Projection-Free Algorithm for Stochastic Bi-level Optimization

10/22/2021
by   Zeeshan Akhtar, et al.
0

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed Stochastic Bi-level Frank-Wolfe (SBFW) algorithm can be applied to streaming settings and does not make use of large batches or checkpoints. The sample complexity of SBFW is shown to be 𝒪(ϵ^-3) for convex objectives and 𝒪(ϵ^-4) for non-convex objectives. Improved rates are derived for the stochastic compositional problem, which is a special case of the bi-level problem, and entails minimizing the composition of two expected-value functions. The proposed Stochastic Compositional Frank-Wolfe (SCFW) is shown to achieve a sample complexity of 𝒪(ϵ^-2) for convex objectives and 𝒪(ϵ^-3) for non-convex objectives, at par with the state-of-the-art sample complexities for projection-free algorithms solving single-level problems. We demonstrate the advantage of the proposed methods by solving the problem of matrix completion with denoising and the problem of policy value evaluation in reinforcement learning.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/15/2022

Optimal Algorithms for Stochastic Multi-Level Compositional Optimization

In this paper, we investigate the problem of stochastic multi-level comp...
05/05/2021

Randomized Stochastic Variance-Reduced Methods for Stochastic Bilevel Optimization

In this paper, we consider non-convex stochastic bilevel optimization (S...
12/19/2019

Zeroth-order Stochastic Compositional Algorithms for Risk-Aware Learning

We present Free-MESSAGEp, the first zeroth-order algorithm for convex me...
08/26/2019

Stochastic Optimization for Non-convex Inf-Projection Problems

In this paper, we study a family of non-convex and possibly non-smooth i...
04/27/2017

Optimal Sample Complexity for Matrix Completion and Related Problems via ℓ_2-Regularization

We study the strong duality of non-convex matrix factorization: we show ...
06/15/2021

A Value-Function-based Interior-point Method for Non-convex Bi-level Optimization

Bi-level optimization model is able to capture a wide range of complex l...
02/24/2022

Finite-Sum Compositional Stochastic Optimization: Theory and Applications

This paper studies stochastic optimization for a sum of compositional fu...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.