Related papers: Efficient Implementation of Second-Order Stochasti…
We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…
This paper studies the complexity of finding an $\epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
We investigate the problem of finding second-order stationary points (SOSP) in differentially private (DP) stochastic non-convex optimization. Existing methods suffer from two key limitations: (i) inaccurate convergence error rate due to…
There is an increasing need in solving high-dimensional optimization problems under non-deterministic environment. The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
Fractional-order stochastic gradient descent (FOSGD) leverages fractional exponents to capture long-memory effects in optimization. However, its utility is often limited by the difficulty of tuning and stabilizing these exponents. We…
In this paper, we propose several new stochastic second-order algorithms for policy optimization that only require gradient and Hessian-vector product in each iteration, making them computationally efficient and comparable to policy…
Two-time-scale Stochastic Approximation (SA) is an iterative algorithm with applications in reinforcement learning and optimization. Prior finite time analysis of such algorithms has focused on fixed point iterations with mappings…
Scalable machine learning over big data is an important problem that is receiving a lot of attention in recent years. On popular distributed environments such as Hadoop running on a cluster of commodity machines, communication costs are…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Discrete stochastic optimization considers the problem of minimizing (or maximizing) loss functions defined on discrete sets, where only noisy measurements of the loss functions are available. The discrete stochastic optimization problem is…
Service systems are labor intensive due to the large variation in the tasks required to address service requests from multiple customers. Aligning the staffing levels to the forecasted workloads adaptively in such systems is nontrivial…
Policy gradient (PG) is widely used in reinforcement learning due to its scalability and good performance. In recent years, several variance-reduced PG methods have been proposed with a theoretical guarantee of converging to an approximate…
In this paper, we propose a distributed stochastic second-order proximal method that enables agents in a network to cooperatively minimize the sum of their local loss functions without any centralized coordination. The proposed algorithm,…
Simulated annealing (SA) is a well-known algorithm for solving combinatorial optimization problems. However, the computation time of SA increases rapidly, as the size of the problem grows. Recently, a stochastic simulated annealing (SSA)…
Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, $L(\boldsymbol{\theta})$, with respect to a parameter vector $\boldsymbol{\theta}$, when…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems.…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…