Simulations using machine learning (ML) models and mechanistic models are often run to inform decision-making processes. Uncertainty estimates of simulation results are critical to the decision-making process because simulation results of specific scenarios may have wide, but unspecified, confidence bounds that may impact subsequent analyses and decisions. The objective of this work is to develop a protocol to assess uncertainties in predictions of machine learning and mechanistic simulation models. The protocol will outline an uncertainty quantification workflow that may be used to establish credible bounds of predictability on computed quantities of interest and to assess model sufficiency. The protocol identifies key sources of uncertainties in machine learning and mechanistic modeling, defines applicable methods of uncertainty propagation for these sources, and includes statistically rational estimators for output uncertainties. The work applies the protocol to test cases relevant to the gas distribution industry and presents learnings from its application. The paper concludes with a brief discussion outlining a pathway to the wider adoption of uncertainty quantification within the industry

This work is concerned with solving neural network-based feedback controllers efficiently for optimal control problems. We first conduct a comparative study of two mainstream approaches: offline supervised learning and online direct policy optimization. Albeit the training part of the supervised learning approach is relatively easy, the success of the method heavily depends on the optimal control dataset generated by open-loop optimal control solvers. In contrast, direct optimization turns the optimal control problem into an optimization problem directly without any requirement of pre-computing, but the dynamics-related objective can be hard to optimize when the problem is complicated. Our results highlight the priority of offline supervised learning in terms of both optimality and training time. To overcome the main challenges, dataset, and optimization, in the two approaches respectively, we complement them and propose the Pre-train and Fine-tune strategy as a unified training paradigm for optimal feedback control, which further improves the performance and robustness significantly. Our code is available at https://github.com/yzhao98/DeepOptimalControl.

Bayesian optimization (BO) is a popular global optimization scheme for sample-efficient optimization in domains with expensive function evaluations. The existing BO techniques are capable of finding a single global optimum solution. However, finding a set of global and local optimum solutions is crucial in a wide range of real-world problems, as implementing some of the optimal solutions might not be feasible due to various practical restrictions (e.g., resource limitation, physical constraints, etc.). In such domains, if multiple solutions are known, the implementation can be quickly switched to another solution, and the best possible system performance can still be obtained. This paper develops a multimodal BO framework to effectively find a set of local/global solutions for expensive-to-evaluate multimodal objective functions. We consider the standard BO setting with Gaussian process regression representing the objective function. We analytically derive the joint distribution of the objective function and its first-order derivatives. This joint distribution is used in the body of the BO acquisition functions to search for local optima during the optimization process. We introduce variants of the well-known BO acquisition functions to the multimodal setting and demonstrate the performance of the proposed framework in locating a set of local optimum solutions using multiple optimization problems.

In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one objective must come at a cost to another. But as the set of Pareto optimal vectors can be very large, we further consider a more practically significant Pareto-constrained optimization problem, where the goal is to optimize a preference function constrained to the Pareto set. We investigate local methods for solving this constrained optimization problem, which poses significant challenges because the constraint set is (i) implicitly defined, and (ii) generally non-convex and non-smooth, even when the objectives are. We define notions of optimality and stationarity, and provide an algorithm with a last-iterate convergence rate of $O(K^{-1/2})$ to stationarity when the objectives are strongly convex and Lipschitz smooth.

On-demand ride services or ride-sourcing services have been experiencing fast development in the past decade. Various mathematical models and optimization algorithms have been developed to help ride-sourcing platforms design operational strategies with higher efficiency. However, due to cost and reliability issues (implementing an immature algorithm for real operations may result in system turbulence), it is commonly infeasible to validate these models and train/test these optimization algorithms within real-world ride sourcing platforms. Acting as a useful test bed, a simulation platform for ride-sourcing systems will be very important to conduct algorithm training/testing or model validation through trails and errors. While previous studies have established a variety of simulators for their own tasks, it lacks a fair and public platform for comparing the models or algorithms proposed by different researchers. In addition, the existing simulators still face many challenges, ranging from their closeness to real environments of ride-sourcing systems, to the completeness of different tasks they can implement. To address the challenges, we propose a novel multi-functional and open-sourced simulation platform for ride-sourcing systems, which can simulate the behaviors and movements of various agents on a real transportation network. It provides a few accessible portals for users to train and test various optimization algorithms, especially reinforcement learning algorithms, for a variety of tasks, including on-demand matching, idle vehicle repositioning, and dynamic pricing. In addition, it can be used to test how well the theoretical models approximate the simulated outcomes. Evaluated on real-world data based experiments, the simulator is demonstrated to be an efficient and effective test bed for various tasks related to on-demand ride service operations.

