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This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems common in nonlinear partial differential equations (PDEs). Diverging from traditional methods, TPDv iteratively updates time-evolving preconditioning operators, enhancing adaptability. The algorithm is derived and analyzed, demonstrating global linear convergence rates under mild assumptions. Numerical experiments on challenging nonlinear PDEs, including the Darcy-Forchheimer model and a nonlinear electromagnetic problem, showcase the algorithm's superiority over existing methods in terms of iteration numbers and computational efficiency. The paper concludes with a comprehensive convergence analysis.

We consider the problem of policy transfer between two Markov Decision Processes (MDPs). We introduce a lemma based on existing theoretical results in reinforcement learning to measure the relativity gap between two arbitrary MDPs, that is the difference between any two cumulative expected returns defined on different policies and environment dynamics. Based on this lemma, we propose two new algorithms referred to as Relative Policy Optimization (RPO) and Relative Transition Optimization (RTO), which offer fast policy transfer and dynamics modelling, respectively. RPO transfers the policy evaluated in one environment to maximize the return in another, while RTO updates the parameterized dynamics model to reduce the gap between the dynamics of the two environments. Integrating the two algorithms results in the complete Relative Policy-Transition Optimization (RPTO) algorithm, in which the policy interacts with the two environments simultaneously, such that data collections from two environments, policy and transition updates are completed in one closed loop to form a principled learning framework for policy transfer. We demonstrate the effectiveness of RPTO on a set of MuJoCo continuous control tasks by creating policy transfer problems via variant dynamics.

Decision-makers often observe the occurrence of events through a reporting process. City governments, for example, rely on resident reports to find and then resolve urban infrastructural problems such as fallen street trees, flooded basements, or rat infestations. Without additional assumptions, there is no way to distinguish events that occur but are not reported from events that truly did not occur--a fundamental problem in settings with positive-unlabeled data. Because disparities in reporting rates correlate with resident demographics, addressing incidents only on the basis of reports leads to systematic neglect in neighborhoods that are less likely to report events. We show how to overcome this challenge by leveraging the fact that events are spatially correlated. Our framework uses a Bayesian spatial latent variable model to infer event occurrence probabilities and applies it to storm-induced flooding reports in New York City, further pooling results across multiple storms. We show that a model accounting for under-reporting and spatial correlation predicts future reports more accurately than other models, and further induces a more equitable set of inspections: its allocations better reflect the population and provide equitable service to non-white, less traditionally educated, and lower-income residents. This finding reflects heterogeneous reporting behavior learned by the model: reporting rates are higher in Census tracts with higher populations, proportions of white residents, and proportions of owner-occupied households. Our work lays the groundwork for more equitable proactive government services, even with disparate reporting behavior.

Traditional evaluation metrics like ROUGE compare lexical overlap between the reference and generated summaries without taking argumentative structure into account, which is important for legal summaries. In this paper, we propose a novel legal summarization evaluation framework that utilizes GPT-4 to generate a set of question-answer pairs that cover main points and information in the reference summary. GPT-4 is then used to generate answers based on the generated summary for the questions from the reference summary. Finally, GPT-4 grades the answers from the reference summary and the generated summary. We examined the correlation between GPT-4 grading with human grading. The results suggest that this question-answering approach with GPT-4 can be a useful tool for gauging the quality of the summary.

Most existing causal discovery methods rely on the assumption of no latent confounders, limiting their applicability in solving real-life problems. In this paper, we introduce a novel, versatile framework for causal discovery that accommodates the presence of causally-related hidden variables almost everywhere in the causal network (for instance, they can be effects of observed variables), based on rank information of covariance matrix over observed variables. We start by investigating the efficacy of rank in comparison to conditional independence and, theoretically, establish necessary and sufficient conditions for the identifiability of certain latent structural patterns. Furthermore, we develop a Rank-based Latent Causal Discovery algorithm, RLCD, that can efficiently locate hidden variables, determine their cardinalities, and discover the entire causal structure over both measured and hidden ones. We also show that, under certain graphical conditions, RLCD correctly identifies the Markov Equivalence Class of the whole latent causal graph asymptotically. Experimental results on both synthetic and real-world personality data sets demonstrate the efficacy of the proposed approach in finite-sample cases.

