Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an explicit constant factor that holds true for the entire function class. Furthermore, in the stochastic setting, only a modified version of AdaGrad, different from the one commonly used in practice, in which the latest gradient is not used to update the stepsize, has been analyzed. Our paper aims at bridging these gaps and developing a deeper understanding of AdaGrad and its variants in the standard setting of smooth convex functions as well as the more general setting of quasar convex functions. First, we demonstrate new techniques to explicitly bound the convergence rate of the vanilla AdaGrad for unconstrained problems in both deterministic and stochastic settings. Second, we propose a variant of AdaGrad for which we can show the convergence of the last iterate, instead of the average iterate. Finally, we give new accelerated adaptive algorithms and their convergence guarantee in the deterministic setting with explicit dependency on the problem parameters, improving upon the asymptotic rate shown in previous works.
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Because $\Sigma^p_2$- and $\Sigma^p_3$-hardness proofs are usually tedious and difficult, not so many complete problems for these classes are known. This is especially true in the areas of min-max regret robust optimization, network interdiction, most vital vertex problems, blocker problems, and two-stage adjustable robust optimization problems. Even though these areas are well-researched for over two decades and one would naturally expect many (if not most) of the problems occurring in these areas to be complete for the above classes, almost no completeness results exist in the literature. We address this lack of knowledge by introducing over 70 new $\Sigma^p_2$-complete and $\Sigma^p_3$-complete problems. We achieve this result by proving a new meta-theorem, which shows $\Sigma^p_2$- and $\Sigma^p_3$-completeness simultaneously for a huge class of problems. The majority of all earlier publications on $\Sigma^p_2$- and $\Sigma^p_3$-completeness in said areas are special cases of our meta-theorem. Our precise result is the following: We introduce a large list of problems for which the meta-theorem is applicable (including clique, vertex cover, knapsack, TSP, facility location and many more). For every problem on this list, we show: The interdiction/minimum cost blocker/most vital nodes problem (with element costs) is $\Sigma^p_2$-complete. The min-max-regret problem with interval uncertainty is $\Sigma^p_2$-complete. The two-stage adjustable robust optimization problem with discrete budgeted uncertainty is $\Sigma^p_3$-complete. In summary, our work reveals the interesting insight that a large amount of NP-complete problems have the property that their min-max versions are 'automatically' $\Sigma^p_2$-complete.
Nonparametric learning is a fundamental concept in machine learning that aims to capture complex patterns and relationships in data without making strong assumptions about the underlying data distribution. Owing to simplicity and familiarity, one of the most well-known algorithms under this paradigm is the $k$-nearest neighbors ($k$-NN) algorithm. Driven by the usage of machine learning in safety-critical applications, in this work, we shed new light on the traditional nearest neighbors algorithm from the perspective of information theory and propose a robust and interpretable framework for tasks such as classification, regression, and anomaly detection using a single model. Instead of using a traditional distance measure which needs to be scaled and contextualized, we use a novel formulation of \textit{surprisal} (amount of information required to explain the difference between the observed and expected result). Finally, we demonstrate this architecture's capability to perform at-par or above the state-of-the-art on classification, regression, and anomaly detection tasks using a single model with enhanced interpretability by providing novel concepts for characterizing data and predictions.
Factuality is a crucial requirement in information seeking dialogue: the system should respond to the user's queries so that the responses are meaningful and aligned with the knowledge provided to the system. However, most modern large language models suffer from hallucinations, that is, they generate responses not supported by or contradicting the knowledge source. To mitigate the issue and increase faithfulness of information-seeking dialogue systems, we introduce BeInfo, a simple yet effective method that applies behavioural tuning to aid information-seeking dialogue. Relying on three standard datasets, we show that models tuned with BeInfo} become considerably more faithful to the knowledge source both for datasets and domains seen during BeInfo-tuning, as well as on unseen domains, when applied in a zero-shot manner. In addition, we show that the models with 3B parameters (e.g., Flan-T5) tuned with BeInfo demonstrate strong performance on data from real `production' conversations and outperform GPT4 when tuned on a limited amount of such realistic in-domain dialogues.
