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Unmanned aerial vehicles (UAVs), commonly known as drones, are being increasingly deployed throughout the globe as a means to streamline monitoring, inspection, mapping, and logistic routines. When dispatched on autonomous missions, drones require an intelligent decision-making system for trajectory planning and tour optimization. Given the limited capacity of their onboard batteries, a key design challenge is to ensure the underlying algorithms can efficiently optimize the mission objectives along with recharging operations during long-haul flights. With this in view, the present work undertakes a comprehensive study on automated tour management systems for an energy-constrained drone: (1) We construct a machine learning model that estimates the energy expenditure of typical multi-rotor drones while accounting for real-world aspects and extrinsic meteorological factors. (2) Leveraging this model, the joint program of flight mission planning and recharging optimization is formulated as a multi-criteria Asymmetric Traveling Salesman Problem (ATSP), wherein a drone seeks for the time-optimal energy-feasible tour that visits all the target sites and refuels whenever necessary. (3) We devise an efficient approximation algorithm with provable worst-case performance guarantees and implement it in a drone management system, which supports real-time flight path tracking and re-computation in dynamic environments. (4) The effectiveness and practicality of the proposed approach are validated through extensive numerical simulations as well as real-world experiments.

Data collection and research methodology represents a critical part of the research pipeline. On the one hand, it is important that we collect data in a way that maximises the validity of what we are measuring, which may involve the use of long scales with many items. On the other hand, collecting a large number of items across multiple scales results in participant fatigue, and expensive and time consuming data collection. It is therefore important that we use the available resources optimally. In this work, we consider how a consideration for theory and the associated causal/structural model can help us to streamline data collection procedures by not wasting time collecting data for variables which are not causally critical for subsequent analysis. This not only saves time and enables us to redirect resources to attend to other variables which are more important, but also increases research transparency and the reliability of theory testing. In order to achieve this streamlined data collection, we leverage structural models, and Markov conditional independency structures implicit in these models to identify the substructures which are critical for answering a particular research question. In this work, we review the relevant concepts and present a number of didactic examples with the hope that psychologists can use these techniques to streamline their data collection process without invalidating the subsequent analysis. We provide a number of simulation results to demonstrate the limited analytical impact of this streamlining.

On-demand delivery has become increasingly popular around the world. Motivated by a large grocery chain store who offers fast on-demand delivery services, we model and solve a stochastic dynamic driver dispatching and routing problem for last-mile delivery systems where on-time performance is the main target. The system operator needs to dispatch a set of drivers and specify their delivery routes facing random demand that arrives over a fixed number of periods. The resulting stochastic dynamic program is challenging to solve due to the curse of dimensionality. We propose a novel structured approximation framework to approximate the value function via a parametrized dispatching and routing policy. We analyze the structural properties of the approximation framework and establish its performance guarantee under large-demand scenarios. We then develop efficient exact algorithms for the approximation problem based on Benders decomposition and column generation, which deliver verifiably optimal solutions within minutes. The evaluation results on a real-world data set show that our framework outperforms the current policy of the company by 36.53% on average in terms of delivery time. We also perform several policy experiments to understand the value of dynamic dispatching and routing with varying fleet sizes and dispatch frequencies.

Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this paper a reformulation of the usual set-theoretical semantics of the description logic $\mathcal{ALC}$ by using categorical language. In this setting, ALC concepts are represented as objects, concept subsumptions as arrows, and memberships as logical quantifiers over objects and arrows of categories. Such a category-theoretical semantics provides a more modular representation of the semantics of $\mathcal{ALC}$ and a new way to design algorithms for reasoning.

We study dynamic algorithms for the problem of maximizing a monotone submodular function over a stream of $n$ insertions and deletions. We show that any algorithm that maintains a $(0.5+\epsilon)$-approximate solution under a cardinality constraint, for any constant $\epsilon>0$, must have an amortized query complexity that is $\mathit{polynomial}$ in $n$. Moreover, a linear amortized query complexity is needed in order to maintain a $0.584$-approximate solution. This is in sharp contrast with recent dynamic algorithms of [LMNF+20, Mon20] that achieve $(0.5-\epsilon)$-approximation with a $\mathsf{poly}\log(n)$ amortized query complexity. On the positive side, when the stream is insertion-only, we present efficient algorithms for the problem under a cardinality constraint and under a matroid constraint with approximation guarantee $1-1/e-\epsilon$ and amortized query complexities $\smash{O(\log (k/\epsilon)/\epsilon^2)}$ and $\smash{k^{\tilde{O}(1/\epsilon^2)}\log n}$, respectively, where $k$ denotes the cardinality parameter or the rank of the matroid.

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic.

Recently, federated learning has emerged as a promising approach for training a global model using data from multiple organizations without leaking their raw data. Nevertheless, directly applying federated learning to real-world tasks faces two challenges: (1) heterogeneity in the data among different organizations; and (2) data noises inside individual organizations. In this paper, we propose a general framework to solve the above two challenges simultaneously. Specifically, we propose using distributionally robust optimization to mitigate the negative effects caused by data heterogeneity paradigm to sample clients based on a learnable distribution at each iteration. Additionally, we observe that this optimization paradigm is easily affected by data noises inside local clients, which has a significant performance degradation in terms of global model prediction accuracy. To solve this problem, we propose to incorporate mixup techniques into the local training process of federated learning. We further provide comprehensive theoretical analysis including robustness analysis, convergence analysis, and generalization ability. Furthermore, we conduct empirical studies across different drug discovery tasks, such as ADMET property prediction and drug-target affinity prediction.

The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question answering or machine translation). However, it builds upon the assumption that the data distribution is stationary, ie. that the data is sampled from a fixed distribution both at training and test time. This way of training is inconsistent with how we as humans are able to learn from and operate within a constantly changing stream of information. Moreover, it is ill-adapted to real-world use cases where the data distribution is expected to shift over the course of a model's lifetime. The first goal of this thesis is to characterize the different forms this shift can take in the context of natural language processing, and propose benchmarks and evaluation metrics to measure its effect on current deep learning architectures. We then proceed to take steps to mitigate the effect of distributional shift on NLP models. To this end, we develop methods based on parametric reformulations of the distributionally robust optimization framework. Empirically, we demonstrate that these approaches yield more robust models as demonstrated on a selection of realistic problems. In the third and final part of this thesis, we explore ways of efficiently adapting existing models to new domains or tasks. Our contribution to this topic takes inspiration from information geometry to derive a new gradient update rule which alleviate catastrophic forgetting issues during adaptation.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.

Modern neural network training relies heavily on data augmentation for improved generalization. After the initial success of label-preserving augmentations, there has been a recent surge of interest in label-perturbing approaches, which combine features and labels across training samples to smooth the learned decision surface. In this paper, we propose a new augmentation method that leverages the first and second moments extracted and re-injected by feature normalization. We replace the moments of the learned features of one training image by those of another, and also interpolate the target labels. As our approach is fast, operates entirely in feature space, and mixes different signals than prior methods, one can effectively combine it with existing augmentation methods. We demonstrate its efficacy across benchmark data sets in computer vision, speech, and natural language processing, where it consistently improves the generalization performance of highly competitive baseline networks.