Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SVGD has remained a challenging problem. For sampling from a Gaussian target, the SVGD dynamics with a bilinear kernel will remain Gaussian as long as the initializer is Gaussian. Inspired by this fact, we undertake a detailed theoretical study of the Gaussian-SVGD, i.e., SVGD projected to the family of Gaussian distributions via the bilinear kernel, or equivalently Gaussian variational inference (GVI) with SVGD. We present a complete picture by considering both the mean-field PDE and discrete particle systems. When the target is strongly log-concave, the mean-field Gaussian-SVGD dynamics is proven to converge linearly to the Gaussian distribution closest to the target in KL divergence. In the finite-particle setting, there is both uniform in time convergence to the mean-field limit and linear convergence in time to the equilibrium if the target is Gaussian. In the general case, we propose a density-based and a particle-based implementation of the Gaussian-SVGD, and show that several recent algorithms for GVI, proposed from different perspectives, emerge as special cases of our unified framework. Interestingly, one of the new particle-based instance from this framework empirically outperforms existing approaches. Our results make concrete contributions towards obtaining a deeper understanding of both SVGD and GVI.
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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.
Covariate shift may impact the operational safety performance of neural networks. A re-evaluation of the safety performance, however, requires collecting new operational data and creating corresponding ground truth labels, which often is not possible during operation. We are therefore proposing to reshape the initial test set, as used for the safety performance evaluation prior to deployment, based on an approximation of the operational data. This approximation is obtained by observing and learning the distribution of activation patterns of neurons in the network during operation. The reshaped test set reflects the distribution of neuron activation values as observed during operation, and may therefore be used for re-evaluating safety performance in the presence of covariate shift. First, we derive conservative bounds on the values of neurons by applying finite binning and static dataflow analysis. Second, we formulate a mixed integer linear programming (MILP) constraint for constructing the minimum set of data points to be removed in the test set, such that the difference between the discretized test and operational distributions is bounded. We discuss potential benefits and limitations of this constraint-based approach based on our initial experience with an implemented research prototype.
Gradient-based methods for value estimation in reinforcement learning have favorable stability properties, but they are typically much slower than Temporal Difference (TD) learning methods. We study the root causes of this slowness and show that Mean Square Bellman Error (MSBE) is an ill-conditioned loss function in the sense that its Hessian has large condition-number. To resolve the adverse effect of poor conditioning of MSBE on gradient based methods, we propose a low complexity batch-free proximal method that approximately follows the Gauss-Newton direction and is asymptotically robust to parameterization. Our main algorithm, called RANS, is efficient in the sense that it is significantly faster than the residual gradient methods while having almost the same computational complexity, and is competitive with TD on the classic problems that we tested.
Knitting interloops one-dimensional yarns into three-dimensional fabrics that exhibit behaviours beyond their constitutive materials. How extensibility and anisotropy emerge from the hierarchical organization of yarns into knitted fabrics has long been unresolved. We sought to unravel the mechanical roles of tensile mechanics, assembly and dynamics arising from the yarn level on fabric nonlinearity by developing a yarn-based dynamical model. This physically validated model captures the fundamental mechanical response of knitted fabrics, analogous to flexible metamaterials and biological fiber networks due to geometric nonlinearity within such hierarchical systems. We identify the dictating factors of the mechanics of knitted fabrics, highlighting the previously overlooked but critical effect of pre-tension. Fabric anisotropy originates from observed yarn--yarn rearrangements during alignment dynamics and is topology-dependent. This yarn-based model also provides design flexibility of knitted fabrics to embed functionalities by allowing variation in both geometric configuration and material property. Our hierarchical approach to build up a knitted fabrics computationally modernizes an ancient craft and represents a first step towards mechanical programmability of knitted fabrics in wide engineering applications.
In this paper, we simultaneously tackle the problem of energy optimal and safe navigation of electric vehicles in a data-driven robust optimization framework. We consider a dynamic model of the electric vehicle which includes kinematic variables in both inertial and body coordinate systems in order to capture both longitudinal and lateral motion as well as state-of-energy of the battery. We leverage past data of obstacle motion to construct a future occupancy set with probabilistic guarantees, and formulate robust collision avoidance constraints with respect to such an occupancy set using convex programming duality. Consequently, we present the finite horizon optimal control problem subject to robust collision avoidance constraints while penalizing resulting energy consumption. Finally, we show the effectiveness of the proposed approach in reducing energy consumption and ensuring safe navigation via extensive simulations involving curved roads and multiple obstacles.
