Saeed Ghadimi

Stochastic Multi-level Composition Optimization Algorithms with Level-Independent Convergence Rates

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
  • Anthony Nguyen
    • Categories Nonlinear Optimization, Statistics, Stochastic Programming Tags , , ,

    In this paper, we study smooth stochastic multi-level composition optimization problems, where the objective function is a nested composition of $T$ functions. We assume access to noisy evaluations of the functions and their gradients, through a stochastic first-order oracle. For solving this class of problems, we propose two algorithms using moving-average stochastic estimates, and analyze … Read more

    Non-asymptotic Results for Langevin Monte Carlo: Coordinate-wise and Black-box Sampling

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
  • Lingqing Shen
    • Categories Nonlinear Optimization, Statistics Tags , , ,

    Euler-Maruyama and Ozaki discretization of a continuous time diffusion process is a popular technique for sampling, that uses (upto) gradient and Hessian information of the density respectively. The Euler-Maruyama discretization has been used particularly for sampling under the name of Langevin Monte Carlo (LMC) for sampling from strongly log-concave densities. In this work, we make … Read more

    Zeroth-order Nonconvex Stochastic Optimization: Handling Constraints, High-Dimensionality, and Saddle-Points

  • Krishnakumar Balasubramanian
  • Saeed Ghadimi
    • Categories Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting, and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. To … Read more

    A Single Time-Scale Stochastic Approximation Method for Nested Stochastic Optimization

  • Saeed Ghadimi
  • Andrzej Ruszczyński
  • Mengdi Wang
    • Categories Nonlinear Optimization, Stochastic Programming Tags , ,

    We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm … Read more

    Reinforcement Learning via Parametric Cost Function Approximation for Multistage Stochastic Programming

  • Saeed Ghadimi
  • Raymond Perkins
  • Warren B. Powell
    • Categories Applications - OR and Management Sciences, Optimization of Simulated Systems, Stochastic Programming Tags , , , ,

    The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions (“dynamic programming”) or scenario trees (“stochastic programming”) to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier … Read more

    Conditional gradient type methods for composite nonlinear and stochastic optimization

  • Saeed Ghadimi
    • Categories Nonlinear Optimization Tags , , , , ,

    In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While including a strongly convex term in the subproblems of the classical conditional gradient (CG) method improves its rate of … Read more

    Generalized Uniformly Optimal Methods for Nonlinear Programming

  • Saeed Ghadimi
  • Guanghui Lan
  • Hongchao Zhang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , , ,

    In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search step (gradient descent or Quasi-Newton iteration) into these uniformly optimal convex programming methods, and then enforce a monotone decreasing property of … Read more

    Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming

  • Saeed Ghadimi
  • Guanghui Lan
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    In this paper, we generalize the well-known Nesterov’s accelerated gradient (AG) method, originally designed for convex smooth optimization, to solve nonconvex and possibly stochastic optimization problems. We demonstrate that by properly specifying the stepsize policy, the AG method exhibits the best known rate of convergence for solving general nonconvex smooth optimization problems by using first-order … Read more

    Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization

  • Saeed Ghadimi
  • Guanghui Lan
  • Hongchao Zhang
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , , , ,

    This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are … Read more

    Optimal Stochastic Approximation Algorithms for Strongly Convex Stochastic Composite Optimization, II: Shrinking Procedures and Optimal Algorithms

  • Saeed Ghadimi
  • Guanghui Lan
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    In this paper we study new stochastic approximation (SA) type algorithms, namely, the accelerated SA (AC-SA), for solving strongly convex stochastic composite optimization (SCO) problems. Specifically, by introducing a domain shrinking procedure, we significantly improve the large-deviation results associated with the convergence rate of a nearly optimal AC-SA algorithm presented by the authors. Moreover, we … Read more