# Competitive Algorithms for Online Budget-Constrained Continuous DR-Submodular Problems

## TL;DR

This paper introduces a primal-dual algorithm for online optimization of DR-submodular functions under budget constraints, achieving a competitive ratio that matches the best known bounds in special cases.

## Contribution

It provides the first competitive ratio bound for online monotone DR-submodular maximization with linear packing constraints, extending prior results.

## Key findings

- First bound on competitive ratio for this class of problems
- Matches tight bounds in the linear case
- Applicable to online monotone DR-submodular maximization

## Abstract

In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain the first bound on the competitive ratio of online monotone DR-submodular function maximization subject to linear packing constraints which matches the known tight bound in the special case of linear objective function.