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The distributed flocking control of collective aerial vehicles has extraordinary advantages in scalability and reliability, \emph{etc.} However, it is still challenging to design a reliable, efficient, and responsive flocking algorithm. In this paper, a distributed predictive flocking framework is presented based on a Markov random field (MRF). The MRF is used to characterize the optimization problem that is eventually resolved by discretizing the input space. Potential functions are employed to describe the interactions between aerial vehicles and as indicators of flight performance. The dynamic constraints are taken into account in the candidate feasible trajectories which correspond to random variables. Numerical simulation shows that compared with some existing latest methods, the proposed algorithm has better-flocking cohesion and control efficiency performances. Experiments are also conducted to demonstrate the feasibility of the proposed algorithm.

Matrix factor model is drawing growing attention for simultaneous two-way dimension reduction of well-structured matrix-valued observations. This paper focuses on robust statistical inference for matrix factor model in the ``diverging dimension" regime. We derive the convergence rates of the robust estimators for loadings, factors and common components under finite second moment assumption of the idiosyncratic errors. In addition, the asymptotic distributions of the estimators are also derived under mild conditions. We propose a rank minimization and an eigenvalue-ratio method to estimate the pair of factor numbers consistently. Numerical studies confirm the iterative Huber regression algorithm is a practical and reliable approach for the estimation of matrix factor model, especially under the cases with heavy-tailed idiosyncratic errors . We illustrate the practical usefulness of the proposed methods by two real datasets, one on financial portfolios and one on the macroeconomic indices of China.

The evolving data framework was first proposed by Anagnostopoulos et al., where an evolver makes small changes to a structure behind the scenes. Instead of taking a single input and producing a single output, an algorithm judiciously probes the current state of the structure and attempts to continuously maintain a sketch of the structure that is as close as possible to its actual state. There have been a number of problems that have been studied in the evolving framework including our own work on labeled trees. We were motivated by the problem of maintaining a labeling in the plane, where updating the labels require physically moving them. Applications involve tracking evolving disease hot-spots via mobile testing units , and tracking unmanned aerial vehicles. To be specific, we consider the problem of tracking labeled nodes in the plane, where an evolver continuously swaps labels of any two nearby nodes in the background unknown to us. We are tasked with maintaining a hypothesis, an approximate sketch of the locations of these labels, which we can only update by physically moving them over a sparse graph. We assume the existence of an Oracle, which when suitably probed, guides us in fixing our hypothesis.

Learning high-quality Q-value functions plays a key role in the success of many modern off-policy deep reinforcement learning (RL) algorithms. Previous works focus on addressing the value overestimation issue, an outcome of adopting function approximators and off-policy learning. Deviating from the common viewpoint, we observe that Q-values are indeed underestimated in the latter stage of the RL training process, primarily related to the use of inferior actions from the current policy in Bellman updates as compared to the more optimal action samples in the replay buffer. We hypothesize that this long-neglected phenomenon potentially hinders policy learning and reduces sample efficiency. Our insight to address this issue is to incorporate sufficient exploitation of past successes while maintaining exploration optimism. We propose the Blended Exploitation and Exploration (BEE) operator, a simple yet effective approach that updates Q-value using both historical best-performing actions and the current policy. The instantiations of our method in both model-free and model-based settings outperform state-of-the-art methods in various continuous control tasks and achieve strong performance in failure-prone scenarios and real-world robot tasks.

Autonomous terrain traversal of articulated tracked robots can reduce operator cognitive load to enhance task efficiency and facilitate extensive deployment. We present a novel hybrid trajectory optimization method aimed at generating smooth, stable, and efficient traversal motions. To achieve this, we develop a planar robot-terrain interaction model and partition the robot's motion into hybrid modes of driving and traversing. By using a generalized coordinate description, the configuration space dimension is reduced, which provides real-time planning capability. The hybrid trajectory optimization is transcribed into a nonlinear programming problem and solved in a receding-horizon planning fashion. Mode switching is facilitated by associating optimized motion durations with a predefined traversal sequence. A multi-objective cost function is formulated to further improve the traversal performance. Additionally, map sampling, terrain simplification, and tracking controller modules are integrated into the autonomous terrain traversal system. Our approach is validated in simulation and real-world experiments with the Searcher robotic platform, effectively achieving smooth and stable motion with high time and energy efficiency compared to expert operator control.

