Online Resource Allocation With General Constraints

TL;DR

This paper extends online resource allocation to include general constraints like ROI, proposing an algorithm with strong regret guarantees and strict constraint satisfaction in both stochastic and adversarial settings.

Contribution

It introduces a novel algorithm that handles both budget and general constraints, achieving best-of-both-world guarantees and strict feasibility.

Findings

Achieves ( ilde{O}(\u221a{T})) regret in stochastic regime.

Achieves ( ilde{O}({{T}})) -regret in adversarial regime.

Guarantees strict budget satisfaction and ( ilde{O}({T})) violation for general constraints.

Abstract

Online resource allocation (ORA) is a fundamental framework for sequential decision-making problems under budget constraints, with applications ranging from online advertising to revenue management. In this work, we study a broader setting that includes both budget constraints and general constraints, extending the classical budget-only model. This extension is essential for modeling critical economic requirements, such as Return-on-Investment (ROI) constraints. We develop an algorithm that achieves best-of-both-world guarantees within this generalized framework. In particular, against a dynamic benchmark, our algorithm achieves $\widetilde{\mathcal O}(\sqrt{T})$ regret in the \emph{stochastic} regime and $\alpha$-regret of order $\widetilde{\mathcal O}(\sqrt{T})$ in the \emph{adversarial} regime, where $\alpha$ depends on the feasibility margin of the corresponding offline problem. At the same time, our algorithm guarantees strict satisfaction of the budget constraints and $\widetilde{\mathcal O}(\sqrt{T})$ cumulative violation for the general ones. From a technical perspective, introducing general constraints alongside budgets precludes the use of standard budget-focus methods. While budget methods rely on a zero-consumption ``safe'' action to ensure feasibility, general constraints are much less ``aligned'' towards feasibility. We overcome these difficulties with a new analysis that exploits \emph{weak adaptivity} to get boundedness of the Lagrangian multipliers and best-of-both-world guarantees.