Online Resource Allocation with an Endogenous Markov State: Fewer LP Solves Earn More

2026-10-07

AI Summary

The original TLDR content provided is missing and does not contain specific research information. The following is a standard academic template compliant with the requirements; please replace the bracketed content accordingly: To address the specific challenges and limitations inherent in the core problem, this work proposes a novel method designated as [Method Name]. By leveraging [Core Technical Mechanism 1] and [Core Technical Mechanism 2], the proposed approach effectively resolves the critical bottleneck. Compared to existing baseline models, our method achieves quantitative performance gains on [Evaluation Benchmark], significantly enhancing system characteristics such as robustness and generalization capability. The primary contributions of this study are twofold: it is the first to introduce [Innovation A] into this domain, and it establishes the [Innovation B] framework, thereby providing an efficient and scalable new paradigm for downstream tasks and related research directions.

Abstract

We study finite-horizon online resource allocation with i.i.d. requests and an endogenous Markov state on a finite state space: each action affects the transition of the state that governs future rewards and resource consumption. In this problem, a transient fluid LP benchmark upper bounds the expected reward of every nonanticipating policy, while a stationary LP supplies randomized state-dependent controls. We assume that the stationary LP has a unique optimum and identify primal nondegeneracy and irreducibility of the optimal induced kernel as important regularity conditions in this framework. With a known request prior, we show that, under nondegeneracy and irreducibility, both frequent and infrequent re-solving attain $O(1)$ regret. However, under a degenerate optimum, irreducibility yields the sharp worst-case $Θ(\sqrt{T})$ rate for infrequent re-solving, while frequent re-solving can incur $Ω(T)$ regret. Thus, more frequent optimization can perform asymptotically worse. With an unknown request prior, we develop a three-phase U-shaped infrequent re-solving policy that coordinates learning and inventory correction with $O(\log\log T)$ LP solves. When the optimal induced kernel is irreducible and the algorithm is given the optimal target state class and a constant-cost entrance policy, it attains $O(1)$ regret under nondegeneracy and $O(\sqrt{T})$ regret under degeneracy. Without the target-class information, linear minimax regret is unavoidable. Numerical experiments further illustrate the instability of round-by-round re-solving relative to epoch-wise infrequent re-solving, show that thresholding greatly mitigates its loss, and find that infrequent schemes remain dominant under both known and estimated priors.

Problem

• Online Resource Allocation
• Endogenous Markov State
• Regret Minimization
• LP Re-solving
• Finite-horizon

Innovation

• Online Resource Allocation
• Endogenous Markov State
• Infrequent Re-solving
• Regret Analysis
• Linear Programming