With the rapid proliferation of smart mobile devices, federated learning (FL) has been widely considered for application in wireless networks for distributed model training. However, data heterogeneity, e.g., non-independently identically distributions and different sizes of training data among clients, poses major challenges to wireless FL. Limited communication resources complicate the implementation of fair scheduling which is required for training on heterogeneous data, and further deteriorate the overall performance. To address this issue, this paper focuses on performance analysis and optimization for wireless FL, considering data heterogeneity, combined with wireless resource allocation. Specifically, we first develop a closed-form expression for an upper bound on the FL loss function, with a particular emphasis on data heterogeneity described by a dataset size vector and a data divergence vector. Then we formulate the loss function minimization problem, under constraints on long-term energy consumption and latency, and jointly optimize client scheduling, resource allocation, and the number of local training epochs (CRE). Next, via the Lyapunov drift technique, we transform the CRE optimization problem into a series of tractable problems. Extensive experiments on real-world datasets demonstrate that the proposed algorithm outperforms other benchmarks in terms of the learning accuracy and energy consumption.

The quadrotor is a $6$ degrees-of-freedom (DoF) system with underactuation. Adding a spherical pendulum on top of a quadrotor further complicates the task of achieving any output tracking while stabilizing the rest. In this report, we present different types of controllers for the nonlinear dynamical system of quadrotor and pendulum combination, utilizing feedback-linearization and control Lyapunov function with quadratic programming (CLF-QP) approaches. We demonstrated trajectory tracking for quadrotor-only case as well as quadrotor-pendulum-combined case.

Dictionary learning can be used for image superresolution by learning a pair of coupled dictionaries of image patches from high-resolution and low-resolution image pairs such that the corresponding pairs share the same sparse vector when represented by the coupled dictionaries. These dictionaries then can be used to to reconstruct the corresponding high-resolution patches from low-resolution input images based on sparse recovery. The idea is to recover the shared sparse vector using the low-resolution dictionary and then multiply it by the high-resolution dictionary to recover the corresponding high-resolution image patch. In this work, we study the effect of the sparse recovery algorithm that we use on the quality of the reconstructed images. We offer empirical experiments to search for the best sparse recovery algorithm that can be used for this purpose. Image super-resolution is an important problem in computer vision due to its numerous practical applications and significant impact on various domains. Super-resolution techniques can significantly enhance the visual quality of images by increasing their resolution without improving the imaging device. This is particularly valuable in applications where high-quality images are crucial, such as medical imaging, satellite imagery, and surveillance.

We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such bounds use linear programming (LP) formulations that quickly become intractable for existing solvers because the size of the LP grows exponentially in the number of edges in the causal graph. We show that this LP can be significantly pruned, allowing us to compute bounds for significantly larger causal inference problems compared to existing techniques. This pruning procedure allows us to compute bounds in closed form for a special class of problems, including a well-studied family of problems where multiple confounded treatments influence an outcome. We extend our pruning methodology to fractional LPs which compute bounds for causal queries which incorporate additional observations about the unit. We show that our methods provide significant runtime improvement compared to benchmarks in experiments and extend our results to the finite data setting. For causal inference without additional observations, we propose an efficient greedy heuristic that produces high quality bounds, and scales to problems that are several orders of magnitude larger than those for which the pruned LP can be solved.

Robots in 3D spaces with more than six degrees of freedom are redundant. A redundant robot allows multiple configurations of the robot for the given target point in the dexterous workspace. The presence of multiple solutions helps in resolving constraints in workspace such as object avoidance and energy minimization during trajectory planning. Inverse kinematics solutions of such redundant robotics are intricate. The present study involves comparison of different metaheuristic optimization algorithms (MOA), which have a positional error, and identify a MOA for high precision of positioning of the end effector of the robot. This study applies recent MOA for the inverse kinematics of hyper redundant nine degrees of freedom (DOF) robot arm by using forward kinematics of the Denavit-Hartenberg (DH) parameters and compares the performance of these algorithms. The comparative study shows Bald Eagle Search (BES) algorithm has better performance over other metaheuristic algorithms. BES algorithm outperforms the other MOA in achieving the desired position with very high precision and least positional error for a 9-DOF robot arm.