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We study the training dynamics of shallow neural networks, in a two-timescale regime in which the stepsizes for the inner layer are much smaller than those for the outer layer. In this regime, we prove convergence of the gradient flow to a…
Recent studies observed a surprising concept on model test error called the double descent phenomenon, where the increasing model complexity decreases the test error first and then the error increases and decreases again. To observe this,…
Future prediction is a fundamental principle of intelligence that helps plan actions and avoid possible dangers. As the future is uncertain to a large extent, modeling the uncertainty and multimodality of the future states is of great…
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…
Educational policymakers often lack data on student outcomes where standardized tests were not administered. Machine learning can predict unobserved outcomes in target populations using source population data. However, covariate…
Softmax is the most commonly used output function for multiclass problems and is widely used in areas such as vision, natural language processing, and recommendation. A softmax model has linear costs in the number of classes which makes it…
A continual learning agent learns online with a non-stationary and never-ending stream of data. The key to such learning process is to overcome the catastrophic forgetting of previously seen data, which is a well known problem of neural…
This paper studies directed exploration for reinforcement learning agents by tracking uncertainty about the value of each available action. We identify two sources of uncertainty that are relevant for exploration. The first originates from…
The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm…
A model among many may only be best under certain states of the world. Switching from a model to another can also be costly. Finding a procedure to dynamically choose a model in these circumstances requires to solve a complex estimation…
The reinforcement learning algorithms that focus on how to compute the gradient and choose next actions, are effectively improved the performance of the agents. However, these algorithms are environment-agnostic. This means that the…
Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may…
Although recent model-free reinforcement learning algorithms have been shown to be capable of mastering complicated decision-making tasks, the sample complexity of these methods has remained a hurdle to utilizing them in many real-world…
Negative sampling approaches are prevalent in implicit collaborative filtering for obtaining negative labels from massive unlabeled data. As two major concerns in negative sampling, efficiency and effectiveness are still not fully achieved…
In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine learning as a coding and dimensionality reduction problem, and further proposed a simple unsupervised dimensionality reduction method, entitled deep distributed…
Stochastic control with both inherent random system noise and lack of knowledge on system parameters constitutes the core and fundamental topic in reinforcement learning (RL), especially under non-episodic situations where online learning…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…