Related papers: On the Convergence of Single-Loop Stochastic Bilev…
We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
Bilevel optimization problems consist of minimizing a value function whose evaluation depends on the solution of an inner optimization problem. These problems are typically tackled using first-order methods that require computing the…
In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…
This paper studies the unconstrained nonconvex-strongly-convex bilevel optimization problem. A common approach to solving this problem is to alternately update the upper-level and lower-level variables using (biased) stochastic gradients or…
We introduce a novel and efficient algorithm called the stochastic approximate gradient descent (SAGD), as an alternative to the stochastic gradient descent for cases where unbiased stochastic gradients cannot be trivially obtained.…
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…
We aim to make stochastic gradient descent (SGD) adaptive to (i) the noise $\sigma^2$ in the stochastic gradients and (ii) problem-dependent constants. When minimizing smooth, strongly-convex functions with condition number $\kappa$, we…
Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…
This paper considers stochastic first-order algorithms for convex-concave minimax problems of the form $\min_{\bf x}\max_{\bf y}f(\bf x, \bf y)$, where $f$ can be presented by the average of $n$ individual components which are $L$-average…
Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings…
Recent advances in end-to-end autonomous driving show that policies trained on patch-aligned features extracted from foundation models generalize better to Out-of-Distribution (OOD). We hypothesize that due to the self-attention mechanism,…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the…
We develop and analyze a single-loop algorithm for minimizing the sum of a Lipschitz differentiable function $f$, a prox-friendly proper closed function $g$ (with a closed domain on which $g$ is continuous) and the composition of another…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…
We study stochastic convex optimization under infinite noise variance. Specifically, when the stochastic gradient is unbiased and has uniformly bounded $(1+\kappa)$-th moment, for some $\kappa \in (0,1]$, we quantify the convergence rate of…
While variance reduction methods have shown great success in solving large scale optimization problems, many of them suffer from accumulated errors and, therefore, should periodically require the full gradient computation. In this paper, we…
Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging, we…
Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…