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In this paper, we explore how a natural generalization of Shortest Remaining Processing Time (SRPT) can be a powerful \emph{meta-algorithm} for online scheduling. The meta-algorithm processes jobs to maximally reduce the objective of the corresponding offline scheduling problem of the remaining jobs: minimizing the total weighted completion time of them (the residual optimum). We show that it achieves scalability for minimizing total weighted flow time when the residual optimum exhibits \emph{supermodularity}. Scalability here means it is $O(1)$-competitive with an arbitrarily small speed augmentation advantage over the adversary, representing the best possible outcome achievable for various scheduling problems. Thanks to this finding, our approach does not require the residual optimum to have a closed mathematical form. Consequently, we can obtain the schedule by solving a linear program, which makes our approach readily applicable to a rich body of applications. Furthermore, by establishing a novel connection to \emph{substitute valuations in Walrasian markets}, we show how to achieve supermodularity, thereby obtaining scalable algorithms for various scheduling problems, such as matroid scheduling, generalized network flow, and generalized arbitrary speed-up curves, etc., and this is the \emph{first} non-trivial or scalable algorithm for many of them.

Online load balancing for heterogeneous machines aims to minimize the makespan (maximum machine workload) by scheduling arriving jobs with varying sizes on different machines. In the adversarial setting, where an adversary chooses not only the collection of job sizes but also their arrival order, the problem is well-understood and the optimal competitive ratio is known to be $\Theta(\log m)$ where $m$ is the number of machines. In the more realistic random arrival order model, the understanding is limited. Previously, the best lower bound on the competitive ratio was only $\Omega(\log \log m)$. We significantly improve this bound by showing an $\Omega( \sqrt {\log m})$ lower bound, even for the restricted case where each job has a unit size on two machines and infinite size on the others. On the positive side, we propose an $O(\log m/\log \log m)$-competitive algorithm, demonstrating that better performance is possible in the random arrival model.

Learning-augmented algorithms -- in which, traditional algorithms are augmented with machine-learned predictions -- have emerged as a framework to go beyond worst-case analysis. The overarching goal is to design algorithms that perform near-optimally when the predictions are accurate yet retain certain worst-case guarantees irrespective of the accuracy of the predictions. This framework has been successfully applied to online problems such as caching where the predictions can be used to alleviate uncertainties. In this paper we introduce and study the setting in which the learning-augmented algorithm can utilize the predictions parsimoniously. We consider the caching problem -- which has been extensively studied in the learning-augmented setting -- and show that one can achieve quantitatively similar results but only using a sublinear number of predictions.

We consider the problem of learning linear classifiers when both features and labels are binary. In addition, the features are noisy, i.e., they could be flipped with an unknown probability. In Sy-De attribute noise model, where all features could be noisy together with same probability, we show that $0$-$1$ loss ($l_{0-1}$) need not be robust but a popular surrogate, squared loss ($l_{sq}$) is. In Asy-In attribute noise model, we prove that $l_{0-1}$ is robust for any distribution over 2 dimensional feature space. However, due to computational intractability of $l_{0-1}$, we resort to $l_{sq}$ and observe that it need not be Asy-In noise robust. Our empirical results support Sy-De robustness of squared loss for low to moderate noise rates., Comment: Accepted for Student Abstract presentation at AAAI2020