Related papers: Variance Reduced Online Gradient Descent for Kerne…
A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the…
We prove the familiar Lazy Online Gradient Descent algorithm is universal on polytope domains. That means it gets $O(1)$ pseudo-regret against i.i.d opponents, while simultaneously achieving the well-known $O(\sqrt N)$ worst-case regret…
This paper addresses Online Convex Optimization (OCO) problems where the constraints have additive perturbations that (i) vary over time and (ii) are not known at the time to make a decision. Perturbations may not be i.i.d. generated and…
We study various discrete nonlinear combinatorial optimization problems in an online learning framework. In the first part, we address the question of whether there are negative results showing that getting a vanishing (or even vanishing…
Detecting out-of-distribution (OOD) samples is essential for ensuring the reliability of deep neural networks (DNNs) in real-world scenarios. While previous research has predominantly investigated the disparity between in-distribution (ID)…
Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…
In reinforcement learning (RL), offline learning decoupled learning from data collection and is useful in dealing with exploration-exploitation tradeoff and enables data reuse in many applications. In this work, we study two offline…
We consider distributed online learning for joint regret with communication constraints. In this setting, there are multiple agents that are connected in a graph. Each round, an adversary first activates one of the agents to issue a…
This paper addresses safe distributed online optimization over an unknown set of linear safety constraints. A network of agents aims at jointly minimizing a global, time-varying function, which is only partially observable to each…
Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative. Treating the coupled variables independently while ignoring the interaction, however, leads to an insufficient optimization…
Decentralized Online Learning (online learning in decentralized networks) attracts more and more attention, since it is believed that Decentralized Online Learning can help the data providers cooperatively better solve their online problems…
This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify…
We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties: The degree of sparsity is continuous -- a…
We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex loss, we provide…
In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural…
In this paper, we consider the problem of distributed online convex optimization, where a group of agents collaborate to track the global minimizers of a sum of time-varying objective functions in an online manner. Specifically, we propose…
We consider the problem of learning multiple tasks in a continual learning setting in which data from different tasks is presented to the learner in a streaming fashion. A key challenge in this setting is the so-called "catastrophic…
We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the…