Measurement-based quantum computing (MBQC) is a promising quantum computing paradigm that performs computation through ``one-way'' measurements on entangled quantum qubits. It is widely used in photonic quantum computing (PQC), where the computation is carried out on photonic cluster states (i.e., a 2-D mesh of entangled photons). In MBQC-based PQC, the cluster state depth (i.e., the length of one-way measurements) to execute a quantum circuit plays an important role in the overall execution time and error. Thus, it is important to reduce the cluster state depth. In this paper, we propose FMCC, a compilation framework that employs dynamic programming to efficiently minimize the cluster state depth. Experimental results on five representative quantum algorithms show that FMCC achieves 53.6%, 60.6%, and 60.0% average depth reductions in small, medium, and large qubit counts compared to the state-of-the-art MBQC compilation frameworks.

Non-contrastive self-supervised learning (NC-SSL) methods like BarlowTwins and VICReg have shown great promise for label-free representation learning in computer vision. Despite the apparent simplicity of these techniques, researchers must rely on several empirical heuristics to achieve competitive performance, most notably using high-dimensional projector heads and two augmentations of the same image. In this work, we provide theoretical insights on the implicit bias of the BarlowTwins and VICReg loss that can explain these heuristics and guide the development of more principled recommendations. Our first insight is that the orthogonality of the features is more critical than projector dimensionality for learning good representations. Based on this, we empirically demonstrate that low-dimensional projector heads are sufficient with appropriate regularization, contrary to the existing heuristic. Our second theoretical insight suggests that using multiple data augmentations better represents the desiderata of the SSL objective. Based on this, we demonstrate that leveraging more augmentations per sample improves representation quality and trainability. In particular, it improves optimization convergence, leading to better features emerging earlier in the training. Remarkably, we demonstrate that we can reduce the pretraining dataset size by up to 4x while maintaining accuracy and improving convergence simply by using more data augmentations. Combining these insights, we present practical pretraining recommendations that improve wall-clock time by 2x and improve performance on CIFAR-10/STL-10 datasets using a ResNet-50 backbone. Thus, this work provides a theoretical insight into NC-SSL and produces practical recommendations for enhancing its sample and compute efficiency.

Federated Learning (FL) is a decentralized machine learning (ML) technique that allows a number of participants to train an ML model collaboratively without having to share their private local datasets with others. When participants are unmanned aerial vehicles (UAVs), UAV-enabled FL would experience heterogeneity due to the majorly skewed (non-independent and identically distributed -IID) collected data. In addition, UAVs may demonstrate unintentional misbehavior in which the latter may fail to send updates to the FL server due, for instance, to UAVs' disconnectivity from the FL system caused by high mobility, unavailability, or battery depletion. Such challenges may significantly affect the convergence of the FL model. A recent way to tackle these challenges is client selection, based on customized criteria that consider UAV computing power and energy consumption. However, most existing client selection schemes neglected the participants' reliability. Indeed, FL can be targeted by poisoning attacks, in which malicious UAVs upload poisonous local models to the FL server, by either providing targeted false predictions for specifically chosen inputs or by compromising the global model's accuracy through tampering with the local model. Hence, we propose in this paper a novel client selection scheme that enhances convergence by prioritizing fast UAVs with high-reliability scores, while eliminating malicious UAVs from training. Through experiments, we assess the effectiveness of our scheme in resisting different attack scenarios, in terms of convergence and achieved model accuracy. Finally, we demonstrate the performance superiority of the proposed approach compared to baseline methods.

Non-IID data present a tough challenge for federated learning. In this paper, we explore a novel idea of facilitating pairwise collaborations between clients with similar data. We propose FedAMP, a new method employing federated attentive message passing to facilitate similar clients to collaborate more. We establish the convergence of FedAMP for both convex and non-convex models, and propose a heuristic method to further improve the performance of FedAMP when clients adopt deep neural networks as personalized models. Our extensive experiments on benchmark data sets demonstrate the superior performance of the proposed methods.

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.