Policy gradient methods have recently been shown to enjoy global convergence at a $\Theta(1/t)$ rate in the non-regularized tabular softmax setting. Accordingly, one important research question is whether this convergence rate can be further improved, with only first-order updates. In this paper, we answer the above question from the perspective of momentum by adapting the celebrated Nesterov's accelerated gradient (NAG) method to reinforcement learning (RL), termed \textit{Accelerated Policy Gradient} (APG). To demonstrate the potential of APG in achieving faster global convergence, we formally show that with the true gradient, APG with softmax policy parametrization converges to an optimal policy at a $\tilde{O}(1/t^2)$ rate. To the best of our knowledge, this is the first characterization of the global convergence rate of NAG in the context of RL. Notably, our analysis relies on one interesting finding: Regardless of the initialization, APG could end up reaching a locally nearly-concave regime, where APG could benefit significantly from the momentum, within finite iterations. By means of numerical validation, we confirm that APG exhibits $\tilde{O}(1/t^2)$ rate as well as show that APG could significantly improve the convergence behavior over the standard policy gradient.
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We consider the k-diameter clustering problem, where the goal is to partition a set of points in a metric space into $k$ clusters, minimizing the maximum distance between any two points in the same cluster. In general metrics, k-diameter is known to be NP-hard, while it has a $2$-approximation algorithm (Gonzalez'85). Complementing this algorithm, it is known that k-diameter is NP-hard to approximate within a factor better than $2$ in the $\ell_1$ and $\ell_\infty$ metrics, and within a factor of $1.969$ in the $\ell_2$ metric (Feder-Greene'88). When $k\geq 3$ is fixed, k-diameter remains NP-hard to approximate within a factor better than $2$ in the $\ell_\infty$ metric (Megiddo'90). However, its approximability in this setting has not previously been studied in the $\ell_1$ and $\ell_2$ metrics, though a $1.415$-approximation algorithm in the $\ell_2$ metric follows from a known result (Badoiu et al.'02). In this paper, we address the remaining gap by showing new hardness of approximation results that hold even when $k=3$. Specifically, we prove that 3-diameter is NP-hard to approximate within a factor better than $1.5$ in the $\ell_1$ metric, and within a factor of $1.304$ in the $\ell_2$ metric.
Two linearly uncorrelated binary variables must be also independent because non-linear dependence cannot manifest with only two possible states. This inherent linearity is the atom of dependency constituting any complex form of relationship. Inspired by this observation, we develop a framework called binary expansion linear effect (BELIEF) for understanding arbitrary relationships with a binary outcome. Models from the BELIEF framework are easily interpretable because they describe the association of binary variables in the language of linear models, yielding convenient theoretical insight and striking Gaussian parallels. With BELIEF, one may study generalized linear models (GLM) through transparent linear models, providing insight into how the choice of link affects modeling. For example, setting a GLM interaction coefficient to zero does not necessarily lead to the kind of no-interaction model assumption as understood under their linear model counterparts. Furthermore, for a binary response, maximum likelihood estimation for GLMs paradoxically fails under complete separation, when the data are most discriminative, whereas BELIEF estimation automatically reveals the perfect predictor in the data that is responsible for complete separation. We explore these phenomena and provide related theoretical results. We also provide preliminary empirical demonstration of some theoretical results.
Describing the relationship between the variables in a study domain and modelling the data generating mechanism is a fundamental problem in many empirical sciences. Probabilistic graphical models are one common approach to tackle the problem. Learning the graphical structure for such models is computationally challenging and a fervent area of current research with a plethora of algorithms being developed. To facilitate the benchmarking of different methods, we present a novel Snakemake workflow, called Benchpress for producing scalable, reproducible, and platform-independent benchmarks of structure learning algorithms for probabilistic graphical models. Benchpress is interfaced via a simple JSON-file, which makes it accessible for all users, while the code is designed in a fully modular fashion to enable researchers to contribute additional methodologies. Benchpress currently provides an interface to a large number of state-of-the-art algorithms from libraries such as BDgraph, BiDAG, bnlearn, causal-learn, gCastle, GOBNILP, pcalg, r.blip, scikit-learn, TETRAD, and trilearn as well as a variety of methods for data generating models and performance evaluation. Alongside user-defined models and randomly generated datasets, the workflow also includes a number of standard datasets and graphical models from the literature, which may be included in a benchmarking study. We demonstrate the applicability of this workflow for learning Bayesian networks in five typical data scenarios. The source code and documentation is publicly available from //benchpressdocs.readthedocs.io.
The surge in real-time data collection across various industries has underscored the need for advanced anomaly detection in both univariate and multivariate time series data. Traditional methods, while comprehensive, often struggle to capture the complex interdependencies in such data. This paper introduces TransNAS-TSAD, a novel framework that synergizes transformer architecture with neural architecture search (NAS), enhanced through NSGA-II algorithm optimization. This innovative approach effectively tackles the complexities of both univariate and multivariate time series, balancing computational efficiency with detection accuracy. Our evaluation reveals that TransNAS-TSAD surpasses conventional anomaly detection models, demonstrating marked improvements in diverse data scenarios. We also propose the Efficiency-Accuracy-Complexity Score (EACS) as a new metric for assessing model performance, emphasizing the crucial balance between accuracy and computational resources. TransNAS-TSAD sets a new benchmark in time series anomaly detection, offering a versatile, efficient solution for complex real-world applications. This research paves the way for future developments in the field, highlighting its potential in a wide range of industry applications.
Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) data and simultaneously learns simpler equations governing the latent space. These equations are interpolated with Gaussian Processes, allowing for uncertainty quantification and active learning, even with limited access to the FOM solver. Our framework is able to achieve up to 100,000 times speed-up and less than 7% relative error on fluid mechanics problems.
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We prove that the well-known (strong) fully-concurrent bisimilarity and the novel i-causal-net bisimilarity, which is a sligtlhy coarser variant of causal-net bisimilarity, are decidable for finite bounded Petri nets. The proofs are based on a generalization of the ordered marking proof technique that Vogler used to demonstrate that (strong) fully-concurrent bisimilarity (or, equivalently, history-preserving bisimilarity) is decidable on finite safe nets.
Modeling the ratio of two dependent components as a function of covariates is a frequently pursued objective in observational research. Despite the high relevance of this topic in medical studies, where biomarker ratios are often used as surrogate endpoints for specific diseases, existing models are based on oversimplified assumptions, assuming e.g.\@ independence or strictly positive associations between the components. In this paper, we close this gap in the literature and propose a regression model where the marginal distributions of the two components are linked by Frank copula. A key feature of our model is that it allows for both positive and negative correlations between the components, with one of the model parameters being directly interpretable in terms of Kendall's rank correlation coefficient. We study our method theoretically, evaluate finite sample properties in a simulation study and demonstrate its efficacy in an application to diagnosis of Alzheimer's disease via ratios of amyloid-beta and total tau protein biomarkers.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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