Online Unrelated Machine Load Balancing with Predictions Revisited

We study the online load balancing problem with machine learned predictions, and give results that improve upon and extend those in a recent paper by Lattanzi et al. (2020). First, we design deterministic and randomized online rounding algorithms for the problem in the unrelated machine setting, with $O(\frac{\log m}{\log \log m})$- and $O(\frac{\log \log m}{\log \log \log m})$-competitive ratios. They respectively improve upon the previous ratios of $O(\log m)$ and $O(\log^3\log m)$, and match the lower bounds given by Lattanzi et al. Second, we extend their prediction scheme from the identical machine restricted assignment setting to the unrelated machine setting. With the knowledge of two vectors over machines, a dual vector and a weight vector, we can construct a good fractional assignment online, that can be passed to an online rounding algorithm. Finally, we consider the learning model introduced by Lavastida et al. (2020), and show that under the model, the two vectors can be learned efficiently with a few samples of instances.