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Primal-dual methods have a natural application in Safe Reinforcement Learning (SRL), posed as a constrained policy optimization problem. In practice however, applying primal-dual methods to SRL is challenging, due to the inter-dependency of the learning rate (LR) and Lagrangian multipliers (dual variables) each time an embedded unconstrained RL problem is solved. In this paper, we propose, analyze and evaluate adaptive primal-dual (APD) methods for SRL, where two adaptive LRs are adjusted to the Lagrangian multipliers so as to optimize the policy in each iteration. We theoretically establish the convergence, optimality and feasibility of the APD algorithm. Finally, we conduct numerical evaluation of the practical APD algorithm with four well-known environments in Bullet-Safey-Gym employing two state-of-the-art SRL algorithms: PPO-Lagrangian and DDPG-Lagrangian. All experiments show that the practical APD algorithm outperforms (or achieves comparable performance) and attains more stable training than the constant LR cases. Additionally, we substantiate the robustness of selecting the two adaptive LRs by empirical evidence.

Object detection and multiple object tracking (MOT) are essential components of self-driving systems. Accurate detection and uncertainty quantification are both critical for onboard modules, such as perception, prediction, and planning, to improve the safety and robustness of autonomous vehicles. Collaborative object detection (COD) has been proposed to improve detection accuracy and reduce uncertainty by leveraging the viewpoints of multiple agents. However, little attention has been paid to how to leverage the uncertainty quantification from COD to enhance MOT performance. In this paper, as the first attempt to address this challenge, we design an uncertainty propagation framework called MOT-CUP. Our framework first quantifies the uncertainty of COD through direct modeling and conformal prediction, and propagates this uncertainty information into the motion prediction and association steps. MOT-CUP is designed to work with different collaborative object detectors and baseline MOT algorithms. We evaluate MOT-CUP on V2X-Sim, a comprehensive collaborative perception dataset, and demonstrate a 2% improvement in accuracy and a 2.67X reduction in uncertainty compared to the baselines, e.g. SORT and ByteTrack. In scenarios characterized by high occlusion levels, our MOT-CUP demonstrates a noteworthy $4.01\%$ improvement in accuracy. MOT-CUP demonstrates the importance of uncertainty quantification in both COD and MOT, and provides the first attempt to improve the accuracy and reduce the uncertainty in MOT based on COD through uncertainty propagation. Our code is public on //coperception.github.io/MOT-CUP/.

Although reinforcement learning (RL) can solve many challenging sequential decision making problems, achieving zero-shot transfer across related tasks remains a challenge. The difficulty lies in finding a good representation for the current task so that the agent understands how it relates to previously seen tasks. To achieve zero-shot transfer, we introduce the function encoder, a representation learning algorithm which represents a function as a weighted combination of learned, non-linear basis functions. By using a function encoder to represent the reward function or the transition function, the agent has information on how the current task relates to previously seen tasks via a coherent vector representation. Thus, the agent is able to achieve transfer between related tasks at run time with no additional training. We demonstrate state-of-the-art data efficiency, asymptotic performance, and training stability in three RL fields by augmenting basic RL algorithms with a function encoder task representation.

3D neural implicit representations play a significant component in many robotic applications. However, reconstructing neural radiance fields (NeRF) from realistic event data remains a challenge due to the sparsities and the lack of information when only event streams are available. In this paper, we utilize motion, geometry, and density priors behind event data to impose strong physical constraints to augment NeRF training. The proposed novel pipeline can directly benefit from those priors to reconstruct 3D scenes without additional inputs. Moreover, we present a novel density-guided patch-based sampling strategy for robust and efficient learning, which not only accelerates training procedures but also conduces to expressions of local geometries. More importantly, we establish the first large dataset for event-based 3D reconstruction, which contains 101 objects with various materials and geometries, along with the groundtruth of images and depth maps for all camera viewpoints, which significantly facilitates other research in the related fields. The code and dataset will be publicly available at //github.com/Mercerai/PAEv3d.

Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to tackle this issue: 1) restricting the number of possible representations by sorting the nodes, or 2) using permutation-invariant/equivariant functions, specifically Graph Neural Networks (GNNs). In this paper, we introduce a new framework named Discrete Graph Auto-Encoder (DGAE), which leverages the strengths of both strategies and mitigate their respective limitations. In essence, we propose a strategy in 2 steps. We first use a permutation-equivariant auto-encoder to convert graphs into sets of discrete latent node representations, each node being represented by a sequence of quantized vectors. In the second step, we sort the sets of discrete latent representations and learn their distribution with a specifically designed auto-regressive model based on the Transformer architecture. Through multiple experimental evaluations, we demonstrate the competitive performances of our model in comparison to the existing state-of-the-art across various datasets. Various ablation studies support the interest of our method.

Kernel methods are applied to many problems in pattern recognition, including subspace clustering (SC). That way, nonlinear problems in the input data space become linear in mapped high-dimensional feature space. Thereby, computationally tractable nonlinear algorithms are enabled through implicit mapping by the virtue of kernel trick. However, kernelization of linear algorithms is possible only if square of the Froebenious norm of the error term is used in related optimization problem. That, however, implies normal distribution of the error. That is not appropriate for non-Gaussian errors such as gross sparse corruptions that are modeled by -norm. Herein, to the best of our knowledge, we propose for the first time robust kernel sparse SC (RKSSC) algorithm for data with gross sparse corruptions. The concept, in principle, can be applied to other SC algorithms to achieve robustness to the presence of such type of corruption. We validated proposed approach on two well-known datasets with linear robust SSC algorithm as a baseline model. According to Wilcoxon test, clustering performance obtained by the RKSSC algorithm is statistically significantly better than corresponding performance obtained by the robust SSC algorithm. MATLAB code of proposed RKSSC algorithm is posted on //github.com/ikopriva/RKSSC.

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample performance due to distributional uncertainty. In the spirit of distributionally robust optimization, we propose a novel robust criterion by combining insights from Bayesian nonparametric (i.e., Dirichlet Process) theory and recent decision-theoretic models of smooth ambiguity-averse preferences. First, we highlight novel connections with standard regularized empirical risk minimization techniques, among which Ridge and LASSO regressions. Then, we theoretically demonstrate the existence of favorable finite-sample and asymptotic statistical guarantees on the performance of the robust optimization procedure. For practical implementation, we propose and study tractable approximations of the criterion based on well-known Dirichlet Process representations. We also show that the smoothness of the criterion naturally leads to standard gradient-based numerical optimization. Finally, we provide insights into the workings of our method by applying it to high-dimensional sparse linear regression and robust location parameter estimation tasks.

For turbulent problems of industrial scale, computational cost may become prohibitive due to the stability constraints associated with explicit time discretization of the underlying conservation laws. On the other hand, implicit methods allow for larger time-step sizes but require exorbitant computational resources. Implicit-explicit (IMEX) formulations combine both temporal approaches, using an explicit method in nonstiff portions of the domain and implicit in stiff portions. While these methods can be shown to be orders of magnitude faster than typical explicit discretizations, they are still limited by their implicit discretization in terms of cost. Hybridization reduces the scaling of these systems to an effective lower dimension, which allows the system to be solved at significant speedup factors compared to standard implicit methods. This work proposes an IMEX scheme that combines hybridized and standard flux reconstriction (FR) methods to tackle geometry-induced stiffness. By using the so-called transmission conditions, an overall conservative formulation can be obtained after combining both explicit FR and hybridized implicit FR methods. We verify and apply our approach to a series of numerical examples, including a multi-element airfoil at Reynolds number 1.7 million. Results demonstrate speedup factors of four against standard IMEX formulations and at least 15 against standard explicit formulations for the same problem.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.