Related papers: High Probability Complexity Bounds for Adaptive St…
The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are…
We study the generalization performance of $\text{full-batch}$ optimization algorithms for stochastic convex optimization: these are first-order methods that only access the exact gradient of the empirical risk (rather than gradients with…
There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate.…
We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Consider the problem of minimizing functions that are Lipschitz and strongly convex, but not necessarily differentiable. We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with…
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…
We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…
In this paper we analyze the necessary number of samples to estimate the gradient of any multidimensional smooth (possibly non-convex) function in a zero-order stochastic oracle model. In this model, an estimator has access to noisy values…
This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…
In this paper, we deal with algorithms to solve the finite-sum problems related to fitting over-parametrized models, that typically satisfy the interpolation condition. In particular, we focus on approaches based on stochastic line searches…
This paper presents a sufficient condition for stochastic gradients not to slow down the convergence of Nesterov's accelerated gradient method. The new condition has the strong-growth condition by Schmidt \& Roux as a special case, and it…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
We propose approximately exact line search (AELS), which uses only function evaluations to select a step size within a constant fraction of the exact line search minimizer of a unimodal objective. We bound the number of iterations and…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
Zeroth-order optimization is the process of minimizing an objective $f(x)$, given oracle access to evaluations at adaptively chosen inputs $x$. In this paper, we present two simple yet powerful GradientLess Descent (GLD) algorithms that do…
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…
This paper studies the complexity of projected gradient descent methods for a class of strongly convex constrained optimization problems where the objective function is expressed as a summation of $m$ component functions, each possessing a…
In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…
We study the secure stochastic convex optimization problem. A learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle. In the meantime, there exists an adversary who aims to…