An official website of the United States government
Online Allocation of Reusable Resources: New Algorithms and Analytical Tools In the paper “Asymptotically Optimal Competitive Ratio for Online Allocation of Reusable Resources,” the authors develop novel algorithms and analysis techniques for online allocation of reusable resources. Their approach leads to an algorithm with the highest possible competitive ratio, a result that was previously out of reach with the algorithms and techniques that are used in classic settings in which resources are nonreusable. More generally, their LP-free analysis approach is useful for analyzing the performance of online algorithms for various other settings in which the standard primal-dual approach fails.
more »
« less
This content will become publicly available on December 23, 2025
Function Design for Improved Competitive Ratio in Online Resource Allocation with Procurement Costs
We study the problem of online resource allocation, where customers arrive sequentially, and the seller must irrevocably allocate resources to each incoming customer while also facing a prespecified procurement cost function over the total allocation. The objective is to maximize the reward obtained from fulfilling the customers’ requests sans the cumulative procurement cost. We analyze the competitive ratio of a primal-dual algorithm in this setting and develop an optimization framework for designing a surrogate function for the procurement cost to be used by the algorithm to improve the competitive ratio of the primal-dual algorithm. We use the optimal surrogate function for polynomial procurement cost functions to improve on previous bounds. For general procurement cost functions, our design method uses quasiconvex optimization to find optimal design parameters. We then implement the design techniques and show the improved performance of the algorithm in numerical examples. Finally, we extend the analysis by devising a posted pricing mechanism in which the algorithm does not require the customers’ preferences to be revealed. Funding: M. Fazel’s work was supported in part by the National Science Foundation [Awards 2023166, 2007036, and 1740551]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2021.0012 .
more »
« less
- PAR ID:
- 10569705
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- INFORMS Journal on Optimization
- ISSN:
- 2575-1484
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper studies online resource allocation with replenishable budgets, where budgets can be replenished on top of the initial budget and an agent sequentially chooses online allocation decisions without violating the available budget constraint at each round. We propose a novel online algorithm, called OACP (Opportunistic Allocation with Conservative Pricing), that conservatively adjusts dual variables while opportunistically utilizing available resources. OACP achieves a bounded asymptotic competitive ratio in adversarial settings as the number of decision rounds T gets large. Importantly, the asymptotic competitive ratio of OACP is optimal in the absence of additional assumptions on budget replenishment. To further improve the competitive ratio, we make a mild assumption that there is budget replenishment every T* ≥ 1 decision rounds and propose OACP+ to dynamically adjust the total budget assignment for online allocation. Next, we move beyond the worst-case and propose LA-OACP (Learning-Augmented OACP/OACP+), a novel learning-augmented algorithm for online allocation with replenishable budgets. We prove that LA-OACP can improve the average utility compared to OACP/OACP+ when the ML predictor is properly trained, while still offering worst-case utility guarantees when the ML predictions are arbitrarily wrong. Finally, we run simulation studies of sustainable AI inference powered by renewables, validating our analysis and demonstrating the empirical benefits of LA-OACP.more » « less
-
null (Ed.)There has been significant interest in leveraging limited look-ahead to achieve low competitive ratios for online convex optimization (OCO). However, existing online algorithms (such as Averaging Fixed Horizon Control (AFHC)) that can leverage look-ahead to reduce the competitive ratios still produce competitive ratios that grow unbounded as the coefficient ratio (i.e., the maximum ratio of the switching-cost coefficient and the service-cost coefficient) increases. On the other hand, the regularization method can attain a competitive ratio that remains bounded when the coefficient ratio is large, but it does not benefit from look-ahead. In this paper, we propose a new algorithm, called Regularization with Look-Ahead (RLA), that can get the best of both AFHC and the regularization method, i.e., its competitive ratio decreases with the look-ahead window size when the coefficient ratio is small, and remains bounded when the coefficient ratio is large. We also provide a matching lower bound for the competitive ratios of all online algorithms with look-ahead, which differs from the achievable competitive ratio of RLA by a factor that only depends on the problem size. The competitive analysis of RLA involves a non-trivial generalization of online primal-dual analysis to the case with look-ahead.more » « less
-
Electricity bill constitutes a significant portion of operational costs for large scale data centers. Empowering data centers with on-site storages can reduce the electricity bill by shaping the energy procurement from deregulated electricity markets with real-time price fluctuations. This work focuses on designing energy procurement and storage management strategies to minimize the electricity bill of storage-assisted data centers. Designing such strategies is challenging since the net energy demand of the data center and electricity market prices are not known in advance, and the underlying problem is coupled over time due to evolution of the storage level. Using competitive ratio as the performance measure, we propose an online algorithm that determines the energy procurement and storage management strategies using a threshold based policy. Our algorithm achieves the optimal competitive ratio of as a function of the price fluctuation ratio. We validate the algorithm using data traces from electricity markets and data-center energy demands. The results show that our algorithm achieves close to the offline optimal performance and outperforms existing alternatives.%more » « less
-
We consider an in-network optimal resource allocation problem in which a group of agents interacting over a connected graph want to meet a demand while minimizing their collective cost. The contribution of this paper is to design a distributed continuous-time algorithm for this problem inspired by a recently developed first-order transformed primal-dual method. The solution applies to cluster-based setting where each agent may have a set of subagents, and its local cost is the sum of the cost of these subagents. The proposed algorithm guarantees an exponential convergence for strongly convex costs and asymptotic convergence for convex costs. Exponential convergence when the local cost functions are strongly convex is achieved even when the local gradients are only locally Lipschitz. For convex local cost functions, our algorithm guarantees asymptotic convergence to a point in the minimizer set. Through numerical examples, we show that our proposed algorithm delivers a faster convergence compared to existing distributed resource allocation algorithms.more » « less
