Joint Pricing and Resource Allocation: An Optimal Online-Learning Approach

TL;DR

This paper introduces an optimal online-learning algorithm for joint pricing and resource allocation, effectively handling demand stochasticity and non-convexity to maximize profit with proven regret bounds.

Contribution

It develops a novel LCB-based meta-strategy algorithm that achieves optimal regret in dynamic pricing and resource allocation with stochastic demand.

Findings

Achieves $ ilde{O}( oot{T}mn)$ regret, proven to be optimal.

Effectively handles demand dependence and non-convexity.

Integrates statistical learning with complex operations research problems.

Abstract

We study an online learning problem on dynamic pricing and resource allocation, where we make joint pricing and inventory decisions to maximize the overall net profit. We consider the stochastic dependence of demands on the price, which complicates the resource allocation process and introduces significant non-convexity and non-smoothness to the problem. To solve this problem, we develop an efficient algorithm that utilizes a "Lower-Confidence Bound (LCB)" meta-strategy over multiple OCO agents. Our algorithm achieves $\tilde{O}(\sqrt{Tmn})$ regret (for $m$ suppliers and $n$ consumers), which is optimal with respect to the time horizon $T$. Our results illustrate an effective integration of statistical learning methodologies with complex operations research problems.