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Optimizing Online Knapsack Allocation with Time Fairness Guarantees
核心概念
This work formalizes a notion of time fairness for the online knapsack problem, where the probability of an item being accepted depends only on its value density and not its arrival time. It proposes deterministic and learning-augmented algorithms that achieve a Pareto-optimal trade-off between fairness and competitiveness.
要約
The paper addresses the online knapsack problem (OKP), which models a resource allocation process where a provider allocates a limited resource (knapsack capacity) to consumers (items) arriving sequentially to maximize the total value.
The key contributions are:
Formalization of a notion of time-independent fairness (TIF) for OKP, which requires the probability of an item's acceptance to depend only on its value density and not its arrival time. The paper shows this is not achievable for any nontrivial OKP algorithm.
Proposal of a relaxed notion of α-conditional time-independent fairness (α-CTIF), which requires fairness only within a subinterval of the knapsack's capacity.
Design of a deterministic algorithm (ECT) that achieves the Pareto-optimal trade-off between α-CTIF and competitiveness, as characterized by a lower bound.
Exploration of randomization, showing it can achieve optimal competitiveness and fairness in theory, but underperforms in practice.
Development of a learning-augmented algorithm (LA-ECT) that is fair, consistent, and robust, showing substantial performance improvements in numerical experiments.
The paper provides a comprehensive understanding of the inherent challenges in achieving fairness and efficiency simultaneously in the online knapsack problem, and proposes practical algorithms that balance these objectives.
Time Fairness in Online Knapsack Problems
統計
The paper does not contain any explicit numerical data or statistics. It focuses on theoretical analysis and algorithm design.
引用
"The online knapsack problem (OKP) is a well-studied problem in online algorithms. It models a resource allocation process, in which one provider allocates a limited resource (i.e., the knapsack's capacity) to consumers (i.e., items) arriving sequentially in order to maximize the total return (i.e., optimally pack items subject to the capacity constraint)."
"We define the quality of a job as the ratio of the price paid by the client over the resources required. How do we algorithmically solve the problem posed in Example 1.1? Note that the limited resource implies that the problem of accepting and rejecting items reduces precisely to OKP."
"Existing optimal algorithms for OKP do not fulfill this second requirement. In particular, although two jobs may have a priori identical quality, the optimal algorithm discriminates between them based on their arrival time in the online queue: a typical job, therefore, has a higher chance of being accepted if it happens to arrive earlier rather than later."
深掘り質問
What other online resource allocation problems could benefit from the notion of conditional time-independent fairness proposed in this work
The notion of conditional time-independent fairness proposed in this work could be beneficial for other online resource allocation problems that involve sequential decision-making and trade-offs between efficiency and fairness. One such problem could be online job scheduling in a multi-agent system, where tasks with varying values and deadlines need to be allocated to different agents in real-time. By incorporating the concept of conditional time-independent fairness, algorithms can ensure that the allocation decisions are based on the value of the task and not biased by the order of arrival or other factors. This can lead to more equitable task assignments and improved overall system performance.
How could the learning-augmented algorithm (LA-ECT) be extended to handle more complex prediction models or incorporate additional side information about the input instance
The learning-augmented algorithm (LA-ECT) can be extended to handle more complex prediction models or incorporate additional side information about the input instance by integrating advanced machine learning techniques. One approach could be to use deep learning models to learn complex patterns in the input data and make more accurate predictions about the optimal offline solution. By leveraging neural networks or reinforcement learning algorithms, LA-ECT can adapt to changing environments and make more informed decisions in real-time. Additionally, incorporating side information such as task dependencies or agent capabilities can further enhance the algorithm's performance and fairness guarantees.
Are there other fairness criteria beyond time fairness that could be relevant for the online knapsack problem, such as group fairness or demographic parity
Beyond time fairness, there are several other fairness criteria that could be relevant for the online knapsack problem. One such criterion is group fairness, which ensures that different groups of items or agents are treated fairly in the allocation process. For example, in a scenario where tasks belong to different categories or priority levels, group fairness can ensure that each category receives a proportional share of resources based on their importance or value. Another criterion could be demographic parity, which aims to prevent discrimination based on specific characteristics such as gender, race, or age. By incorporating these additional fairness criteria, algorithms for the online knapsack problem can promote equity and inclusivity in resource allocation decisions.
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