Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process, which limits the general applicability of such methods. Furthermore, current approaches often ignore the complex dependence structure inherent in discrete data and consider only linear effects. We propose a differentiable structure learning framework that is capable of capturing arbitrary dependencies among discrete variables. We show that although general discrete models are unidentifiable from purely observational data, it is possible to characterize the complete set of compatible parameters and structures. Additionally, we establish identifiability up to the Markov equivalence class (MEC) under mild assumptions. We formulate the learning problem as a single differentiable optimization task in the most general form, thereby avoiding the unrealistic simplifications adopted by previous methods. Empirical results demonstrate that our approach effectively captures complex relationships in discrete data.

With the popularity of confidential computing, confidential virtual machines (CVMs) have been widely adopted and they guarantee strong security by hardware. However, there still exist some problems in memory management in CVMs. Since private memory pages of CVMs are encrypted and cannot be accessed by hypervisors, existing CVMs employ static page management to avoid crashes due to the relocation of encrypted memory pages, leading cloud platforms managing CVMs to face more severe memory management pressures than before. Memory ballooning, as an efficient, flexible, and highly compatible memory management mechanism in virtualization, is not available in CVMs based on SEV (Secure Encrypted Virtualization). In this paper, we analyze the design of SEV CVMs and memory ballooning, and enable memory ballooning on SEV CVMs by substituting static page management with dynamic page management and addressing communication issues between the guest frontend and the host backend. Besides, we propose three performance optimization strategies for memory ballooning on SEV CVMs, including asynchronous reclaiming on the host side, an additional shadow vCPU on the guest side, and accelerating cache flushing operations in the host kernel. Experiments show that the time cost of reclaiming memory from SEV CVMs by memory ballooning can be reduced by up to 38 times and up to 55% overhead caused by delaying reclamation in real-world applications like MYSQL can be eliminated.

Existing approaches to differentiable structure learning of directed acyclic graphs (DAGs) rely on strong identifiability assumptions in order to guarantee that global minimizers of the acyclicity-constrained optimization problem identifies the true DAG. Moreover, it has been observed empirically that the optimizer may exploit undesirable artifacts in the loss function. We explain and remedy these issues by studying the behavior of differentiable acyclicity-constrained programs under general likelihoods with multiple global minimizers. By carefully regularizing the likelihood, it is possible to identify the sparsest model in the Markov equivalence class, even in the absence of an identifiable parametrization. We first study the Gaussian case in detail, showing how proper regularization of the likelihood defines a score that identifies the sparsest model. Assuming faithfulness, it also recovers the Markov equivalence class. These results are then generalized to general models and likelihoods, where the same claims hold. These theoretical results are validated empirically, showing how this can be done using standard gradient-based optimizers (without resorting to approximations such as Gumbel-Softmax), thus paving the way for differentiable structure learning under general models and losses. Open-source code is available at \url{https://github.com/duntrain/dagrad}.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimality challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order optimization schemes to solve this problem, proving the global optimality of such approaches has proven elusive. The difficulty lies in the fact that unlike other non-convex problems in the literature, this problem is not "benign", and possesses multiple spurious solutions that standard approaches can easily get trapped in. In this paper, we prove that a simple path-following optimization scheme globally converges to the global minimum of the population loss in the bivariate setting.

In multi-task learning, the training losses of different tasks are varying. There are many works to handle this situation and we classify them into five categories. In this paper, we propose a Balanced Multi-Task Learning (BMTL) framework. Different from existing studies which rely on task weighting, the BMTL framework proposes to transform the training loss of each task to balance different tasks based on an intuitive idea that tasks with larger training losses will receive more attention during the optimization procedure. We analyze the transformation function and derive necessary conditions as well as some properties. The proposed BMTL framework is very simple and it can be combined with most multi-task learning models. Empirical studies show the state-of-the-art performance of the proposed BMTL framework.

