16 accepted papers
Adaptive methods like Adam have become the *de facto* standard for large-scale vector and Euclidean optimization due to their coordinate-wise adaptation with a second-order nature. More recently, matrix-based spectral optimizers like Muon (Jordan et al., 2024b) show the power of treating weight matr…
We develop optimization methods which offer new trade-offs between the number of gradient and Hessian computations needed to compute the critical point of a non-convex function. We provide a method that for a twice-differentiable $f\colon \mathbb{R}^d \rightarrow \mathbb{R}$ with $L_2$-Lipschitz Hes…
Model immunization aims to pre-train models that are difficult to fine-tune on harmful tasks while retaining their utility on other non-harmful tasks. Though prior work has shown empirical evidence for immunizing text-to-image models, the key understanding of when immunization is possible and a prec…
While popular optimization methods such as SGD, AdamW, and Lion depend on steepest descent updates in either $\ell_2$ or $\ell_\infty$ norms, there remains a critical gap in handling the non-Euclidean structure observed in modern deep networks training. In this work, we address this need by introduc…
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order Hölder smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are Hölder continuous with degree $\nu$ and parameter $H$, and that is uniformly convex with deg…
Distributed optimization (DO) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean space, whereas ML problems often involve constraints or n…
We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO), a gradient-based method that incorporates the interactions between two players in zero-sum games for its iterative updates. We provide a continuous-time analysis of CGO an…
We resolve the min-max complexity of distributed stochastic convex optimization (up to a log factor) in the intermittent communication setting, where M machines work in parallel over the course of R rounds of communication to optimize the objective, and during each round of communication, each machi…
We study the problem of distributed stochastic non-convex optimization with intermittent communication. We consider the full participation setting where $M$ machines work in parallel over $R$ communication rounds and the partial participation setting where $M$ machines are sampled independently ever…
We propose and analyze a stochastic Newton algorithm for homogeneous distributed stochastic convex optimization, where each machine can calculate stochastic gradients of the same population objective, as well as stochastic Hessian-vector products (products of an independent unbiased estimator of the…
We provide several algorithms for constrained optimization of a large class of convex problems, including softmax, $\ell_p$ regression, and logistic regression. Central to our approach is the notion of width reduction, a technique which has proven immensely useful in the context of maximum flow [Chr…
We study local SGD (also known as parallel SGD and federated SGD), a natural and frequently used distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch S…
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to mak…
We study the control of linear dynamical systems with adversarial disturbances, as opposed to statistical noise. We present an efficient algorithm that achieves nearly-tight regret bounds in this setting. Our result generalizes upon previous work in two main aspects: the algorithm can accommodate ad…
We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and gener…
We study regression and classification in a setting where the learning algorithm is allowed to access only a limited number of attributes per example, known as the limited attribute observation model. In this well-studied model, we provide the first lower bounds giving a limit on the precision attai…