In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam) have been applied to the parameter optimization of several deep learning models with higher accuracies or lower errors. These optimization algorithms may need to set the values of several hyperparameters which include a learning rate, momentum coefficients, etc. Furthermore, the convergence speed and solution accuracy may be influenced by the values of hyperparameters. Therefore, this study proposes an analytical framework to use mathematical models for analyzing the mean error of each objective function based on various gradient descent algorithms. Moreover, the suitable value of each hyperparameter could be determined by minimizing the mean error. The principles of hyperparameter value setting have been generalized based on analysis results for model optimization. The experimental results show that higher efficiency convergences and lower errors can be obtained by the proposed method.

CS 221 ― Artificial Intelligence My twin brother Afshine and I created this set of illustrated Artificial Intelligence cheatsheets covering the content of the CS 221 class, which I TA-ed in Spring 2019 at Stanford. They can (hopefully!) be useful to all future students of this course as well as to anyone else interested in Artificial Intelligence. You can help us translating them on GitHub!

To lower the communication complexity of federated min-max learning, a natural approach is to utilize the idea of infrequent communications (through multiple local updates) same as in conventional federated learning. However, due to the more complicated inter-outer problem structure in federated min-max learning, theoretical understandings of communication complexity for federated min-max learning with infrequent communications remain very limited in the literature. This is particularly true for settings with non-i.i.d. datasets and partial client participation. To address this challenge, in this paper, we propose a new algorithmic framework called stochastic sampling averaging gradient descent ascent (SAGDA), which i) assembles stochastic gradient estimators from randomly sampled clients as control variates and ii) leverages two learning rates on both server and client sides. We show that SAGDA achieves a linear speedup in terms of both the number of clients and local update steps, which yields an $\mathcal{O}(\epsilon^{-2})$ communication complexity that is orders of magnitude lower than the state of the art. Interestingly, by noting that the standard federated stochastic gradient descent ascent (FSGDA) is in fact a control-variate-free special version of SAGDA, we immediately arrive at an $\mathcal{O}(\epsilon^{-2})$ communication complexity result for FSGDA. Therefore, through the lens of SAGDA, we also advance the current understanding on communication complexity of the standard FSGDA method for federated min-max learning.

An oft-cited open problem of federated learning is the existence of data heterogeneity at the clients. One pathway to understanding the drastic accuracy drop in federated learning is by scrutinizing the behavior of the clients' deep models on data with different levels of "difficulty", which has been left unaddressed. In this paper, we investigate a different and rarely studied dimension of FL: ordered learning. Specifically, we aim to investigate how ordered learning principles can contribute to alleviating the heterogeneity effects in FL. We present theoretical analysis and conduct extensive empirical studies on the efficacy of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random curriculum. We find that curriculum learning largely alleviates non-IIDness. Interestingly, the more disparate the data distributions across clients the more they benefit from ordered learning. We provide analysis explaining this phenomenon, specifically indicating how curriculum training appears to make the objective landscape progressively less convex, suggesting fast converging iterations at the beginning of the training procedure. We derive quantitative results of convergence for both convex and nonconvex objectives by modeling the curriculum training on federated devices as local SGD with locally biased stochastic gradients. Also, inspired by ordered learning, we propose a novel client selection technique that benefits from the real-world disparity in the clients. Our proposed approach to client selection has a synergic effect when applied together with ordered learning in FL.

The Information Bottleneck theory provides a theoretical and computational framework for finding approximate minimum sufficient statistics. Analysis of the Stochastic Gradient Descent (SGD) training of a neural network on a toy problem has shown the existence of two phases, fitting and compression. In this work, we analyze the SGD training process of a Deep Neural Network on MNIST classification and confirm the existence of two phases of SGD training. We also propose a setup for estimating the mutual information for a Deep Neural Network through Variational Inference.

