Solving the Online Assignment Problem with Machine Learned Advice
This work addresses the challenge of incomplete information in online algorithms for operational research and computer science, but it is incremental as it builds on existing advice-based methods.
The study tackled the online assignment problem by incorporating machine-learned advice to improve the competitive ratio, showing that solution quality decreases as prediction error increases, with error magnitude proportional to input size.
The online assignment problem plays an important role in operational research and computer science which is why immense attention has been given to improving its solution quality. Due to the incomplete information about the input, it is difficult for online algorithms to produce the optimal solution. The quality of the solution of an online algorithm is measured using a competitive ratio. No online deterministic algorithm can achieve a competitive ratio better than (2n-1). It has been shown that advice in online computation improves the lower bound of the competitive ratio of online problems. Advice in online computation can be interpreted as additional information for the online algorithm to compensate for the lack of information about the whole input sequence. In this study, we investigate how introducing machine-learned advice could improve the competitive ratio for this problem. We provide an online algorithm for the online assignment problem by simulating a machine learning algorithm that predicts the whole input in advance. We utilize an optimal offline algorithm to provide a matching solution from the predicted input. Furthermore, we investigate how the prediction error of machine learning affects the competitive ratio of the online algorithm. We utilize a benchmark data set to perform our empirical analysis. We show that as the Machine Learning prediction error increases, the solution quality decreases. Moreover, the magnitude of error is directly proportional to the size of the input. This result is analogous to the competitive ratio of the best deterministic algorithm for the online assignment problem which is dependent also on the parameter n.