Online Weighted Paging with Unknown Weights

TL;DR

This paper introduces the first online weighted paging algorithm that learns page weights through sampling rather than prior knowledge, achieving competitive performance.

Contribution

It develops a novel algorithm for weighted paging that learns page weights via sampling, bridging the gap between known and unknown weight scenarios.

Findings

First to handle unknown page weights in online paging

Uses sampling to inform fractional solutions and randomized rounding

Achieves competitive ratio similar to known-weight algorithms

Abstract

Online paging is a fundamental problem in the field of online algorithms, in which one maintains a cache of $k$ slots as requests for fetching pages arrive online. In the weighted variant of this problem, each page has its own fetching cost; a substantial line of work on this problem culminated in an (optimal) $O(\log k)$-competitive randomized algorithm, due to Bansal, Buchbinder and Naor (FOCS'07). Existing work for weighted paging assumes that page weights are known in advance, which is not always the case in practice. For example, in multi-level caching architectures, the expected cost of fetching a memory block is a function of its probability of being in a mid-level cache rather than the main memory. This complex property cannot be predicted in advance; over time, however, one may glean information about page weights through sampling their fetching cost multiple times. We present the first algorithm for online weighted paging that does not know page weights in advance, but rather learns from weight samples. In terms of techniques, this requires providing (integral) samples to a fractional solver, requiring a delicate interface between this solver and the randomized rounding scheme; we believe that our work can inspire online algorithms to other problems that involve cost sampling.