Related papers: A general sample complexity analysis of vanilla po…

Stochastic gradient descent (SGD) is the workhorse of large-scale learning, yet classical analyses rely on assumptions that can be either too strong (bounded variance) or too coarse (uniform noise). The expected smoothness (ES) condition…

The vast majority of convergence rates analysis for stochastic gradient methods in the literature focus on convergence in expectation, whereas trajectory-wise almost sure convergence is clearly important to ensure that any instantiation of…

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an…

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

We study estimation of a gradient-sparse parameter vector $\boldsymbol{\theta}^* \in \mathbb{R}^p$, having strong gradient-sparsity $s^*:=\|\nabla_G \boldsymbol{\theta}^*\|_0$ on an underlying graph $G$. Given observations $Z_1,\ldots,Z_n$…

Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…

In this paper, we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free…

We consider stochastic gradient descent algorithms for minimizing a non-smooth, strongly-convex function. Several forms of this algorithm, including suffix averaging, are known to achieve the optimal $O(1/T)$ convergence rate in…

Several emerging post-Bayesian methods target a probability distribution for which an entropy-regularised variational objective is minimised. This increased flexibility introduces a computational challenge, as one loses access to an…

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…

There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…

Projected policy gradient (PPG) is a basic policy optimization method in reinforcement learning. Given access to exact policy evaluations, previous studies have established the sublinear convergence of PPG for sufficiently small step sizes…

Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference…

Despite recent theoretical progress on the non-convex optimization of two-layer neural networks, it is still an open question whether gradient descent on neural networks without unnatural modifications can achieve better sample complexity…

Approximate Bayesian Computation (ABC) is a powerful method for carrying out Bayesian inference when the likelihood is computationally intractable. However, a drawback of ABC is that it is an approximate method that induces a systematic…

In distributed learning, a central server trains a model according to updates provided by nodes holding local data samples. In the presence of one or more malicious servers sending incorrect information (a Byzantine adversary), standard…

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…

This work revisits standard policy gradient methods used on restricted policy classes, which are known to get stuck in suboptimal critical points. We identify an important cause for this phenomenon to be that the policy gradient is itself…

This work establishes new convergence guarantees for gradient descent in smooth convex optimization via a computer-assisted analysis technique. Our theory allows nonconstant stepsize policies with frequent long steps potentially violating…

The policy gradient approach is a flexible and powerful reinforcement learning method particularly for problems with continuous actions such as robot control. A common challenge in this scenario is how to reduce the variance of policy…