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We study a scenario where an aircraft has multiple heterogeneous sensors collecting measurements to track a target vehicle of unknown location. The measurements are sampled along the flight path and our goals to optimize sensor placement to minimize estimation error. We select as a metric the Fisher Information Matrix (FIM), as "minimizing" the inverse of the FIM is required to achieve small estimation error. We propose to generate the optimal path from the Hamilton-Jacobi (HJ) partial differential equation (PDE) as it is the necessary and sufficient condition for optimality. A traditional method of lines (MOL) approach, based on a spatial grid, lends itself well to the highly non-linear and non-convex structure of the problem induced by the FIM matrix. However, the sensor placement problem results in a state space dimension that renders a naive MOL approach intractable. We present a new hybrid approach, whereby we decompose the state space into two parts: a smaller subspace that still uses a grid and takes advantage of the robustness to non-linearities and non-convexities, and the remaining state space that can by found efficiently from a system of ODEs, avoiding formation of a spatial grid.

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《計算機信息》雜志發表高質量的論文,擴大了運籌學和計算的范圍,尋求有關理論、方法、實驗、系統和應用方面的原創研究論文、新穎的調查和教程論文,以及描述新的和有用的軟件工具的論文。官網鏈接: · 優化器 · motivation · state-of-the-art · 曲率 ·
2023 年 3 月 8 日

Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of self-concordance to Riemannian manifolds and show that it gives the same structural results and guarantees as in the Euclidean setting, in particular local quadratic convergence of Newton's method. We then analyze a short-step path-following method for optimizing compatible objectives over a convex domain for which one has a self-concordant barrier, and obtain the standard complexity guarantees as in the Euclidean setting. We show that on the positive-definite matrices and other symmetric spaces, the squared distance to a point is a self-concordant function. Our work is motivated by recent progress on scaling problems and non-commutative optimization, and we show that these fit into our framework, yielding algorithms with state-of-the-art complexity guarantees. Furthermore, we show how to apply our methods to computing geometric medians on spaces with constant negative curvature.

Beyond providing accurate movements, achieving smooth motion trajectories is a long-standing goal of robotics control theory for arms aiming to replicate natural human movements. Drawing inspiration from biological agents, whose reaching control networks effortlessly give rise to smooth and precise movements, can simplify these control objectives for robot arms. Neuromorphic processors, which mimic the brain's computational principles, are an ideal platform to approximate the accuracy and smoothness of biological controllers while maximizing their energy efficiency and robustness. However, the incompatibility of conventional control methods with neuromorphic hardware limits the computational efficiency and explainability of their existing adaptations. In contrast, the neuronal subnetworks underlying smooth and accurate reaching movements are effective, minimal, and inherently compatible with neuromorphic hardware. In this work, we emulate these networks with a biologically realistic spiking neural network for motor control on neuromorphic hardware. The proposed controller incorporates experimentally-identified short-term synaptic plasticity and specialized neurons that regulate sensory feedback gain to provide smooth and accurate joint control across a wide motion range. Concurrently, it preserves the minimal complexity of its biological counterpart and is directly deployable on Intel's neuromorphic processor. Using the joint controller as a building block and inspired by joint coordination in human arms, we scaled up this approach to control real-world robot arms. The trajectories and smooth, bell-shaped velocity profiles of the resulting motions resembled those of humans, verifying the biological relevance of the controller. Notably, the method achieved state-of-the-art control performance while decreasing the motion jerk by 19% to improve motion smoothness.

Markerless pose estimation allows reconstructing human movement from multiple synchronized and calibrated views, and has the potential to make movement analysis easy and quick, including gait analysis. This could enable much more frequent and quantitative characterization of gait impairments, allowing better monitoring of outcomes and responses to interventions. However, the impact of different keypoint detectors and reconstruction algorithms on markerless pose estimation accuracy has not been thoroughly evaluated. We tested these algorithmic choices on data acquired from a multicamera system from a heterogeneous sample of 25 individuals seen in a rehabilitation hospital. We found that using a top-down keypoint detector and reconstructing trajectories with an implicit function enabled accurate, smooth and anatomically plausible trajectories, with a noise in the step width estimates compared to a GaitRite walkway of only 8mm.

Soft robots are becoming extremely popular thanks to their intrinsic safety to contacts and adaptability. However, the potentially infinite number of Degrees of Freedom makes their modeling a daunting task, and in many cases only an approximated description is available. This challenge makes reinforcement learning (RL) based approaches inefficient when deployed on a realistic scenario, due to the large domain gap between models and the real platform. In this work, we demonstrate, for the first time, how Domain Randomization (DR) can solve this problem by enhancing RL policies with: i) a higher robustness w.r.t. environmental changes; ii) a higher affordability of learned policies when the target model differs significantly from the training model; iii) a higher effectiveness of the policy, which can even autonomously learn to exploit the environment to increase the robot capabilities (environmental constraints exploitation). Moreover, we introduce a novel algorithmic extension of previous adaptive domain randomization methods for the automatic inference of dynamics parameters for deformable objects. We provide results on four different tasks and two soft robot designs, opening interesting perspectives for future research on Reinforcement Learning for closed-loop soft robot control.

