相关论文: On-line PCA with Optimal Regrets

We consider online convex optimization with time-varying stage costs and additional switching costs. Since the switching costs introduce coupling across all stages, multi-step-ahead (long-term) predictions are incorporated to improve the…

We consider the problem of the Zinkevich (2003)-style dynamic regret minimization in online learning with exp-concave losses. We show that whenever improper learning is allowed, a Strongly Adaptive online learner achieves the dynamic regret…

Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing modalities such as cameras. In this paper, we tailor the…

Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality,…

In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter $\beta_{1}$ (typically between $0.9$ and $0.99$). In…

We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation…

In this paper, we consider the problem of distributed online convex optimization, where a network of local agents aim to jointly optimize a convex function over a period of multiple time steps. The agents do not have any information about…

Online learning aims to perform nearly as well as the best hypothesis in hindsight. For some hypothesis classes, though, even finding the best hypothesis offline is challenging. In such offline cases, local search techniques are often…

Adversarial attacks on deep neural network models have seen rapid development and are extensively used to study the stability of these networks. Among various adversarial strategies, Projected Gradient Descent (PGD) is a widely adopted…

We investigate distributed online convex optimization with compressed communication, where $n$ learners connected by a network collaboratively minimize a sequence of global loss functions using only local information and compressed data…

In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it…

Gradient Descent Ascent (GDA) methods are the mainstream algorithms for minimax optimization in generative adversarial networks (GANs). Convergence properties of GDA have drawn significant interest in the recent literature. Specifically,…

The trade-off between regret and computational cost is a fundamental problem for online kernel regression, and previous algorithms worked on the trade-off can not keep optimal regret bounds at a sublinear computational complexity. In this…

We revisit the problem of online learning with sleeping experts/bandits: in each time step, only a subset of the actions are available for the algorithm to choose from (and learn about). The work of Kleinberg et al. (2010) showed that there…

The generalization mystery of overparametrized deep nets has motivated efforts to understand how gradient descent (GD) converges to low-loss solutions that generalize well. Real-life neural networks are initialized from small random values…

This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret…

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow…

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral…

A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better…

This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number…