In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded trajectory planning method that looks for continuous-time trajectories with guaranteed bounded risk over the planning time horizon. Risk is defined as the probability of collision with uncertain obstacles. Existing approaches to address risk bounded trajectory planning problems either are limited to Gaussian uncertainties and convex obstacles or rely on sampling-based methods that need uncertainty samples and time discretization. To address the risk bounded trajectory planning problem, we leverage the notion of risk contours to transform the risk bounded planning problem into a deterministic optimization problem. Risk contours are the set of all points in the uncertain environment with guaranteed bounded risk. The obtained deterministic optimization is, in general, nonlinear and nonconvex time-varying optimization. We provide convex methods based on sum-of-squares optimization to efficiently solve the obtained nonconvex time-varying optimization problem and obtain the continuous-time risk bounded trajectories without time discretization. The provided approach deals with arbitrary (and known) probabilistic uncertainties, nonconvex and nonlinear, static and dynamic obstacles, and is suitable for online trajectory planning problems. In addition, we provide convex methods based on sum-of-squares optimization to build the max-sized tube with respect to its parameterization along the trajectory so that any state inside the tube is guaranteed to have bounded risk.

Large Language Models (LLMs) and other large foundation models have achieved noteworthy success, but their size exacerbates existing resource consumption and latency challenges. In particular, the large-scale deployment of these models is hindered by the significant resource requirements during inference. In this paper, we study two approaches for mitigating these challenges: employing a cache to store previous queries and learning a model multiplexer to choose from an ensemble of models for query processing. Theoretically, we provide an optimal algorithm for jointly optimizing both approaches to reduce the inference cost in both offline and online tabular settings. By combining a caching algorithm, namely Greedy Dual Size with Frequency (GDSF) or Least Expected Cost (LEC), with a model multiplexer, we achieve optimal rates in both offline and online settings. Empirically, simulations show that the combination of our caching and model multiplexing algorithms greatly improves over the baselines, with up to $50\times$ improvement over the baseline when the ratio between the maximum cost and minimum cost is $100$. Experiments on real datasets show a $4.3\times$ improvement in FLOPs over the baseline when the ratio for FLOPs is $10$, and a $1.8\times$ improvement in latency when the ratio for average latency is $1.85$.

Extracting information from geographic images and text is crucial for autonomous vehicles to determine in advance the best cell stations to connect to along their future path. Multiple artificial neural network models can address this challenge; however, there is no definitive guidance on the selection of an appropriate model for such use cases. Therefore, we experimented two architectures to solve such a task: a first architecture with chained models where each model in the chain addresses a sub-task of the task; and a second architecture with a single model that addresses the whole task. Our results showed that these two architectures achieved the same level performance with a root mean square error (RMSE) of 0.055 and 0.056; The findings further revealed that when the task can be decomposed into sub-tasks, the chain architecture exhibits a twelve-fold increase in training speed compared to the composite model. Nevertheless, the composite model significantly alleviates the burden of data labeling.

The inference of a large symmetric signal-matrix $\mathbf{S} \in \mathbb{R}^{N\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks $M=\Theta(N^\alpha)$ with $\alpha\in(0,1)$ the mutual information and minimum mean-square error (MMSE) are derived for two classes of signal-matrices: (a) $\mathbf{S}=\mathbf{X}\mathbf{X}^\intercal$ with entries of $\mathbf{X}\in\mathbb{R}^{N\times M}$ independent identically distributed; (b) $\mathbf{S}$ sampled from a rotationally invariant distribution. Surprisingly, the formulas match the rank-one case. Two efficient algorithms are explored and conjectured to saturate the MMSE when no statistical-to-computational gap is present: (1) Decimation Approximate Message Passing; (2) a spectral algorithm based on a Rotation Invariant Estimator. For linear ranks $M=\Theta(N)$ the mutual information is rigorously derived for signal-matrices from a rotationally invariant distribution. Close connections with scalar inference in free probability are uncovered, which allow to deduce a simple formula for the MMSE as an integral involving the limiting spectral measure of the data matrix only. An interesting issue is whether the known information theoretic phase transitions for rank-one, and hence also sub-linear-rank, still persist in linear-rank. Our analysis suggests that only a smoothed-out trace of the transitions persists. Furthermore, the change of behavior between low and truly high-rank regimes only happens at the linear scale $\alpha=1$.

Accurate understanding and prediction of human behaviors are critical prerequisites for autonomous vehicles, especially in highly dynamic and interactive scenarios such as intersections in dense urban areas. In this work, we aim at identifying crossing pedestrians and predicting their future trajectories. To achieve these goals, we not only need the context information of road geometry and other traffic participants but also need fine-grained information of the human pose, motion and activity, which can be inferred from human keypoints. In this paper, we propose a novel multi-task learning framework for pedestrian crossing action recognition and trajectory prediction, which utilizes 3D human keypoints extracted from raw sensor data to capture rich information on human pose and activity. Moreover, we propose to apply two auxiliary tasks and contrastive learning to enable auxiliary supervisions to improve the learned keypoints representation, which further enhances the performance of major tasks. We validate our approach on a large-scale in-house dataset, as well as a public benchmark dataset, and show that our approach achieves state-of-the-art performance on a wide range of evaluation metrics. The effectiveness of each model component is validated in a detailed ablation study.