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Kfir Y. Levy

Kfir Y. Levy appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine Learningmath.OC

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Published work

8 published item(s)

preprint2026arXiv

Bringing Order to Asynchronous SGD: Towards Optimality under Data-Dependent Delays with Momentum

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically attenuate or discard delayed gradients, introducing systematic bias: updates from simpler or faster-to-process samples are overrepresented, while gradients from more complex samples are delayed or suppressed. In contrast, prior approaches to data-dependent delays rely on a Lipschitz assumption that yields suboptimal rates or leave the smooth, convex case unaddressed. We propose a momentum-based asynchronous framework designed to preserve information from delayed gradients while mitigating the effects of staleness. We establish the first optimal convergence rates for data-dependent delays in both convex and non-convex smooth setups, providing a new result for asynchronous optimization under standard assumptions. Additionally, we derive robust learning-rate schedules that simplify hyperparameter tuning in practice.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A universal black-box optimization method with almost dimension-free convergence rate guarantees

Universal methods for optimization are designed to achieve theoretically optimal convergence rates without any prior knowledge of the problem's regularity parameters or the accurarcy of the gradient oracle employed by the optimizer. In this regard, existing state-of-the-art algorithms achieve an $\mathcal{O}(1/T^2)$ value convergence rate in Lipschitz smooth problems with a perfect gradient oracle, and an $\mathcal{O}(1/\sqrt{T})$ convergence rate when the underlying problem is non-smooth and/or the gradient oracle is stochastic. On the downside, these methods do not take into account the problem's dimensionality, and this can have a catastrophic impact on the achieved convergence rate, in both theory and practice. Our paper aims to bridge this gap by providing a scalable universal gradient method - dubbed UnderGrad - whose oracle complexity is almost dimension-free in problems with a favorable geometry (like the simplex, linearly constrained semidefinite programs and combinatorial bandits), while retaining the order-optimal dependence on $T$ described above. These "best-of-both-worlds" results are achieved via a primal-dual update scheme inspired by the dual exploration method for variational inequalities.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Online Meta-Learning in Adversarial Multi-Armed Bandits

We study meta-learning for adversarial multi-armed bandits. We consider the online-within-online setup, in which a player (learner) encounters a sequence of multi-armed bandit episodes. The player's performance is measured as regret against the best arm in each episode, according to the losses generated by an adversary. The difficulty of the problem depends on the empirical distribution of the per-episode best arm chosen by the adversary. We present an algorithm that can leverage the non-uniformity in this empirical distribution, and derive problem-dependent regret bounds. This solution comprises an inner learner that plays each episode separately, and an outer learner that updates the hyper-parameters of the inner algorithm between the episodes. In the case where the best arm distribution is far from uniform, it improves upon the best bound that can be achieved by any online algorithm executed on each episode individually without meta-learning.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Robust Linear Regression for General Feature Distribution

We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been previously analyzed under strong assumptions. Concretely, $\textbf{(i)}$ all previous works assume that the covariance matrix of the features is positive definite; and $\textbf{(ii)}$ most of them assume that the features are centered (i.e. zero mean). Additionally, all previous works make additional restrictive assumption, e.g., assuming that the features are Gaussian or that the corruptions are symmetrically distributed. In this work we go beyond these assumptions and investigate robust regression under a more general set of assumptions: $\textbf{(i)}$ we allow the covariance matrix to be either positive definite or positive semi definite, $\textbf{(ii)}$ we do not necessarily assume that the features are centered, $\textbf{(iii)}$ we make no further assumption beyond boundedness (sub-Gaussianity) of features and measurement noise. Under these assumption we analyze a natural SGD variant for this problem and show that it enjoys a fast convergence rate when the covariance matrix is positive definite. In the positive semi definite case we show that there are two regimes: if the features are centered we can obtain a standard convergence rate; otherwise the adversary can cause any learner to fail arbitrarily.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

The Power of Normalization: Faster Evasion of Saddle Points

A commonly used heuristic in non-convex optimization is Normalized Gradient Descent (NGD) - a variant of gradient descent in which only the direction of the gradient is taken into account and its magnitude ignored. We analyze this heuristic and show that with carefully chosen parameters and noise injection, this method can provably evade saddle points. We establish the convergence of NGD to a local minimum, and demonstrate rates which improve upon the fastest known first order algorithm due to Ge e al. (2015). The effectiveness of our method is demonstrated via an application to the problem of online tensor decomposition; a task for which saddle point evasion is known to result in convergence to global minima.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Beyond Convexity: Stochastic Quasi-Convex Optimization

Stochastic convex optimization is a basic and well studied primitive in machine learning. It is well known that convex and Lipschitz functions can be minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves. In this paper we analyze a stochastic version of NGD and prove its convergence to a global minimum for a wider class of functions: we require the functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens the con- cept of unimodality to multidimensions and allows for certain types of saddle points, which are a known hurdle for first-order optimization methods such as gradient descent. Locally-Lipschitz functions are only required to be Lipschitz in a small region around the optimum. This assumption circumvents gradient explosion, which is another known hurdle for gradient descent variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic normalized gradient descent algorithm provably requires a minimal minibatch size.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

On Graduated Optimization for Stochastic Non-Convex Problems

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms of theoretical convergence analysis. In this paper we describe a new first-order algorithm based on graduated optimiza- tion and analyze its performance. We characterize a parameterized family of non- convex functions for which this algorithm provably converges to a global optimum. In particular, we prove that the algorithm converges to an ε-approximate solution within O(1/ε^2) gradient-based steps. We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate. Additionally, we discuss the setting of zero-order optimization, and devise a a variant of our algorithm which converges at rate of O(d^2/ε^4).

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Logistic Regression: Tight Bounds for Stochastic and Online Optimization

The logistic loss function is often advocated in machine learning and statistics as a smooth and strictly convex surrogate for the 0-1 loss. In this paper we investigate the question of whether these smoothness and convexity properties make the logistic loss preferable to other widely considered options such as the hinge loss. We show that in contrast to known asymptotic bounds, as long as the number of prediction/optimization iterations is sub exponential, the logistic loss provides no improvement over a generic non-smooth loss function such as the hinge loss. In particular we show that the convergence rate of stochastic logistic optimization is bounded from below by a polynomial in the diameter of the decision set and the number of prediction iterations, and provide a matching tight upper bound. This resolves the COLT open problem of McMahan and Streeter (2012).

0 citations0 reviewsNo code linkedOpen access