Lossless Robustification of Packet Scheduling Algorithms

Heuristics on what online algorithms should do at any given time can give large improvements to the performance of the algorithm. Today, such heuristics are mostly generated by some machine learning algorithm that was trained on what is hoped to be a similar input. A heuristic can also be viewed as action predictions where, at each time step, the predictor tries to predict the action that an optimal algorithm would have taken. We consider the online packet scheduling problem where unit size packets arrive over time, each is associated with a value and a deadline. The goal is to schedule the packets to maximize the value of the packets transmitted by their deadline. We consider an arbitrary algorithm (heuristic) and robustify it without loss. Specifically, we provide an algorithm that is at least as good as the heuristic for any input, while guaranteeing it is 3-competitive regardless of the heuristic's performance. Finally, we show that it is not possible to be as good as the heuristic and remain constant-competitive if we consider the asynchronous model.