Related papers: SOREL: A Stochastic Algorithm for Spectral Risks M…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
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…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy…
Machine learning algorithms with empirical risk minimization are vulnerable under distributional shifts due to the greedy adoption of all the correlations found in training data. There is an emerging literature on tackling this problem by…
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…
While traditional distributionally robust optimization (DRO) aims to minimize the maximal risk over a set of distributions, Agarwal and Zhang (2022) recently proposed a variant that replaces risk with excess risk. Compared to DRO, the new…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
The minimax excess risk optimization (MERO) problem is a new variation of the traditional distributionally robust optimization (DRO) problem, which achieves uniformly low regret across all test distributions under suitable conditions. In…
Sample efficiency remains a major obstacle for real world adoption of reinforcement learning (RL): success has been limited to settings where simulators provide access to essentially unlimited environment interactions, which in reality are…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
We present a uniform analysis of biased stochastic gradient methods for minimizing convex, strongly convex, and non-convex composite objectives, and identify settings where bias is useful in stochastic gradient estimation. The framework we…
Many real-world optimization problems contain parameters that are unknown before deployment time, either due to stochasticity or to lack of information (e.g., demand or travel times in delivery problems). A common strategy in such cases is…
Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is…