[Paper Review] Online Algorithms for Weighted Paging with Predictions

Zhihao Jiang, Debmalya Panigrahi+1 more|arXiv (Cornell University)|Jan 1, 2020

Optimization and Search Problems14 citations

TL;DR

This paper introduces the Strong Per-Request Prediction (SPRP) model for weighted paging with predictions, showing that combining next-request predictions and a strong lookahead enables a deterministic 2-competitive algorithm—overcoming classical online lower bounds. Unlike unweighted paging, neither per-request prediction nor fixed lookahead alone suffices, but their combination yields constant competitiveness with graceful degradation under prediction error.

ABSTRACT

In this paper, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA 2020) on unweighted paging with predictions. We show that unlike unweighted paging, neither a fixed lookahead nor knowledge of the next request for every page is sufficient information for an algorithm to overcome existing lower bounds in weighted paging. However, a combination of the two, which we call the strong per request prediction (SPRP) model, suffices to give a 2-competitive algorithm. We also explore the question of gracefully degrading algorithms with increasing prediction error, and give both upper and lower bounds for a set of natural measures of prediction error.

Motivation & Objective

• To study weighted paging with future predictions, extending recent work on unweighted paging with predictions.
• To determine whether partial future information can overcome classical online lower bounds in weighted paging.
• To design algorithms that are both competitive when predictions are accurate and robust to increasing prediction error.
• To establish tight upper and lower bounds for prediction error measures in the weighted paging setting.

Proposed method

• Proposes the SPRP model, combining per-request prediction (next request time) and ℓ-strong lookahead (future sequence of ℓ distinct pages).
• Introduces the Follow algorithm, which runs a static offline algorithm on predicted sequences and mimics its evictions on the real input.
• Uses constrained edit distance and dynamic programming techniques to bound the cost difference between predicted and actual request sequences.
• Analyzes competitive ratio via recursive cost decomposition and matching arguments between predicted and real request sequences.
• Establishes lower bounds using adversarial constructions for PRP and ℓ-strong lookahead models, showing Ω(k) and Ω(log k) competitiveness for deterministic and randomized algorithms respectively.
• Introduces a novel error measure ℓ1 to quantify prediction quality and proves that cost degrades gracefully with increasing ℓ1.

Experimental results

Research questions

• RQ1 Can future predictions overcome the Ω(k) deterministic and Ω(log k) randomized lower bounds in weighted paging?
• RQ2 Is per-request prediction (PRP) or fixed lookahead (ℓ-strong) alone sufficient to achieve constant competitiveness in weighted paging?
• RQ3 Can a combined prediction model—SPRP—enable constant-competitive algorithms in weighted paging?
• RQ4 How does algorithm performance degrade with increasing prediction error, and can this degradation be bounded?
• RQ5 What is the minimal prediction model that enables constant competitiveness while maintaining robustness?

Key findings

• The SPRP model enables a deterministic 2-competitive algorithm for weighted paging, overcoming classical online lower bounds.
• Per-request prediction (PRP) alone yields Ω(k)-competitive deterministic and Ω(log k)-competitive randomized algorithms, matching standard online lower bounds.
• ℓ-strong lookahead with ℓ ≤ n−k also yields Ω(k) and Ω(log k) lower bounds, showing no improvement over standard online paging.
• For ℓ ≥ n−k+1, the lower bound degrades to Ω(n−ℓ) for deterministic and Ω(log(n−ℓ)) for randomized algorithms, indicating diminishing returns with smaller lookahead.
• The Follow algorithm achieves O(1)·(OPT + ℓ1) cost, proving graceful degradation with prediction error ℓ1.
• No algorithm can achieve sublinear dependence on ℓ1 while maintaining constant competitiveness unless the cache is enlarged by one slot.