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We show that robustness-consistency trade-offs are deeply intrinsic to the design of online algorithms that are robust in the worst case yet perform well when machine-learned predictions are accurate

Optimal Robustness-Consistency Trade-offs for Learning-Augmented Online Algorithms

NIPS 2020, (2020)

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Abstract

We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when predictions are accurate and maintains worst-case guarantees. Such algorithms have been studied in a rece...More

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Introduction
  • The vast gains in predictive ability by machine learning models in recent years have made them an attractive approach for algorithmic problems under uncertainty: One can train a model to predict outcomes on historical data and respond according to the model’s predictions in future scenarios.
  • The company could try to optimize their purchasing based on a model learned from past demand.
  • Modern machine learning models may produce predictions that are embarrassingly inaccurate (e.g., [SZS+14]), especially when trying to generalize to unfamiliar inputs.
  • The potential for such non-robust behavior is be problematic in practice, when users of machine learning-based systems desire at least some baseline level of performance in the worst case
Highlights
  • The vast gains in predictive ability by machine learning models in recent years have made them an attractive approach for algorithmic problems under uncertainty: One can train a model to predict outcomes on historical data and respond according to the model’s predictions in future scenarios
  • We provide the first set of optimal results for online algorithms using machine-learned predictions
  • We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions
  • We show that robustness-consistency trade-offs are deeply intrinsic to the design of online algorithms that are robust in the worst case yet perform well when machine-learned predictions are accurate
Results
  • The authors study the problem of improving the performance of online algorithms by incorporating machine-learned predictions.
  • The authors provide a significantly better trade-off (Figure 1.2) and a matching lower bound in this regime
Conclusion
  • The authors give lower bounds for the learning-augmented versions of the ski-rental problem and non-clairvoyant scheduling.
  • The authors show that robustness-consistency trade-offs are deeply intrinsic to the design of online algorithms that are robust in the worst case yet perform well when machine-learned predictions are accurate.
  • A broad future direction is to use the techniques to investigate tight robustness-consistency trade-offs for other learning-augmented online algorithms following the spate of recent works on this topic
Related work
  • For learning-based ski-rental, the result of [KPS18] has since been extended by [LHL19, GP19]. Scheduling with predictions is also studied by [LLMV20, Mit20, Mit19], though under different prediction models or problem settings. The results of [LV18] on online caching with ML predictions have been improved and generalized by [ACE+20, Roh20, JPS20, Wei20]. Several other learningaugmented online problems have also been considered in the literature, including matching, optimal auctions and bin packing [DH09, KPS+19, MV17, AGKK20, ADJ+20].

    Online algorithms (without ML predictions) are a classical subject in the algorithms literature. The (classic) ski-rental problem is well-understood: It is known that there exists a 2-competitive deterministic algorithm [KMRS88]. This can be further improved to e/(e−1) using randomization and is known to be optimal [KMMO94]. There are also numerous extensions of the problem, including snoopy caching [KMRS88] and dynamic TCP acknowledgment [KKR03]. The non-clairvoyant scheduling problem was first studied by [MPT94]. They show that for n jobs the round-robin heuristic achieves a competitive ratio of 2 − 2/(n + 1) and provide a matching lower bound. They also show that randomization provides at most a minor lower-order improvement to the competitive ratio. Our work revisits these classical results by extending their lower bounds to settings where we want to optimize for consistency (with respect to a prediction) in addition to worst-case competitive ratio.
Funding
  • We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions
  • We provide a significantly better trade-off (Figure 1.2) and a matching lower bound in this regime
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Author
Alexander Wei
Alexander Wei
Fred Zhang
Fred Zhang
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