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Optimizing static risk-averse objectives in Markov decision processes is difficult because they do not admit standard dynamic programming equations common in Reinforcement Learning (RL) algorithms. Dynamic programming decompositions that augment the state space with discrete risk levels have recently gained popularity in the RL community. Prior work has shown that these decompositions are optimal when the risk level is discretized sufficiently. However, we show that these popular decompositions for Conditional-Value-at-Risk (CVaR) and Entropic-Value-at-Risk (EVaR) are inherently suboptimal regardless of the discretization level. In particular, we show that a saddle point property assumed to hold in prior literature may be violated. However, a decomposition does hold for Value-at-Risk and our proof demonstrates how this risk measure differs from CVaR and EVaR. Our findings are significant because risk-averse algorithms are used in high-stake environments, making their correctness much more critical.

Light Detection and Ranging (LiDAR) technology has proven to be an important part of many robotics systems. Surface normals estimated from LiDAR data are commonly used for a variety of tasks in such systems. As most of the today's mechanical LiDAR sensors produce sparse data, estimating normals from a single scan in a robust manner poses difficulties. In this paper, we address the problem of estimating normals for sparse LiDAR data avoiding the typical issues of smoothing out the normals in high curvature areas. Mechanical LiDARs rotate a set of rigidly mounted lasers. One firing of such a set of lasers produces an array of points where each point's neighbor is known due to the known firing pattern of the scanner. We use this knowledge to connect these points to their neighbors and label them using the angles of the lines connecting them. When estimating normals at these points, we only consider points with the same label as neighbors. This allows us to avoid estimating normals in high curvature areas. We evaluate our approach on various data, both self-recorded and publicly available, acquired using various sparse LiDAR sensors. We show that using our method for normal estimation leads to normals that are more robust in areas with high curvature which leads to maps of higher quality. We also show that our method only incurs a constant factor runtime overhead with respect to a lightweight baseline normal estimation procedure and is therefore suited for operation in computationally demanding environments.

Crowd localization targets on predicting each instance precise location within an image. Current advanced methods propose the pixel-wise binary classification to tackle the congested prediction, in which the pixel-level thresholds binarize the prediction confidence of being the pedestrian head. Since the crowd scenes suffer from extremely varying contents, counts and scales, the confidence-threshold learner is fragile and under-generalized encountering domain knowledge shift. Moreover, at the most time, the target domain is agnostic in training. Hence, it is imperative to exploit how to enhance the generalization of confidence-threshold locator to the latent target domain. In this paper, we propose a Dynamic Proxy Domain (DPD) method to generalize the learner under domain shift. Concretely, based on the theoretical analysis to the generalization error risk upper bound on the latent target domain to a binary classifier, we propose to introduce a generated proxy domain to facilitate generalization. Then, based on the theory, we design a DPD algorithm which is composed by a training paradigm and proxy domain generator to enhance the domain generalization of the confidence-threshold learner. Besides, we conduct our method on five kinds of domain shift scenarios, demonstrating the effectiveness on generalizing the crowd localization. Our code will be available at //github.com/zhangda1018/DPD.

Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the diffusion term is configuration-dependent. One remedy is to construct a transform to a constant-diffusion process and sample the transformed process instead. In this work, we explain how coordinate-based and time-rescaling-based transforms can be used either individually or in combination to map a general class of variable-diffusion Brownian motion processes into constant-diffusion ones. The transforms are invertible, thus allowing recovery of the original dynamics. We motivate our methodology using examples in one dimension before then considering multivariate diffusion processes. We illustrate the benefits of the transforms through numerical simulations, demonstrating how the right combination of integrator and transform can improve computational efficiency and the order of convergence to the invariant distribution. Notably, the transforms that we derive are applicable to a class of multibody, anisotropic Stokes-Einstein diffusion that has applications in biophysical modelling.

