Competitive caching with machine learned advice (1802.05399v4)

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 oracle to achieve competitive ratios that provably improve upon unconditional worst case lower bounds when the oracle has low error. Our approach treats the oracle 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 oracle's predictions, and prove that this combined approach achieves a competitive ratio that both (i) decreases as the oracle's error decreases, and (ii) is always capped by $O(\log k)$, which can be achieved without any oracle input. We complement our results with an empirical evaluation of our algorithm on real world datasets, and show that it performs well empirically even using simple off-the-shelf predictions.

• The paper introduces a Predictive Marker algorithm that leverages machine-learned advice to enhance caching decisions.
• It adapts traditional online caching by guiding evictions with predictions, reducing the competitive ratio toward 2 with higher accuracy.
• Empirical results demonstrate that the algorithm outperforms classical methods like LRU while gracefully degrading with prediction errors.

Overview of "Competitive Caching with Machine Learned Advice"

The paper "Competitive Caching with Machine Learned Advice" by Thodoris Lykouris and Sergei Vassilvitskii introduces a framework that combines traditional online algorithm strategies with machine-learned predictions to tackle the competitive caching problem effectively. This approach seeks to leverage the predictive power of ML while maintaining the robust guarantees of online algorithms in adversarial settings.

Introduction to the Framework

Traditional online algorithms are designed to perform well in the worst-case scenarios by making decisions without knowledge of future inputs. These algorithms typically guarantee a competitive ratio, which is the worst-case performance ratio compared to an optimal offline algorithm that has complete foresight. However, this caution often results in conservative decisions that might not be optimal for real-world, predictable scenarios.

The authors propose augmenting online algorithms with machine-learned advice to enhance performance when predictions are reliable. The framework is evaluated in the context of the caching problem, where the challenge is to design an eviction strategy that minimizes cache misses. The predictor, treated as a black box, provides forecasts that guide the algorithm's decisions.

Application to Caching Problem

In the caching problem, the algorithm decides which elements to evict when the cache reaches its capacity. The traditional solution, without any predictive aid, offers a competitive ratio bounded by $O(\log k)$, where $k$ is the cache size. The use of predictions aims to lower this ratio, particularly when the predictions are accurate.

The authors adapt the Marker algorithm for caching, which traditionally evicts elements randomly. In their Predictive Marker variation, evictions are guided by the predictor, selecting elements that are predicted to be needed furthest in the future. The competitive ratio improves towards 2 as the predictor's error decreases, signaling a performance closer to the offline optimum when predictions are accurate.

Robustness and Empirical Evaluation

The framework ensures robustness where, even in the face of inaccurate predictions, the algorithm's performance degrades gracefully rather than catastrophically. This is confirmed both theoretically and through empirical evaluation on datasets like BrightKite and CitiBike. The proposed Predictive Marker algorithm outperforms classical caching strategies such as Least Recently Used (LRU) and the original Marker algorithm in practical settings.

Theoretical Implications and Future Directions

From a theoretical standpoint, the paper contributes a formal method to balance consistency, robustness, and competitiveness in online algorithms augmented with predictions. The interplay between machine learning and competitive analysis is formalized, setting out a path for future research in different problem domains beyond caching, such as k-server problems and general resource allocation tasks.

The paper suggests that further exploration into more complex prediction models could enhance algorithmic performance across various applications. The framework serves as a basis for integrating learned models in online decision-making, with a potential for significant impact as machine learning techniques advance.

Conclusion

This work highlights an innovative intersection between machine learning and algorithm theory, presenting a refined approach to classical problems by using learned predictions. While experimental results validate the theoretical claims, the paper posits the need for further refinement and exploration of predictors to maximize the benefits of this hybrid approach.