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This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
We introduce a primal-dual stochastic gradient oracle method for distributed convex optimization problems over networks. We show that the proposed method is optimal in terms of communication steps. Additionally, we propose a new analysis…
In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called…
We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…
This paper studies how a stochastic gradient algorithm (SG) can be controlled to hide the estimate of the local stationary point from an eavesdropper. Such problems are of significant interest in distributed optimization settings like…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
We provide a first-order oracle complexity lower bound for finding stationary points of min-max optimization problems where the objective function is smooth, nonconvex in the minimization variable, and strongly concave in the maximization…
Algorithms for bandit convex optimization and online learning often rely on constructing noisy gradient estimates, which are then used in appropriately adjusted first-order algorithms, replacing actual gradients. Depending on the properties…
This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as…
We formulate a private learning model to study an intrinsic tradeoff between privacy and query complexity in sequential learning. Our model involves a learner who aims to determine a scalar value, $v^*$, by sequentially querying an external…
In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…
Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
A landmark result of non-smooth convex optimization is that gradient descent is an optimal algorithm whenever the number of computed gradients is smaller than the dimension $d$. In this paper we study the extension of this result to the…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…