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The analysis of online least squares estimation is at the heart of many stochastic sequential decision making problems. We employ tools from the self-normalized processes to provide a simple and self-contained proof of a tail bound of a…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…

Optimization models used to make discrete decisions often contain uncertain parameters that are context-dependent and estimated through prediction. To account for the quality of the decision made based on the prediction, decision-focused…

The ELM method has become widely used for classification and regressions problems as a result of its accuracy, simplicity and ease of use. The solution of the hidden layer weights by means of a matrix pseudoinverse operation is a…

Backpropagation is the default learning rule for artificial neural networks and is often treated as the settled approach whenever differentiability is available. In this work, we revisit this convention through a theoretical lens of sample…

Pairwise learning refers to learning tasks where the loss function depends on a pair of instances. It instantiates many important machine learning tasks such as bipartite ranking and metric learning. A popular approach to handle streaming…

We introduce a new recursive aggregation procedure called Bernstein Online Aggregation (BOA). The exponential weights include an accuracy term and a second order term that is a proxy of the quadratic variation as in Hazan and Kale (2010).…

We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then…

The great success neural networks have achieved is inseparable from the application of gradient-descent (GD) algorithms. Based on GD, many variant algorithms have emerged to improve the GD optimization process. The gradient for…

We propose an online parametric estimation method of stochastic differential equations with discrete observations and misspecified modelling based on online gradient descent. Our study provides uniform upper bounds for the risks of the…

In computational neuroscience, fixed points of recurrent neural networks are commonly used to model neural responses to static or slowly changing stimuli. These applications raise the question of how to train the weights in a recurrent…

The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

We show that for a general class of convex online learning problems, Mirror Descent can always achieve a (nearly) optimal regret guarantee.

Gradient descent has been a central training principle for artificial neural networks from the early beginnings to today's deep learning networks. The most common implementation is the backpropagation algorithm for training feed-forward…

Bayesian inference is known to provide a general framework for incorporating prior knowledge or specific properties into machine learning models via carefully choosing a prior distribution. In this work, we propose a new type of prior…

With the prosperity of mobile devices, the distributed learning approach enabling model training with decentralized data has attracted wide research. However, the lack of training capability for edge devices significantly limits the energy…

We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for…

We study nonstationary generalized linear bandits (GLBs), where the expected reward is modeled through a nonlinear link function with an unknown time-varying parameter. This framework encompasses a broad class of reward models, including…