Multirotor teams are useful for inspection, delivery, and construction tasks, in which they might be required to fly very close to each other. In such close-proximity cases, nonlinear aerodynamic effects can cause catastrophic crashes, necessitating each robots' awareness of the surroundings. Existing approaches rely on expensive or heavy perception sensors. Instead, we propose to use the often ignored yaw degree-of-freedom of multirotors to spin a single, cheap and lightweight monocular camera at a high angular rate for omnidirectional awareness. We provide a dataset collected with real-world physical flights as well as with 3D rendered scenes and compare two existing learning-based methods in different settings with respect to success rate, relative position estimation, and downwash prediction accuracy. As application we demonstrate that our proposed spinning camera is capable of predicting the presence of aerodynamic downwash in a challenging swapping task.

We study the supervised learning paradigm called Learning Using Privileged Information, first suggested by Vapnik and Vashist (2009). In this paradigm, in addition to the examples and labels, additional (privileged) information is provided only for training examples. The goal is to use this information to improve the classification accuracy of the resulting classifier, where this classifier can only use the non-privileged information of new example instances to predict their label. We study the theory of privileged learning with the zero-one loss under the natural Privileged ERM algorithm proposed in Pechyony and Vapnik (2010a). We provide a counter example to a claim made in that work regarding the VC dimension of the loss class induced by this problem; We conclude that the claim is incorrect. We then provide a correct VC dimension analysis which gives both lower and upper bounds on the capacity of the Privileged ERM loss class. We further show, via a generalization analysis, that worst-case guarantees for Privileged ERM cannot improve over standard non-privileged ERM, unless the capacity of the privileged information is similar or smaller to that of the non-privileged information. This result points to an important limitation of the Privileged ERM approach. In our closing discussion, we suggest another way in which Privileged ERM might still be helpful, even when the capacity of the privileged information is large.

We consider box-constrained integer programs with objective $g(Wx) + c^T x$, where $g$ is a "complicated" function with an $m$ dimensional domain. Here we assume we have $n \gg m$ variables and that $W \in \mathbb Z^{m \times n}$ is an integer matrix with coefficients of absolute value at most $\Delta$. We design an algorithm for this problem using only the mild assumption that the objective can be optimized efficiently when all but $m$ variables are fixed, yielding a running time of $n^m(m \Delta)^{O(m^2)}$. Moreover, we can avoid the term $n^m$ in several special cases, in particular when $c = 0$. Our approach can be applied in a variety of settings, generalizing several recent results. An important application are convex objectives of low domain dimension, where we imply a recent result by Hunkenschr\"oder et al. [SIOPT'22] for the 0-1-hypercube and sharp or separable convex $g$, assuming $W$ is given explicitly. By avoiding the direct use of proximity results, which only holds when $g$ is separable or sharp, we match their running time and generalize it for arbitrary convex functions. In the case where the objective is only accessible by an oracle and $W$ is unknown, we further show that their proximity framework can be implemented in $n (m \Delta)^{O(m^2)}$-time instead of $n (m \Delta)^{O(m^3)}$. Lastly, we extend the result by Eisenbrand and Weismantel [SODA'17, TALG'20] for integer programs with few constraints to a mixed-integer linear program setting where integer variables appear in only a small number of different constraints.

Accurately monitoring road traffic state and speed is crucial for various applications, including travel time prediction, traffic control, and traffic safety. However, the lack of sensors often results in incomplete traffic state data, making it challenging to obtain reliable information for decision-making. This paper proposes a novel method for imputing traffic state data using Gaussian processes (GP) to address this issue. We propose a kernel rotation re-parametrization scheme that transforms a standard isotropic GP kernel into an anisotropic kernel, which can better model the propagation of traffic waves in traffic flow data. This method can be applied to impute traffic state data from fixed sensors or probe vehicles. Moreover, the rotated GP method provides statistical uncertainty quantification for the imputed traffic state, making it more reliable. We also extend our approach to a multi-output GP, which allows for simultaneously estimating the traffic state for multiple lanes. We evaluate our method using real-world traffic data from the Next Generation simulation (NGSIM) and HighD programs. Considering current and future mixed traffic of connected vehicles (CVs) and human-driven vehicles (HVs), we experiment with the traffic state estimation scheme from 5% to 50% available trajectories, mimicking different CV penetration rates in a mixed traffic environment. Results show that our method outperforms state-of-the-art methods in terms of estimation accuracy, efficiency, and robustness.

Hyper-parameter optimization is one of the most tedious yet crucial steps in training machine learning models. There are numerous methods for this vital model-building stage, ranging from domain-specific manual tuning guidelines suggested by the oracles to the utilization of general-purpose black-box optimization techniques. This paper proposes an agent-based collaborative technique for finding near-optimal values for any arbitrary set of hyper-parameters (or decision variables) in a machine learning model (or general function optimization problem). The developed method forms a hierarchical agent-based architecture for the distribution of the searching operations at different dimensions and employs a cooperative searching procedure based on an adaptive width-based random sampling technique to locate the optima. The behavior of the presented model, specifically against the changes in its design parameters, is investigated in both machine learning and global function optimization applications, and its performance is compared with that of two randomized tuning strategies that are commonly used in practice. According to the empirical results, the proposed model outperformed the compared methods in the experimented classification, regression, and multi-dimensional function optimization tasks, notably in a higher number of dimensions and in the presence of limited on-device computational resources.

Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.

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