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Custom Keep-Alive Cache Policies

Sushirdeep Narayana, Ian A. Kash

TL;DR

This work designs a cache allocation policy based on online learning from a mixture of fixed allocation experts and shows that the custom cache allocation policy is asymptotically efficient and monotonically non-increasing with respect to the submitted bid.

Abstract

We study the market design of keep-alive caching policies applicable in serverless computing. Prior work has assumed that the cost of a cache miss (cold start) is uniform across all customer applications. However, the cost of a cache miss depends on the customer's application. We investigate the market design where the customers submit a bid for their cost of a cache miss. We design a cache allocation policy based on online learning from a mixture of fixed allocation experts. We show that our custom cache allocation policy is asymptotically efficient and monotonically non-increasing with respect to the submitted bid. We examine two ways of charging customers to achieve good incentives. In the first payment scheme the customers are charged based on Myerson's theory, whereas in the second payment scheme the customers are charged their externality. We show via a mix of simulations and theory that both schemes have desirable revenue and incentive properties.

Custom Keep-Alive Cache Policies

TL;DR

This work designs a cache allocation policy based on online learning from a mixture of fixed allocation experts and shows that the custom cache allocation policy is asymptotically efficient and monotonically non-increasing with respect to the submitted bid.

Abstract

We study the market design of keep-alive caching policies applicable in serverless computing. Prior work has assumed that the cost of a cache miss (cold start) is uniform across all customer applications. However, the cost of a cache miss depends on the customer's application. We investigate the market design where the customers submit a bid for their cost of a cache miss. We design a cache allocation policy based on online learning from a mixture of fixed allocation experts. We show that our custom cache allocation policy is asymptotically efficient and monotonically non-increasing with respect to the submitted bid. We examine two ways of charging customers to achieve good incentives. In the first payment scheme the customers are charged based on Myerson's theory, whereas in the second payment scheme the customers are charged their externality. We show via a mix of simulations and theory that both schemes have desirable revenue and incentive properties.
Paper Structure (14 sections, 6 theorems, 19 equations, 11 figures, 3 tables)

This paper contains 14 sections, 6 theorems, 19 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Learning a Mixture of Fixed Keep-Alive Policies
  5. Properties of Custom Policies Learned from Fixed Policies
  6. Payments
  7. Myerson Payments
  8. Externality Payments
  9. Simulations
  10. Experiments on Azure Data trace
  11. Discussion
  12. Proof of Lemma 5.1
  13. Omitted Figures
  14. Code

Key Result

lemma 1

The exponentially weighted average custom policy learned from a mixture of fixed keep-alive policies is monotone in $\hat{\theta}$.

Figures (11)

  • Figure 1: Illustration of IC for Externality Payments
  • Figure 2: Trade-off curve of Payments vs number of cold starts for Hawkes and Poisson Process applications
  • Figure 3: Trade-off curve of payments vs cold starts for Azure applications
  • Figure 4: Trade-off curve of cumulative payments vs cold starts for Poisson process (1-8)
  • Figure 5: Trade-off curve of cumulative payments vs cold starts for Poisson process (9-16)
  • ...and 6 more figures

Theorems & Definitions (12)

  • definition 1
  • definition 2
  • definition 3
  • definition 4
  • lemma 1
  • proposition 1
  • corollary 1
  • corollary 2
  • lemma 2
  • proof
  • ...and 2 more