Competitive Caching with Machine Learned Advice

Abstract

Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution, as compared to an offline optimum. On the other hand, machine learning algorithms are in the business of extrapolating patterns found in the data to predict the future, and usually come with strong guarantees on the expected generalization error. In this work, we develop a framework for augmenting online algorithms with a machine learned predictor to achieve competitive ratios that provably improve upon unconditional worst-case lower bounds when the predictor has low error. Our approach treats the predictor as a complete black box and is not dependent on its inner workings or the exact distribution of its errors. We apply this framework to the traditional caching problem—creating an eviction strategy for a cache of size k . We demonstrate that naively following the oracle’s recommendations may lead to very poor performance, even when the average error is quite low. Instead, we show how to modify the Marker algorithm to take into account the predictions and prove that this combined approach achieves a competitive ratio that both (i) decreases as the predictor’s error decreases and (ii) is always capped by O (log k ), which can be achieved without any assistance from the predictor. We complement our results with an empirical evaluation of our algorithm on real-world datasets and show that it performs well empirically even when using simple off-the-shelf predictions.

Uniform Bounds for Scheduling with Job Size Estimates

“…In the wider context of online algorithms with predictions, the three goals discussed in this paper can be stated more generally: Consistency: In the limit as the prediction quality becomes perfect, the performance should approach that of the optimal algorithm with perfect information. For instance, one might try to achieve -consistency [7], which requires that the competitive ratio is bounded by as the error in the predictions goes to 0. Robustness: In the limit as the prediction quality becomes arbitrarily poor, the performance should be comparable to that of the optimal algorithm in with perfect information.…”

“…Robustness: In the limit as the prediction quality becomes arbitrarily poor, the performance should be comparable to that of the optimal algorithm in with perfect information. For instance, one might try to achieve -robustness [7], which requires that the competitive ratio is bounded by under arbitrarily poor predictions. Graceful Degradation: As the prediction quality worsens from perfect to worthless, the performance should degrade smoothly and slowly.…”

“…In the context of online algorithms with predictions [7,11], one typically tries to achieve constantfactor robustness, which requires that the approximation ratio is bounded by a constant under arbitrarily poor predictions.…”

“…In the context of online algorithms with predictions [7,11], there are two key goals for a policy: "consistency", which requires near-optimal performance under low error, and "robustness", which requires bounded approximation ratio under arbitrary error. Unfortunately, as we explain in Appendix B, robustness is provably unachievable in this context.…”

Robustness and Consistency in Linear Quadratic Control with Untrusted Predictions

“…Recently, there has been significant interest in unifying these two perspectives, with the goal of developing algorithms that balance between consistency and robustness. To this point, progress has been made in a few online algorithms settings, e.g., the ski-rental, online matching, non-clairvoyant scheduling problems [15,17,22,4,7,6,5]. In these settings, algorithms have been designed that can achieve near-optimal performance when the prediction error is small while also maintaining robustness when the prediction error is large.…”