Log In Sign Up

Convergence rates of the stochastic alternating algorithm for bi-objective optimization

by   Suyun Liu, et al.

Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a certain number of steps of gradient or subgradient descent on each single objective at each iteration. In this paper, we show that stochastic alternating algorithms achieve a sublinear convergence rate of 𝒪(1/T), under strong convexity, for the determination of a minimizer of a weighted-sum of the two functions, parameterized by the number of steps applied on each of them. An extension to the convex case is presented for which the rate weakens to 𝒪(1/√(T)). These rates are valid also in the non-smooth case. Importantly, by varying the proportion of steps applied to each function, one can determine an approximation to the Pareto front.


page 1

page 2

page 3

page 4


A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering

In the application of data clustering to human-centric decision-making s...

Almost Sure Convergence Rates of Stochastic Zeroth-order Gradient Descent for Łojasiewicz Functions

We prove almost sure convergence rates of Zeroth-order Gradient Descent ...

On the Global Linear Convergence of Frank-Wolfe Optimization Variants

The Frank-Wolfe (FW) optimization algorithm has lately re-gained popular...

A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates

This paper considers the problem of decentralized optimization with a co...

Blended Matching Pursuit

Matching pursuit algorithms are an important class of algorithms in sign...

Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPL...

Novel bi-objective optimization algorithms minimizing the max and sum of vectors of functions

We study a bi-objective optimization problem, which for a given positive...