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We study without-replacement SGD for solving finite-sum optimization problems. Specifically, depending on how the indices of the finite-sum are shuffled, we consider the RandomShuffle (shuffle at the beginning of each epoch) and…

Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…

A long-standing problem in the theory of stochastic gradient descent (SGD) is to prove that its without-replacement version RandomShuffle converges faster than the usual with-replacement version. We present the first (to our knowledge)…

Recently, there has been much interest in studying the convergence rates of without-replacement SGD, and proving that it is faster than with-replacement SGD in the worst case. However, known lower bounds ignore the problem's geometry,…

When solving finite-sum minimization problems, two common alternatives to stochastic gradient descent (SGD) with theoretical benefits are random reshuffling (SGD-RR) and shuffle-once (SGD-SO), in which functions are sampled in cycles…

We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with…

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms…

We uncover how SGD interacts with batch normalization and can exhibit undesirable training dynamics such as divergence. More precisely, we study how Single Shuffle (SS) and Random Reshuffle (RR) -- two widely used variants of SGD --…

Modern machine learning models are often over-parameterized and as a result they can interpolate the training data. Under such a scenario, we study the convergence properties of a sampling-without-replacement variant of stochastic gradient…

While SGD, which samples from the data with replacement is widely studied in theory, a variant called Random Reshuffling (RR) is more common in practice. RR iterates through random permutations of the dataset and has been shown to converge…

In distributed learning, local SGD (also known as federated averaging) and its simple baseline minibatch SGD are widely studied optimization methods. Most existing analyses of these methods assume independent and unbiased gradient estimates…

We study the convergence of the shuffling gradient method, a popular algorithm employed to minimize the finite-sum function with regularization, in which functions are passed to apply (Proximal) Gradient Descent (GD) one by one whose order…

A recent line of ground-breaking results for permutation-based SGD has corroborated a widely observed phenomenon: random permutations offer faster convergence than with-replacement sampling. However, is random optimal? We show that this…

Shuffling strategies for stochastic gradient descent (SGD), including incremental gradient, shuffle-once, and random reshuffling, are supported by rigorous convergence analyses for arbitrary within-epoch permutations. In particular, random…

We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific…

Stochastic optimization algorithms have become indispensable in modern machine learning. An unresolved foundational question in this area is the difference between with-replacement sampling and without-replacement sampling -- does the…

We analyze the convergence rate of the random reshuffling (RR) method, which is a randomized first-order incremental algorithm for minimizing a finite sum of convex component functions. RR proceeds in cycles, picking a uniformly random…

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

Optimization objectives in the form of a sum of intractable expectations are rising in importance (e.g., diffusion models, variational autoencoders, and many more), a setting also known as "finite sum with infinite data." For these…

We analyze the convergence rates of stochastic gradient algorithms for smooth finite-sum minimax optimization and show that, for many such algorithms, sampling the data points without replacement leads to faster convergence compared to…