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This paper introduces a new method of discretization that collocates both endpoints of the domain and enables the complete convergence of the costate variables associated with the Hamilton boundary-value problem. This is achieved through the inclusion of an \emph{exceptional sample} to the roots of the Legendre-Lobatto polynomial, thus promoting the associated differentiation matrix to be full-rank. We study the location of the new sample such that the differentiation matrix is the most robust to perturbations and we prove that this location is also the choice that mitigates the Runge phenomenon associated with polynomial interpolation. Two benchmark problems are successfully implemented in support of our theoretical findings. The new method is observed to converge exponentially with the number of discretization points used.

The abilities to understand the social interaction behaviors between a vehicle and its surroundings while predicting its trajectory in an urban environment are critical for road safety in autonomous driving. Social interactions are hard to explain because of their uncertainty. In recent years, neural network-based methods have been widely used for trajectory prediction and have been shown to outperform hand-crafted methods. However, these methods suffer from their lack of interpretability. In order to overcome this limitation, we combine the interpretability of a discrete choice model with the high accuracy of a neural network-based model for the task of vehicle trajectory prediction in an interactive environment. We implement and evaluate our model using the INTERACTION dataset and demonstrate the effectiveness of our proposed architecture to explain its predictions without compromising the accuracy.

We consider the problem of defending a hash table against a Byzantine attacker that is trying to degrade the performance of query, insertion and deletion operations. Our defense makes use of resource burning (RB) -- the the verifiable expenditure of network resources -- where the issuer of a request incurs some RB cost. Our algorithm, Depth Charge, charges RB costs for operations based on the depth of the appropriate object in the list that the object hashes to in the table. By appropriately setting the RB costs, our algorithm mitigates the impact of an attacker on the hash table's performance. In particular, in the presence of a significant attack, our algorithm incurs a cost which is asymptotically less that the attacker's cost.

Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem is usually difficult to solve and prone to local minima. However, recent advancements in computing hardware allow for parallel trajectory optimisation where multiple solutions are obtained simultaneously, each initialised from a different starting point. Unfortunately, without a strategy preventing two solutions to collapse on each other, naive parallel optimisation can suffer from mode collapse diminishing the efficiency of the approach and the likelihood of finding a global solution. In this paper we leverage on recent advances in the theory of rough paths to devise an algorithm for parallel trajectory optimisation that promotes diversity over the range of solutions, therefore avoiding mode collapses and achieving better global properties. Our approach builds on path signatures and Hilbert space representations of trajectories, and connects parallel variational inference for trajectory estimation with diversity promoting kernels. We empirically demonstrate that this strategy achieves lower average costs than competing alternatives on a range of problems, from 2D navigation to robotic manipulators operating in cluttered environments.

We consider a causal inference model in which individuals interact in a social network and they may not comply with the assigned treatments. In particular, we suppose that the form of network interference is unknown to researchers. To estimate meaningful causal parameters in this situation, we introduce a new concept of exposure mapping, which summarizes potentially complicated spillover effects into a fixed dimensional statistic of instrumental variables. We investigate identification conditions for the intention-to-treat effects and the average treatment effects for compliers, while explicitly considering the possibility of misspecification of exposure mapping. Based on our identification results, we develop nonparametric estimation procedures via inverse probability weighting. Their asymptotic properties, including consistency and asymptotic normality, are investigated using an approximate neighborhood interference framework. For an empirical illustration, we apply our method to experimental data on the anti-conflict intervention school program. The proposed methods are readily available with the companion R package latenetwork.

Many research explore how well computers are able to examine emotions displayed by humans and use that data to perform different tasks. However, there have been very few research which evaluate the computers ability to generate emotion classification information in an attempt to help the user make decisions or perform tasks. This is a crucial area to explore as it is paramount to the two way communication between humans and computers. This research conducted an experiment to investigate the impact of different uncertainty information displays of emotion classification on the human decision making process. Results show that displaying more uncertainty information can help users to be more confident when making decisions.

We study how to extend the use of the diffusion model to answer the causal question from the observational data under the existence of unmeasured confounders. In Pearl's framework of using a Directed Acyclic Graph (DAG) to capture the causal intervention, a Diffusion-based Causal Model (DCM) was proposed incorporating the diffusion model to answer the causal questions more accurately, assuming that all of the confounders are observed. However, unmeasured confounders in practice exist, which hinders DCM from being applicable. To alleviate this limitation of DCM, we propose an extended model called Backdoor Criterion based DCM (BDCM), whose idea is rooted in the Backdoor criterion to find the variables in DAG to be included in the decoding process of the diffusion model so that we can extend DCM to the case with unmeasured confounders. Synthetic data experiment demonstrates that our proposed model captures the counterfactual distribution more precisely than DCM under the unmeasured confounders.

Lengthy evaluation times are common in many optimization problems such as direct policy search tasks, especially when they involve conducting evaluations in the physical world, e.g. in robotics applications. Often, when evaluating a solution over a fixed time period, it becomes clear that the objective value will not increase with additional computation time (for example, when a two-wheeled robot continuously spins on the spot). In such cases, it makes sense to stop the evaluation early to save computation time. However, most approaches to stop the evaluation are problem-specific and need to be specifically designed for the task at hand. Therefore, we propose an early stopping method for direct policy search. The proposed method only looks at the objective value at each time step and requires no problem-specific knowledge. We test the introduced stopping criterion in five direct policy search environments drawn from games, robotics, and classic control domains, and show that it can save up to 75% of the computation time. We also compare it with problem-specific stopping criteria and demonstrate that it performs comparably while being more generally applicable.

The rapid changes in the finance industry due to the increasing amount of data have revolutionized the techniques on data processing and data analysis and brought new theoretical and computational challenges. In contrast to classical stochastic control theory and other analytical approaches for solving financial decision-making problems that heavily reply on model assumptions, new developments from reinforcement learning (RL) are able to make full use of the large amount of financial data with fewer model assumptions and to improve decisions in complex financial environments. This survey paper aims to review the recent developments and use of RL approaches in finance. We give an introduction to Markov decision processes, which is the setting for many of the commonly used RL approaches. Various algorithms are then introduced with a focus on value and policy based methods that do not require any model assumptions. Connections are made with neural networks to extend the framework to encompass deep RL algorithms. Our survey concludes by discussing the application of these RL algorithms in a variety of decision-making problems in finance, including optimal execution, portfolio optimization, option pricing and hedging, market making, smart order routing, and robo-advising.

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.