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In this paper, we propose a reinforcement learning algorithm to solve a multi-agent Markov decision process (MMDP). The goal, inspired by Blackwell's Approachability Theorem, is to lower the time average cost of each agent to below a pre-specified agent-specific bound. For the MMDP, we assume the state dynamics to be controlled by the joint actions of agents, but the per-stage costs to only depend on the individual agent's actions. We combine the Q-learning algorithm for a weighted combination of the costs of each agent, obtained by a gossip algorithm with the Metropolis-Hastings or Multiplicative Weights formalisms to modulate the averaging matrix of the gossip. We use multiple timescales in our algorithm and prove that under mild conditions, it approximately achieves the desired bounds for each of the agents. We also demonstrate the empirical performance of this algorithm in the more general setting of MMDPs having jointly controlled per-stage costs.

Given the ubiquity of non-separable optimization problems in real worlds, in this paper we analyze and extend the large-scale version of the well-known cooperative coevolution (CC), a divide-and-conquer black-box optimization framework, on non-separable functions. First, we reveal empirical reasons of when decomposition-based methods are preferred or not in practice on some non-separable large-scale problems, which have not been clearly pointed out in many previous CC papers. Then, we formalize CC to a continuous-game model via simplification, but without losing its essential property. Different from previous evolutionary game theory for CC, our new model provides a much simpler but useful viewpoint to analyze its convergence, since only the pure Nash equilibrium concept is needed and more general fitness landscapes can be explicitly considered. Based on convergence analyses, we propose a hierarchical decomposition strategy for better generalization, as for any decomposition, there is a risk of getting trapped into a suboptimal Nash equilibrium. Finally, we use powerful distributed computing to accelerate it under the recent multi-level learning framework, which combines the fine-tuning ability from decomposition with the invariance property of CMA-ES. Experiments on a set of high-dimensional test functions validate both its search performance and scalability (w.r.t. CPU cores) on a clustering computing platform with 400 CPU cores.

In this paper, we describe how we changed the structure of problem sessions in an algorithmic subject, in order to improve student confidence. The subject in question is taught to very large cohorts of (around 900) students, though our approach can be applied more broadly. We reflect on our experiences over a number of years, including during the pandemic, and show that by adding clear sectioning indicating the style of the questions and by including simple warm-up questions, student engagement and confidence improves, while making the teaching activities of our teaching assistants easier to manage.

We explore developing rich semantic models of systems. Specifically, we consider structured causal explanations about state changes in those systems. Essentially, we are developing process-based dynamic knowledge graphs. As an example, we construct a model of the causal threads for geological changes proposed by the Snowball Earth theory. Further, we describe an early prototype of a graphical interface to present the explanations. Unlike statistical approaches to summarization and explanation such as Large Language Models (LLMs), our approach of direct representation can be inspected and verified directly.

In this paper, we introduce a novel and computationally efficient method for vertex embedding, community detection, and community size determination. Our approach leverages a normalized one-hot graph encoder and a rank-based cluster size measure. Through extensive simulations, we demonstrate the excellent numerical performance of our proposed graph encoder ensemble algorithm.

To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model builds on the random geometric graphs (Gilbert, 1961), one of the basic models of random graphs for spatial networks, in the same way that the well-studied stochastic block model builds on the Erd\H{o}s-R\'{en}yi random graphs. It is also a natural extension of random community models inspired by the recent theoretical and practical advancements in community detection. To analyze the geometric block model, we first provide new connectivity results for random annulus graphs which are generalizations of random geometric graphs. The connectivity properties of geometric graphs have been studied since their introduction, and analyzing them has been more difficult than their Erd\H{o}s-R\'{en}yi counterparts due to correlated edge formation. We then use the connectivity results of random annulus graphs to provide necessary and sufficient conditions for efficient recovery of communities for the geometric block model. We show that a simple triangle-counting algorithm to detect communities in the geometric block model is near-optimal. For this we consider the following two regimes of graph density. In the regime where the average degree of the graph grows logarithmically with the number of vertices, we show that our algorithm performs extremely well, both theoretically and practically. In contrast, the triangle-counting algorithm is far from being optimum for the stochastic block model in the logarithmic degree regime. We simulate our results on both real and synthetic datasets to show superior performance of both the new model as well as our algorithm.

In this work, using maximal elements in generalized Weierstrass semigroups and its relationship with pure gaps, we extend the results in \cite{CMT2024} and provide a way to completely determine the set of pure gaps at several rational places in an arbitrary function field $F$ over a finite field and its cardinality. As an example, we determine the cardinality and a simple explicit description of the set of pure gaps at several rational places distinct to the infinity place on Kummer extensions, which is a different characterization from that presented by Hu and Yang in \cite{HY2018}. Furthermore, we present some applications in coding theory and AG codes with good parameters.

In this paper, we propose a deep generative time series approach using latent temporal processes for modeling and holistically analyzing complex disease trajectories. We aim to find meaningful temporal latent representations of an underlying generative process that explain the observed disease trajectories in an interpretable and comprehensive way. To enhance the interpretability of these latent temporal processes, we develop a semi-supervised approach for disentangling the latent space using established medical concepts. By combining the generative approach with medical knowledge, we leverage the ability to discover novel aspects of the disease while integrating medical concepts into the model. We show that the learned temporal latent processes can be utilized for further data analysis and clinical hypothesis testing, including finding similar patients and clustering the disease into new sub-types. Moreover, our method enables personalized online monitoring and prediction of multivariate time series including uncertainty quantification. We demonstrate the effectiveness of our approach in modeling systemic sclerosis, showcasing the potential of our machine learning model to capture complex disease trajectories and acquire new medical knowledge.

In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.