In this paper, we present a model describing the collective motion of birds. We explore the dynamic relationship between followers and leaders, wherein a select few agents, known as leaders, can initiate spontaneous changes in direction without being influenced by external factors like predators. Starting at the microscopic level, we develop a kinetic model that characterizes the behaviour of large crowds with transient leadership. One significant challenge lies in managing topological interactions, as identifying nearest neighbors in extensive systems can be computationally expensive. To address this, we propose a novel stochastic particle method to simulate the mesoscopic dynamics and reduce the computational cost of identifying closer agents from quadratic to logarithmic complexity using a $k$-nearest neighbours search algorithm with a binary tree. Lastly, we conduct various numerical experiments for different scenarios to validate the algorithm's effectiveness and investigate collective dynamics in both two and three dimensions.
Uncertainty in timing information pertaining to the start time of microphone recordings and sources' emission time pose significant challenges in various applications, such as joint microphones and sources localization. Traditional optimization methods, which directly estimate this unknown timing information (UTIm), often fall short compared to approaches exploiting the low-rank property (LRP). LRP encompasses an additional low-rank structure, facilitating a linear constraint on UTIm to help formulate related low-rank structure information. This method allows us to attain globally optimal solutions for UTIm, given proper initialization. However, the initialization process often involves randomness, leading to suboptimal, local minimum values. This paper presents a novel, combined low-rank approximation (CLRA) method designed to mitigate the effects of this random initialization. We introduce three new LRP variants, underpinned by mathematical proof, which allow the UTIm to draw on a richer pool of low-rank structural information. Utilizing this augmented low-rank structural information from both LRP and the proposed variants, we formulate four linear constraints on the UTIm. Employing the proposed CLRA algorithm, we derive global optimal solutions for the UTIm via these four linear constraints.Experimental results highlight the superior performance of our method over existing state-of-the-art approaches, measured in terms of both the recovery number and reduced estimation errors of UTIm.
Distributional assumptions have been shown to be necessary for the robust learnability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019). In this paper, we study learning models where the learner is given more power through the use of local queries, and give the first distribution-free algorithms that perform robust empirical risk minimization (ERM) for this notion of robustness. The first learning model we consider uses local membership queries (LMQ), where the learner can query the label of points near the training sample. We show that, under the uniform distribution, LMQs do not increase the robustness threshold of conjunctions and any superclass, e.g., decision lists and halfspaces. Faced with this negative result, we introduce the local equivalence query ($\mathsf{LEQ}$) oracle, which returns whether the hypothesis and target concept agree in the perturbation region around a point in the training sample, as well as a counterexample if it exists. We show a separation result: on the one hand, if the query radius $\lambda$ is strictly smaller than the adversary's perturbation budget $\rho$, then distribution-free robust learning is impossible for a wide variety of concept classes; on the other hand, the setting $\lambda=\rho$ allows us to develop robust ERM algorithms. We then bound the query complexity of these algorithms based on online learning guarantees and further improve these bounds for the special case of conjunctions. We finish by giving robust learning algorithms for halfspaces on $\{0,1\}^n$ and then obtaining robustness guarantees for halfspaces in $\mathbb{R}^n$ against precision-bounded adversaries.
Digital democracy and new forms for direct digital participation in policy making gain unprecedented momentum. This is particularly the case for preferential voting methods and decision-support systems designed to promote fairer, more inclusive and legitimate collective decision-making processes in citizens assemblies, participatory budgeting and elections. However, a systematic human experimentation with different voting methods is cumbersome and costly. This paper introduces VoteLab, an open-source and thoroughly-documented platform for modular and adaptive design of voting experiments. It supports to visually and interactively build reusable campaigns with a choice of different voting methods, while voters can easily respond to subscribed voting questions on a smartphone. A proof-of-concept with four voting methods and questions on COVID-19 in an online lab experiment have been used to study the consistency of voting outcomes. It demonstrates the capability of VoteLab to support rigorous experimentation of complex voting scenarios.
Miniature robots provide unprecedented access to confined environments and show promising potential for novel applications such as search-and-rescue and high-value asset inspection. The capability of body deformation further enhances the reachability of these small robots in complex cluttered terrains similar to those of insects and soft arthropods. Motivated by this concept, we present CLARI, an insect-scale 2.59g quadrupedal robot capable of body deformation with tethered electrical connections for power and control and manufactured using laminate fabrication and assembled using origami pop-up techniques. In order to enable locomotion in multiple shape configurations, we designed a novel body architecture comprising of modular, actuated leg mechanisms. Overall, CLARI has eight independently actuated degrees of freedom (two per modular leg unit) driven by custom piezoelectric actuators, making it mechanically dextrous. We characterize open-loop robot locomotion at multiple stride frequencies (1-10Hz) using multiple gaits (trot, walk, etc.) in three different fixed body shapes (long, symmetric, wide) and illustrate the robot's capabilities. Finally, we demonstrate preliminary results of CLARI locomoting with a compliant body in open terrain and through a laterally constrained gap, a novel capability for legged robots. Our results represent the first step towards achieving effective cluttered terrain navigation with adaptable compliant robots in real-world environments.
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