Optimal Contract Scheduling with Distributional and Multiple Predictions

Core Concepts

Designing optimal contract scheduling algorithms that leverage distributional or multiple predictions about the interruption time to improve performance, while guaranteeing robust worst-case guarantees.

Abstract

The content discusses the problem of contract scheduling, where a system needs to execute a contract algorithm that provides a correct result if given a prescribed computation time, but may return a meaningless result if interrupted before the contract time. The goal is to design schedules that can execute the contract algorithm multiple times with increasing computation times, in order to obtain an interruptible system. The authors introduce and study two novel learning-augmented settings for contract scheduling: Distributional Advice: The prediction oracle provides a probability distribution on the anticipated interruption time. The authors design a collection of schedules that are 4-robust and have consistency arbitrarily close to 4 ln 2 ≈ 2.77. They show this bound is tight and that the performance of the optimal schedule degrades smoothly with the Earth Mover's Distance between the predicted and actual distributions. Multiple Advice: The prediction oracle provides a set of k potential interruption times. The authors provide an algorithm that computes a 4-robust schedule with optimal consistency 2^(2-1/k) in time O(k log k). They show this bound is tight, and that it subsumes the known results for the extreme cases of a single prediction (consistency 2) and no prediction (worst-case acceleration ratio 4). The authors also provide an experimental evaluation that confirms the theoretical findings and illustrates the performance improvements that can be attained in practice.

Stats

The expected interruption time is extremely close to the mean m for sufficiently large m (e.g., m ≥ 100). The consistency of the schedules improves as the number of candidate schedules n increases. The worst-case and average-case consistencies of the multiple advice schedules are below the upper bound of 2^(2-1/k).

Quotes

"For any arbitrarily small ϵ > 0, there is an algorithm with runtime polynomial in O(1/ϵ) for devising a 4-robust schedule that has consistency at most 4 · ln 2 + ϵ." "The schedule of Theorem 9 has consistency at most 2^(2-1/k), where k is the size of P. Furthermore, this bound is tight, in that there exists a prediction P such that every 4-robust schedule has consistency at least 2^(2-1/k)."

Key Insights Distilled From

Contract Scheduling with Distributional and Multiple Advice

by Spyr... at arxiv.org 04-22-2024

https://arxiv.org/pdf/2404.12485.pdf

Deeper Inquiries

How can the techniques developed in this work be applied to more complex variants of contract scheduling, such as those involving multiple instances or processors

The techniques developed in this work for contract scheduling with distributional and multiple advice can be applied to more complex variants of contract scheduling, such as those involving multiple instances or processors, by adapting the scheduling algorithms to handle the increased complexity. For scenarios with multiple instances, the schedules can be designed to allocate resources efficiently across different instances, taking into account the specific requirements and constraints of each instance. By incorporating multiple predictions or advice sets corresponding to different instances, the scheduling algorithm can optimize the allocation of resources to maximize performance while ensuring interruptibility. In the case of multiple processors, the scheduling algorithm can be extended to distribute the workload effectively among the processors, considering factors such as processing capabilities, communication overhead, and task dependencies. By utilizing multiple predictions or advice sets related to each processor, the algorithm can optimize the scheduling decisions to achieve the desired performance outcomes. Overall, the techniques developed in this work provide a foundation for designing adaptive and efficient contract scheduling algorithms that can handle the complexities of real-world systems with multiple instances or processors.

What are the implications of the disconnect between deterministic and distributional predictions observed in this work for other learning-augmented optimization problems

The disconnect between deterministic and distributional predictions observed in this work has significant implications for other learning-augmented optimization problems. In the context of learning-augmented algorithms, where predictions play a crucial role in decision-making, the findings suggest that relying solely on single, deterministic predictions may lead to suboptimal or fragile performance in the face of prediction errors. By considering distributional predictions that capture the uncertainty and variability in the prediction outcomes, algorithms can be designed to be more robust and adaptable to different scenarios. This insight can guide the development of more resilient and reliable learning-augmented systems in various domains. By acknowledging the limitations of deterministic predictions and embracing the richness of distributional predictions, algorithms can better handle uncertainties and variations in the prediction outcomes, leading to more stable and effective decision-making processes. The disconnect observed highlights the importance of considering the full spectrum of prediction possibilities and incorporating robustness measures into learning-augmented optimization problems to enhance their performance and reliability.

Can the insights from this work on the robustness of distributional predictions be leveraged to design more reliable systems in other domains, such as robotics or medical diagnosis

The insights from this work on the robustness of distributional predictions can be leveraged to design more reliable systems in other domains, such as robotics or medical diagnosis, by enhancing the adaptability and resilience of the systems to prediction errors and uncertainties. In robotics, where predictive models are used for navigation, object recognition, and path planning, the findings can inform the development of algorithms that can handle variations in predictions and adapt to changing environments effectively. By incorporating distributional predictions and robust scheduling techniques, robotic systems can improve their decision-making processes and enhance their performance in dynamic and unpredictable scenarios. Similarly, in medical diagnosis applications, where accurate predictions are crucial for patient care and treatment planning, the insights from this work can guide the design of systems that are capable of handling uncertainties in predictions and mitigating the impact of prediction errors. By implementing robust scheduling strategies based on distributional predictions, medical diagnostic systems can improve their reliability and accuracy, leading to better patient outcomes and more effective healthcare delivery. Overall, the robustness principles derived from this work can be applied to various domains to enhance the reliability and performance of systems that rely on predictive models and scheduling algorithms.