Related papers: Online Gradient Descent in Function Space

In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…

Any gradient descent optimization requires to choose a learning rate. With deeper and deeper models, tuning that learning rate can easily become tedious and does not necessarily lead to an ideal convergence. We propose a variation of the…

In this paper, we study a Markov chain-based stochastic gradient algorithm in general Hilbert spaces, aiming at approximating the optimal solution of a quadratic loss function. We establish probabilistic upper bounds on its convergence. We…

In this paper we study the convergence of online gradient descent algorithms in reproducing kernel Hilbert spaces (RKHSs) without regularization. We establish a sufficient condition and a necessary condition for the convergence of excess…

In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…

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,…

Online learning algorithms are fast, memory-efficient, easy to implement, and applicable to many prediction problems, including classification, regression, and ranking. Several online algorithms were proposed in the past few decades, some…

We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…

We propose a decentralized online learning algorithm for distributed random inverse problems over network graphs with online measurements, and unifies the distributed parameter estimation in Hilbert spaces and the least mean square problem…

We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable,…

We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that…

We consider a natural model of online preference aggregation, where sets of preferred items $R_1, R_2, \ldots, R_t$ along with a demand for $k_t$ items in each $R_t$, appear online. Without prior knowledge of $(R_t, k_t)$, the learner…

Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along.…

In this paper, we study the online learning algorithm without explicit regularization terms. This algorithm is essentially a stochastic gradient descent scheme in a reproducing kernel Hilbert space (RKHS). The polynomially decaying step…

One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value…

Online learning to rank (OL2R) optimizes the utility of returned search results based on implicit feedback gathered directly from users. To improve the estimates, OL2R algorithms examine one or more exploratory gradient directions and…

Many real-world data are sequentially collected over time and often exhibit skewed class distributions, resulting in imbalanced data streams. While existing approaches have explored several strategies, such as resampling and reweighting,…

This article provides convergence analysis of online stochastic gradient descent algorithms for functional linear models. Adopting the characterizations of the slope function regularity, the kernel space capacity, and the capacity of the…

We analyze and evaluate an online gradient descent algorithm with adaptive per-coordinate adjustment of learning rates. Our algorithm can be thought of as an online version of batch gradient descent with a diagonal preconditioner. This…