We study an energy-efficient unmanned aerial vehicle (UAV) multicast system, in which ground terminals (GTs) requiring a common information (CI) are grouped and a UAV flies to each group to deliver the CI using minimum energy consumption. A machine learning (ML) empowered joint multicast grouping and UAV trajectory optimization framework is proposed to tackle the challenging joint optimization problem. In this framework, we first propose the compressed-feature regression and clustering machine learning (C2ML) for multicast grouping. A support vector regression (SVR) is trained with the silhouette coefficient, a one- dimensional compressed feature regarding the distribution of GTs, to efficiently determine the number of groups that guides the K-means clustering to approach the optimal multicast grouping. With the C2ML- enabled multicast grouping, we solve the UAV trajectory optimization problem by formulating an equivalent centroid-adjustable traveling salesman problem (CA- TSP). An efficient CA-TSP inspired iterative optimization algorithm is proposed for UAV trajectory planning. The proposed ML-empowered joint optimization framework, which integrates the offline C2ML-enabled multicast grouping and the online CA-TSP inspired UAV- trajectory optimization, is shown to achieve excellent energy-saving performance.

Attributes of an object contain its fundamental properties. Attribute data is the main source of clustering information. Although relationship data is an extrinsic property of objects and is at least as important as attribute data, most clustering methods process only one type of characteristic data. However, attribute and relationship data must be analyzed together for applications such as market segmentation, social network segmentation, and image segmentation. In this study we describe a new algorithm that combines attribute and relationship data for joint clustering analysis. An experimental evaluation demonstrates the usefulness and accuracy of the proposed algorithm when applied to image segmentation.

In this paper, a dynamic fuzzy Q-learning (DFQL) method navigating a mobile robot efficiently is presented. Self-organizing fuzzy inference is introduced to calculate actions and Q-functions which capable of enabling us to deal with continuous-valued states and actions. Consequently, fuzzy rules can be generated automatically. Fuzzy inference systems provide a natural mean of incorporating the bias components for rapid reinforcement learning. Furthermore, the eligibility trace method is employed in our algorithm, leading to faster learning and alleviating the experimentation-sensitive problem where an arbitrarily bad training policy might result in a non-optimal policy. Experimental results demonstrate that the robot is able to learn the right policy with a few trials.

This paper presents a dynamic fuzzy Q-learning (DFQL) method that is capable of tuning fuzzy inference systems (FIS) online. A novel online self-organizing learning algorithm is developed so that structure and parameters identification are accomplished automatically and simultaneously based only on Q-learning. Self-organizing fuzzy inference is introduced to calculate actions and Q-functions so as to enable us to deal with continuous-valued states and actions. Fuzzy rules provide a natural mean of incorporating the bias components for rapid reinforcement learning. Experimental results and comparative studies with the fuzzy Q-learning (FQL) and continuous-action Q-learning in the wall-following task of mobile robots demonstrate that the proposed DFQL method is superior.

This paper presents a dynamic Q-learning (DFQL) method that is capable of tuning the fuzzy inference systems (FIS) online. On-line self-organizing learning is developed so that structure and parameters identification are accomplished automatically and simultaneously based only on Q-learning. Self-organizing fuzzy inference is introduced to calculate actions and Q-functions so as to enable us to deal with continuous-valued states and actions. Fuzzy rules provide a natural mean to incorporate the bias components for rapid reinforcement learning. Experimental results and comparative studies with the fuzzy Q-learning the wall following task of mobile robots demonstrate the superiority of the proposed DFQL method.

This paper presents a novel approach of controlling a mobile robot using Generalized Dynamic Fuzzy Neural Networks (GDFNN). Using the GDFNN learning algorithm, not only the parameters of the controller can be optimized online, but also the structure of the controller can be self-adaptive. In comparison to the state-of-the-art neuro-fuzzy controller which predefines the rules, the proposed approach is more flexible. Moreover, the learning speed of this approach is very fast and fuzzy rules can be automatically generated online. This is in contrast with the state-of-the-art neuro-fuzzy controller which requires offline learning process. Simulations studies on a Khepera II robot show that the performance of the proposed approach is more superior.