arXiv research

Paper tackles NNS under uncertainty with improved algorithms.

New algorithm finds k-centers from noisy distance estimates.

New oracles improve stochastic optimization with noisy or biased measurements.

Algorithm identifies nearest mode in noisy data.

New lower bounds for bilevel optimization with first-order oracles.

We give nearly matching upper and lower bounds on the oracle complexity of finding $ε$-stationary points ($\| \nabla F(x) \| \leqε$) in stochastic convex optimization. We jointly analyze the oracle complexity in both the local stochastic oracle model and the global oracle (or, statistical learning) model. This allows u…

Semi-supervised active clustering (SSAC) utilizes the knowledge of a domain expert to cluster data points by interactively making pairwise "same-cluster" queries. However, it is impractical to ask human oracles to answer every pairwise query. In this paper, we study the influence of allowing "not-sure" answers from a w…

New algorithms solve stochastic variational inequalities without bounded variance assumption.

In the machine learning and optimization community, there are two main approaches for the convex risk minimization problem, namely, the Stochastic Approximation (SA) and the Sample Average Approximation (SAA). In terms of oracle complexity (required number of stochastic gradient evaluations), both approaches are consid…

Vanilla GANs are connected to Wasserstein distance for better understanding.

We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive lower bounds for several specific parallel optimization settings, including delayed …

Extracts fairness truth from classifiers using an oracle.

We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We p…

Improved stochastic Halpern iteration for fixed-point approximation in normed spaces.

Pairwise "same-cluster" queries are one of the most widely used forms of supervision in semi-supervised clustering. However, it is impractical to ask human oracles to answer every query correctly. In this paper, we study the influence of allowing "not-sure" answers from a weak oracle and propose an effective algorithm …

New algorithms solve non-convex optimization problems efficiently.

Paper tackles noisy comparison oracle for robust clustering algorithms.

Paper proposes a new method to stabilize noisy gradient algorithms.

We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and va…

Improved stochastic approximation method reduces residual error.

The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.

New tool for parallel and private stochastic convex optimization reduces query complexity.

Momentum methods such as Polyak's heavy ball (HB) method, Nesterov's accelerated gradient (AG) as well as accelerated projected gradient (APG) method have been commonly used in machine learning practice, but their performance is quite sensitive to noise in the gradients. We study these methods under a first-order stoch…

Improved complexity for machine learning optimization methods.

We present a generic framework for trading off fidelity and cost in computing stochastic gradients when the costs of acquiring stochastic gradients of different quality are not known a priori. We consider a mini-batch oracle that distributes a limited query budget over a number of stochastic gradients and aggregates th…

New method tackles endogeneity in online learning with improved regret bounds.

Improved Frank-Wolfe algorithm for constrained convex optimization with nearest extreme point oracle.

New algorithm solves complex optimization problems without needing projections.

A new hybrid algorithm reduces stochastic gradient evaluations for nonconvex optimization.

Paper addresses online alignment of large language models under uncertain preference feedback.

Study how noisy labels affect semi-supervised learning.

Relative to the large literature on upper bounds on complexity of convex optimization, lesser attention has been paid to the fundamental hardness of these problems. Given the extensive use of convex optimization in machine learning and statistics, gaining an understanding of these complexity-theoretic issues is importa…

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove an information theoretic lower bound on the number of stochastic gradient queries of the log density needed. Several popular sampling algorithms (including many Markov chain Monte Carlo methods) operate by using stochas…

New algorithm samples from log-concave distributions with high accuracy in polynomial time.

New methods optimize complex optimization problems with improved efficiency.

A new method reduces the complexity of decentralized optimization.

In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a …

SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an accuracy-dependent stepsize that slows down the convergence in practice, and cannot handle objec…

Sampling with Markov chain Monte Carlo methods often amounts to discretizing some continuous-time dynamics with numerical integration. In this paper, we establish the convergence rate of sampling algorithms obtained by discretizing smooth Itô diffusions exhibiting fast Wasserstein-$2$ contraction, based on local deviat…

Designing deterministic denominators for SGLD stabilizes large drifts.

Algorithm samples composite logconcave densities efficiently.

New method removes oracle and reduces memory usage for robust MDPs.

New algorithms ensure reproducibility and optimal convergence in convex optimization.

Improved MALA method for neural networks uncertainty quantification.

We present a probabilistic modeling framework and adaptive sampling algorithm wherein unsupervised generative models are combined with black box predictive models to tackle the problem of input design. In input design, one is given one or more stochastic "oracle" predictive functions, each of which maps from the input …

Study efficient algorithms for nonconvex optimization with state-dependent Markov data.

In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…

VR-GHAL method solves stochastic fixed-point equations with high probability.