Large language models (LLMs) have shown complementary strengths in various tasks and instances, motivating the research of ensembling LLMs to push the frontier leveraging the wisdom of the crowd. Existing work achieves this objective via training the extra reward model or fusion model to select or fuse all candidate answers. However, these methods pose a great challenge to the generalizability of the trained models. Besides, existing methods use the textual responses as communication media, ignoring the rich information in the inner representations of neural networks. Therefore, we propose a training-free ensemble framework DEEPEN, averaging the probability distributions outputted by different LLMs. A key challenge in this paradigm is the vocabulary discrepancy between heterogeneous LLMs, which hinders the operation of probability distribution averaging. To address this challenge, DEEPEN maps the probability distribution of each model from the probability space to a universe relative space based on the relative representation theory, and performs aggregation. Then, the result of aggregation is mapped back to the probability space of one LLM via a search-based inverse transformation to determine the generated token. We conduct experiments on the ensemble of various LLMs of 6B to 70B. Experimental results show that DEEPEN achieves consistent improvements across six popular benchmarks involving subject examination, reasoning and knowledge-QA, proving the effectiveness of our approach.

This paper presents a distributed model predictive control (DMPC) algorithm for a heterogeneous platoon using arbitrary communication topologies, as long as each vehicle is able to communicate with a preceding vehicle in the platoon. The proposed DMPC algorithm is able to accommodate any spacing policy that is affine in a vehicle's velocity, which includes constant distance or constant time headway spacing policies. By analyzing the total cost for the entire platoon, a sufficient condition is derived to guarantee platoon asymptotic stability. Simulation experiments with a platoon of 50 vehicles and hardware experiments with a platoon of four 1/10th scale vehicles validate the algorithm and compare performance under different spacing policies and communication topologies.

Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.

Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.

Recommender System (RS) is a hot area where artificial intelligence (AI) techniques can be effectively applied to improve performance. Since the well-known Netflix Challenge, collaborative filtering (CF) has become the most popular and effective recommendation method. Despite their success in CF, various AI techniques still have to face the data sparsity and cold start problems. Previous works tried to solve these two problems by utilizing auxiliary information, such as social connections among users and meta-data of items. However, they process different types of information separately, leading to information loss. In this work, we propose to utilize Heterogeneous Information Network (HIN), which is a natural and general representation of different types of data, to enhance CF-based recommending methods. HIN-based recommender systems face two problems: how to represent high-level semantics for recommendation and how to fuse the heterogeneous information to recommend. To address these problems, we propose to applying meta-graph to HIN-based RS and solve the information fusion problem with a "matrix factorization (MF) + factorization machine (FM)" framework. For the "MF" part, we obtain user-item similarity matrices from each meta-graph and adopt low-rank matrix approximation to get latent features for both users and items. For the "FM" part, we propose to apply FM with Group lasso (FMG) on the obtained features to simultaneously predict missing ratings and select useful meta-graphs. Experimental results on two large real-world datasets, i.e., Amazon and Yelp, show that our proposed approach is better than that of the state-of-the-art FM and other HIN-based recommending methods.

Recently, deep learning has achieved very promising results in visual object tracking. Deep neural networks in existing tracking methods require a lot of training data to learn a large number of parameters. However, training data is not sufficient for visual object tracking as annotations of a target object are only available in the first frame of a test sequence. In this paper, we propose to learn hierarchical features for visual object tracking by using tree structure based Recursive Neural Networks (RNN), which have fewer parameters than other deep neural networks, e.g. Convolutional Neural Networks (CNN). First, we learn RNN parameters to discriminate between the target object and background in the first frame of a test sequence. Tree structure over local patches of an exemplar region is randomly generated by using a bottom-up greedy search strategy. Given the learned RNN parameters, we create two dictionaries regarding target regions and corresponding local patches based on the learned hierarchical features from both top and leaf nodes of multiple random trees. In each of the subsequent frames, we conduct sparse dictionary coding on all candidates to select the best candidate as the new target location. In addition, we online update two dictionaries to handle appearance changes of target objects. Experimental results demonstrate that our feature learning algorithm can significantly improve tracking performance on benchmark datasets.