Zeroth-order (Non)-Convex Stochastic Optimization via Conditional Gradient and Gradient Updates

Authors: Krishnakumar Balasubramanian, Saeed Ghadimi

NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization. Specifically, we propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. Furthermore, under a structural sparsity assumption, we first illustrate an implicit regularization phenomenon where the standard stochastic gradient algorithm with zeroth-order information adapts to the sparsity of the problem at hand by just varying the stepsize. Next, we propose a truncated stochastic gradient algorithm with zeroth-order information, whose rate depends only poly-logarithmically on the dimensionality. Our contributions extend the applicability of zeroth-order stochastic optimization to the constrained and high-dimensional setting and also provide theoretical insights in the form of rates of convergence. A summary of the results is provided in Table 1.
Researcher Affiliation Academia Krishnakumar Balasubramanian Department of Statistics University of California, Davis kbala@ucdavis.edu Saeed Ghadimi Department of Operations Research and Financial Engineering Princeton University sghadimi@princeton.edu
Pseudocode Yes Algorithm 1 Zeroth-order Stochastic Conditional Gradient Method, Algorithm 2 Inexact Conditional Gradient (ICG) method, Algorithm 3 Zeroth-order Stochastic Accelerated Gradient Method with Inexact Updates, Algorithm 4 Zeroth-Order Stochastic Gradient Method, Algorithm 5 Truncated Zeroth-Order Stochastic Gradient Method
Open Source Code No The paper does not provide any explicit statement or link regarding the release of source code for the described methodology.
Open Datasets No The paper is theoretical and does not mention the use of any datasets, public or otherwise, for training or analysis.
Dataset Splits No The paper is theoretical and does not mention any dataset splits for validation or other purposes.
Hardware Specification No The paper is theoretical and does not mention any specific hardware used for running experiments.
Software Dependencies No The paper is theoretical and does not mention any specific software dependencies or version numbers.
Experiment Setup No The paper is theoretical and does not describe an experimental setup, hyperparameters, or system-level training settings.