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to compute all of the eigenvalues. Notable examples are the electronic structure problems where the $k$-th smallest eigenvalue is closely related to the electronic properties of materials. In this paper, we consider the $k$-th eigenvalue problems of symmetric dense matrices with low-rank off-diagonal blocks. We present a linear time generalized LDL decomposition of $\mathcal{H}^2$ matrices and combine it with the bisection eigenvalue algorithm to compute the $k$-th eigenvalue with controllable accuracy. In addition, if more than one eigenvalue is required, some of the previous computations can be reused to compute the other eigenvalues in parallel. Numerical experiments show that our method is more efficient than the state-of-the-art dense eigenvalue solver in LAPACK/ScaLAPACK and ELPA. Furthermore, tests on electronic state calculations of carbon nanomaterials demonstrate that our method outperforms the existing HSS-based bisection eigenvalue algorithm on 3D problems.
Foundation models pretrained on diverse data at scale have demonstrated extraordinary capabilities in a wide range of vision and language tasks. When such models are deployed in real world environments, they inevitably interface with other entities and agents. For example, language models are often used to interact with human beings through dialogue, and visual perception models are used to autonomously navigate neighborhood streets. In response to these developments, new paradigms are emerging for training foundation models to interact with other agents and perform long-term reasoning. These paradigms leverage the existence of ever-larger datasets curated for multimodal, multitask, and generalist interaction. Research at the intersection of foundation models and decision making holds tremendous promise for creating powerful new systems that can interact effectively across a diverse range of applications such as dialogue, autonomous driving, healthcare, education, and robotics. In this manuscript, we examine the scope of foundation models for decision making, and provide conceptual tools and technical background for understanding the problem space and exploring new research directions. We review recent approaches that ground foundation models in practical decision making applications through a variety of methods such as prompting, conditional generative modeling, planning, optimal control, and reinforcement learning, and discuss common challenges and open problems in the field.
The incredible development of federated learning (FL) has benefited various tasks in the domains of computer vision and natural language processing, and the existing frameworks such as TFF and FATE has made the deployment easy in real-world applications. However, federated graph learning (FGL), even though graph data are prevalent, has not been well supported due to its unique characteristics and requirements. The lack of FGL-related framework increases the efforts for accomplishing reproducible research and deploying in real-world applications. Motivated by such strong demand, in this paper, we first discuss the challenges in creating an easy-to-use FGL package and accordingly present our implemented package FederatedScope-GNN (FS-G), which provides (1) a unified view for modularizing and expressing FGL algorithms; (2) comprehensive DataZoo and ModelZoo for out-of-the-box FGL capability; (3) an efficient model auto-tuning component; and (4) off-the-shelf privacy attack and defense abilities. We validate the effectiveness of FS-G by conducting extensive experiments, which simultaneously gains many valuable insights about FGL for the community. Moreover, we employ FS-G to serve the FGL application in real-world E-commerce scenarios, where the attained improvements indicate great potential business benefits. We publicly release FS-G, as submodules of FederatedScope, at //github.com/alibaba/FederatedScope to promote FGL's research and enable broad applications that would otherwise be infeasible due to the lack of a dedicated package.
Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.
Meta-reinforcement learning algorithms can enable robots to acquire new skills much more quickly, by leveraging prior experience to learn how to learn. However, much of the current research on meta-reinforcement learning focuses on task distributions that are very narrow. For example, a commonly used meta-reinforcement learning benchmark uses different running velocities for a simulated robot as different tasks. When policies are meta-trained on such narrow task distributions, they cannot possibly generalize to more quickly acquire entirely new tasks. Therefore, if the aim of these methods is to enable faster acquisition of entirely new behaviors, we must evaluate them on task distributions that are sufficiently broad to enable generalization to new behaviors. In this paper, we propose an open-source simulated benchmark for meta-reinforcement learning and multi-task learning consisting of 50 distinct robotic manipulation tasks. Our aim is to make it possible to develop algorithms that generalize to accelerate the acquisition of entirely new, held-out tasks. We evaluate 6 state-of-the-art meta-reinforcement learning and multi-task learning algorithms on these tasks. Surprisingly, while each task and its variations (e.g., with different object positions) can be learned with reasonable success, these algorithms struggle to learn with multiple tasks at the same time, even with as few as ten distinct training tasks. Our analysis and open-source environments pave the way for future research in multi-task learning and meta-learning that can enable meaningful generalization, thereby unlocking the full potential of these methods.
We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.
Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.
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