Patient triage at emergency departments (EDs) is necessary to prioritize care for patients with critical and time-sensitive conditions. Different tools are used for patient triage and one of the most common ones is the emergency severity index (ESI), which has a scale of five levels, where level 1 is the most urgent and level 5 is the least urgent. This paper proposes a framework for utilizing machine learning to develop an e-triage tool that can be used at EDs. A large retrospective dataset of ED patient visits is obtained from the electronic health record of a healthcare provider in the Midwest of the US for three years. However, the main challenge of using machine learning algorithms is that most of them have many parameters and without optimizing these parameters, developing a high-performance model is not possible. This paper proposes an approach to optimize the hyperparameters of machine learning. The metaheuristic optimization algorithms simulated annealing (SA) and adaptive simulated annealing (ASA) are proposed to optimize the parameters of extreme gradient boosting (XGB) and categorical boosting (CaB). The newly proposed algorithms are SA-XGB, ASA-XGB, SA-CaB, ASA-CaB. Grid search (GS), which is a traditional approach used for machine learning fine-tunning is also used to fine-tune the parameters of XGB and CaB, which are named GS-XGB and GS-CaB. The six algorithms are trained and tested using eight data groups obtained from the feature selection phase. The results show ASA-CaB outperformed all the proposed algorithms with accuracy, precision, recall, and f1 of 83.3%, 83.2%, 83.3%, 83.2%, respectively.

Contextual bandit has been widely used for sequential decision-making based on the current contextual information and historical feedback data. In modern applications, such context format can be rich and can often be formulated as a matrix. Moreover, while existing bandit algorithms mainly focused on reward-maximization, less attention has been paid to the statistical inference. To fill in these gaps, in this work we consider a matrix contextual bandit framework where the true model parameter is a low-rank matrix, and propose a fully online procedure to simultaneously make sequential decision-making and conduct statistical inference. The low-rank structure of the model parameter and the adaptivity nature of the data collection process makes this difficult: standard low-rank estimators are not fully online and are biased, while existing inference approaches in bandit algorithms fail to account for the low-rankness and are also biased. To address these, we introduce a new online doubly-debiasing inference procedure to simultaneously handle both sources of bias. In theory, we establish the asymptotic normality of the proposed online doubly-debiased estimator and prove the validity of the constructed confidence interval. Our inference results are built upon a newly developed low-rank stochastic gradient descent estimator and its non-asymptotic convergence result, which is also of independent interest.

Large language models can perform new tasks in a zero-shot fashion, given natural language prompts that specify the desired behavior. Such prompts are typically hand engineered, but can also be learned with gradient-based methods from labeled data. However, it is underexplored what factors make the prompts effective, especially when the prompts are natural language. In this paper, we investigate common attributes shared by effective prompts. We first propose a human readable prompt tuning method (F LUENT P ROMPT) based on Langevin dynamics that incorporates a fluency constraint to find a diverse distribution of effective and fluent prompts. Our analysis reveals that effective prompts are topically related to the task domain and calibrate the prior probability of label words. Based on these findings, we also propose a method for generating prompts using only unlabeled data, outperforming strong baselines by an average of 7.0% accuracy across three tasks.

In this book chapter, we briefly describe the main components that constitute the gradient descent method and its accelerated and stochastic variants. We aim at explaining these components from a mathematical point of view, including theoretical and practical aspects, but at an elementary level. We will focus on basic variants of the gradient descent method and then extend our view to recent variants, especially variance-reduced stochastic gradient schemes (SGD). Our approach relies on revealing the structures presented inside the problem and the assumptions imposed on the objective function. Our convergence analysis unifies several known results and relies on a general, but elementary recursive expression. We have illustrated this analysis on several common schemes.

Factorization machines (FMs) are a powerful tool for regression and classification in the context of sparse observations, that has been successfully applied to collaborative filtering, especially when side information over users or items is available. Bayesian formulations of FMs have been proposed to provide confidence intervals over the predictions made by the model, however they usually involve Markov-chain Monte Carlo methods that require many samples to provide accurate predictions, resulting in slow training in the context of large-scale data. In this paper, we propose a variational formulation of factorization machines that allows us to derive a simple objective that can be easily optimized using standard mini-batch stochastic gradient descent, making it amenable to large-scale data. Our algorithm learns an approximate posterior distribution over the user and item parameters, which leads to confidence intervals over the predictions. We show, using several datasets, that it has comparable or better performance than existing methods in terms of prediction accuracy, and provide some applications in active learning strategies, e.g., preference elicitation techniques.