ATMA), a leader-follower style vehicle system, utilizes connected and automated vehicle capabilities to enhance safety during transportation infrastructure maintenance in work zones. However, the speed difference between ATMA vehicles and general vehicles creates a moving bottleneck that reduces capacity and increases queue length, resulting in additional delays. The different routes taken by ATMA cause diverse patterns of time-varying capacity drops, which may affect the user equilibrium traffic assignment and lead to different system costs. This manuscript focuses on optimizing the routing for ATMA vehicles in a network to minimize the system cost associated with the slow-moving operation. To achieve this, a queuing-based traffic assignment approach is proposed to identify the system cost caused by the ATMA system. A queuing-based time-dependent (QBTD) travel time function, considering capacity drop, is introduced and applied in the static user equilibrium traffic assignment problem, with a result of adding dynamic characteristics. Subsequently, we formulate the queuing-based traffic assignment problem and solve it using a modified path-based algorithm. The methodology is validated using a small-size and a large-size network and compared with two benchmark models to analyze the benefit of capacity drop modeling and QBTD travel time function. Furthermore, the approach is applied to quantify the impact of different routes on the traffic system and identify an optimal route for ATMA vehicles performing maintenance work. Finally, sensitivity analysis is conducted to explore how the impact changes with variations in traffic demand and capacity reduction.