[Paper Review] Better and Simpler Learning-Augmented Online Caching

Alexander Wei|arXiv (Cornell University)|Jan 1, 2020

Optimization and Search Problems27 references18 citations

TL;DR

This paper proposes a simple yet superior learning-augmented online caching algorithm by combining the BlindOracle algorithm (which naively follows predictions) with an O(log k)-competitive baseline algorithm (e.g., Marker) in a black-box manner. The resulting algorithm achieves a competitive ratio of O(1 + min(η/(k·OPT), log k)), outperforming prior methods while being significantly simpler and optimal among deterministic algorithms for the problem.

ABSTRACT

Lykouris and Vassilvitskii (ICML 2018) introduce a model of online caching with machine-learned advice, where each page request additionally comes with a prediction of when that page will next be requested. In this model, a natural goal is to design algorithms that (1) perform well when the advice is accurate and (2) remain robust in the worst case a la traditional competitive analysis. Lykouris and Vassilvitskii give such an algorithm by adapting the Marker algorithm to the learning-augmented setting. In a recent work, Rohatgi (SODA 2020) improves on their result with an approach also inspired by randomized marking. We continue the study of this problem, but with a somewhat different approach: We consider combining the BlindOracle algorithm, which just naïvely follows the predictions, with an optimal competitive algorithm for online caching in a black-box manner. The resulting algorithm outperforms all existing approaches while being significantly simpler. Moreover, we show that combining BlindOracle with LRU is in fact optimal among deterministic algorithms for this problem.

Motivation & Objective

• To design a learning-augmented online caching algorithm that performs well when predictions are accurate and remains robust in the worst case.
• To simplify existing approaches based on randomized marking, which are complex and intricate.
• To show that combining BlindOracle with a competitive baseline yields optimal performance among deterministic algorithms.
• To provide tighter competitive ratio bounds with explicit constant factors using known algorithm combiners.
• To establish a lower bound proving that a linear dependence on η/(k·OPT) is necessary for deterministic algorithms.

Proposed method

• Combines BlindOracle—naïvely following predictions—with an O(log k)-competitive online caching algorithm (e.g., Marker) via black-box composition.
• Applies known competitive algorithm combiners from Fiat et al. (1991) and Blum & Burch (2000) to merge BlindOracle and the baseline.
• Uses the ℓ1 prediction error η and offline optimal cost OPT as key parameters in the competitive ratio analysis.
• Analyzes the competitive ratio of the combined algorithm using a careful worst-case and optimistic-case decomposition.
• Employs a novel reduction to show that deterministic algorithms must incur a competitive ratio with linear dependence on η/(k·OPT).
• Leverages known optimal bounds for online algorithm composition to minimize constant factors in the competitive ratio.

Experimental results

Research questions

• RQ1 Can a simpler approach combining BlindOracle with a competitive baseline outperform existing learning-augmented caching algorithms?
• RQ2 Is the combination of BlindOracle and a deterministic competitive algorithm (e.g., LRU) optimal among all deterministic algorithms for learning-augmented caching?
• RQ3 What is the tightest possible competitive ratio achievable by deterministic learning-augmented caching algorithms?
• RQ4 Can the constant factors in the competitive ratio be improved by using optimal algorithm combiners instead of ad hoc methods?
• RQ5 Is randomization necessary to achieve a logarithmic dependence on η/(k·OPT), even when this ratio is bounded?

Key findings

• The proposed algorithm achieves a competitive ratio of O(1 + min(η/(k·OPT), log k)), improving upon the O(1 + min(log k / k · η/OPT, log k)) bound of LNonMarker.
• Combining BlindOracle with LRU yields a deterministic algorithm that is optimal among all deterministic algorithms for this problem.
• The competitive ratio bound for any deterministic algorithm must be at least 1 + Ω(min(η/(k·OPT), k)), proving a linear dependence on η/(k·OPT) is necessary.
• The constant factors in the competitive ratio are improved by using optimal algorithm combiners from Fiat et al. (1991) and Blum & Burch (2000).
• A logarithmic dependence on η/(k·OPT) is only possible with randomization, even when η/(k·OPT) is bounded, which is surprisingly counterintuitive.
• The approach is not only theoretically superior but also significantly simpler than prior methods based on randomized marking.