No-Regret Mixing of LRU and LFU with Optimal Switching Cost

2026-09-07

AI Summary

研究解决了缓存系统中LRU和LFU策略结合时的性能保证问题，提出了一种基于Hedge算法的新方法H-MC，确保了在所有请求序列下的次线性遗憾。

Abstract

Caching systems often rely on simple eviction policies such as Least Recently Used (LRU) and Least Frequently Used (LFU), which perform well in complementary request regimes. Recent policies such as LeCar and Cacheus combine LRU and LFU using ideas from the experts problem in online learning. Specifically, upon a miss, they randomize between the two eviction rules using probabilities derived from scores updated by tracking the history of past evictions. While these policies exhibit strong empirical performance, it remains unclear whether they are guaranteed, on every request sequence, to perform asymptotically as well as the better of LRU and LFU, i.e., whether they achieve sublinear regret with respect to this benchmark. We first show that LeCar suffers linear regret against an oblivious adversary, even with unbounded history. We then propose H-MC, a Hedge-based mixture of virtual LRU and LFU caches that preserves Hedge's selection probabilities, and hence its regret guarantees, while minimizing the switching cost among all joint selection rules with these marginals.

Problem

• caching systems
• eviction policies
• regret

Innovation

• H-MC
• sublinear regret
• switching cost
• Hedge algorithm