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This paper presents a new generalization error analysis for Decentralized Stochastic Gradient Descent (D-SGD) based on algorithmic stability. The obtained results overhaul a series of recent works that suggested an increased instability due…
Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators. In such…
Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical…
Low-rank matrix completion has achieved great success in many real-world data applications. A matrix factorization model that learns latent features is usually employed and, to improve prediction performance, the similarities between latent…
The success of minimax learning problems of generative adversarial networks (GANs) has been observed to depend on the minimax optimization algorithm used for their training. This dependence is commonly attributed to the convergence speed…
Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which has been shown to be crucial for attaining fast convergence in games and robustness in stochastic…
We study learning to learn for regression problems through the lens of hyperparameter tuning. We propose the Langevin Gradient Descent Algorithm (LGD), which approximates the mean of the posterior distribution defined by the loss function…
While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step…
A common way to learn and analyze statistical models is to consider operations in the model parameter space. But what happens if we optimize in the parameter space and there is no one-to-one mapping between the parameter space and the…
There is a growing interest in using robust control theory to analyze and design optimization and machine learning algorithms. This paper studies a class of nonconvex optimization problems whose cost functions satisfy the so-called…
Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…
In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution at a linear convergence rate for the quadratic loss…
This work proposes an efficient batch algorithm for feature selection in reinforcement learning (RL) with theoretical convergence guarantees. To mitigate the estimation bias inherent in conventional regularization schemes, the first…
In this paper, we propose the Graph-Fused Multivariate Regression (GFMR) via Total Variation regularization, a novel method for estimating the association between a one-dimensional or multidimensional array outcome and scalar predictors.…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
In this paper we investigate the generalization error of gradient descent (GD) applied to an $\ell_2$-regularized OLS objective function in the linear model. Based on our analysis we develop new methodology for computationally tractable and…
We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…
In federated learning (FL), a cluster of local clients are chaired under the coordination of the global server and cooperatively train one model with privacy protection. Due to the multiple local updates and the isolated non-iid dataset,…
The primary goal of reinforcement learning is to develop decision-making policies that prioritize optimal performance, frequently without considering safety. In contrast, safe reinforcement learning seeks to reduce or avoid unsafe behavior.…
Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the…