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Mechanism design augmented with output advice

George Christodoulou, Alkmini Sgouritsa, Ioannis Vlachos

TL;DR

This work revisits the design of mechanisms via the learning-augmented framework with a perspective in which the mechanism is provided with an output recommendation, and proposes a generic, universal measure, which is called quality of recommendation, to evaluate mechanisms across various information settings.

Abstract

Our work revisits the design of mechanisms via the learning-augmented framework. In this model, the algorithm is enhanced with imperfect (machine-learned) information concerning the input, usually referred to as prediction. The goal is to design algorithms whose performance degrades gently as a function of the prediction error and, in particular, perform well if the prediction is accurate, but also provide a worst-case guarantee under any possible error. This framework has been successfully applied recently to various mechanism design settings, where in most cases the mechanism is provided with a prediction about the types of the players. We adopt a perspective in which the mechanism is provided with an output recommendation. We make no assumptions about the quality of the suggested outcome, and the goal is to use the recommendation to design mechanisms with low approximation guarantees whenever the recommended outcome is reasonable, but at the same time to provide worst-case guarantees whenever the recommendation significantly deviates from the optimal one. We propose a generic, universal measure, which we call quality of recommendation, to evaluate mechanisms across various information settings. We demonstrate how this new metric can provide refined analysis in existing results. This model introduces new challenges, as the mechanism receives limited information comparing to settings that use predictions about the types of the agents. We study, through this lens, several well-studied mechanism design paradigms, devising new mechanisms, but also providing refined analysis for existing ones, using as a metric the quality of recommendation. We complement our positive results, by exploring the limitations of known classes of strategyproof mechanisms that can be devised using output recommendation.

Mechanism design augmented with output advice

TL;DR

This work revisits the design of mechanisms via the learning-augmented framework with a perspective in which the mechanism is provided with an output recommendation, and proposes a generic, universal measure, which is called quality of recommendation, to evaluate mechanisms across various information settings.

Abstract

Our work revisits the design of mechanisms via the learning-augmented framework. In this model, the algorithm is enhanced with imperfect (machine-learned) information concerning the input, usually referred to as prediction. The goal is to design algorithms whose performance degrades gently as a function of the prediction error and, in particular, perform well if the prediction is accurate, but also provide a worst-case guarantee under any possible error. This framework has been successfully applied recently to various mechanism design settings, where in most cases the mechanism is provided with a prediction about the types of the players. We adopt a perspective in which the mechanism is provided with an output recommendation. We make no assumptions about the quality of the suggested outcome, and the goal is to use the recommendation to design mechanisms with low approximation guarantees whenever the recommended outcome is reasonable, but at the same time to provide worst-case guarantees whenever the recommendation significantly deviates from the optimal one. We propose a generic, universal measure, which we call quality of recommendation, to evaluate mechanisms across various information settings. We demonstrate how this new metric can provide refined analysis in existing results. This model introduces new challenges, as the mechanism receives limited information comparing to settings that use predictions about the types of the agents. We study, through this lens, several well-studied mechanism design paradigms, devising new mechanisms, but also providing refined analysis for existing ones, using as a metric the quality of recommendation. We complement our positive results, by exploring the limitations of known classes of strategyproof mechanisms that can be devised using output recommendation.
Paper Structure (40 sections, 24 theorems, 26 equations, 19 figures, 1 table, 6 algorithms)

This paper contains 40 sections, 24 theorems, 26 equations, 19 figures, 1 table, 6 algorithms.

Table of Contents

  1. Introduction
  2. Mechanisms with output advice
  3. Quality of recommendation
  4. Contributions
  5. Facility Location
  6. Scheduling
  7. House Allocation
  8. Combinatorial Auctions
  9. Related Work
  10. Learning-augmented mechanism design
  11. Facility Location
  12. Scheduling
  13. House Allocation
  14. Auctions
  15. Model
  16. ...and 25 more sections

Key Result

Theorem 1

The Minimum Bounding Box mechanism is $\min\{\hat{\rho}, \sqrt{2}+1\}$-approximate.

Figures (19)

  • Figure 1: Quality of recommendation versus prediction error
  • Figure 2: Tight lower bound for the Minimum Bounding Box mechanism.
  • Figure 3: Projected locations on x-axis
  • Figure 4: $d(z, f(\mathbf{t}, \hat{a})) \leq d(z,\hat{a}) + d(z, f(\mathbf{t}))$ for every agent location $z$
  • Figure 5: The instance showing the tight analysis for the Coordinatewise Median with Predictions mechanism.
  • ...and 14 more figures

Theorems & Definitions (49)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Remark 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 2
  • ...and 39 more