[Paper Review] Mechanism Design for Multi-Party Machine Learning

Mengjing Chen, Yang Liu+4 more|arXiv (Cornell University)|Jan 24, 2020

Auction Theory and Applications30 references15 citations

TL;DR

This paper proposes a mechanism design framework for multi-party machine learning where agents have interdependent values and restricted action spaces—unable to over-report data quality. It introduces a truthful, revenue-optimal mechanism under quasi-monotonicity and provides necessary and sufficient conditions for incentive compatibility and individual rationality, with existence heavily dependent on market growth rate.

ABSTRACT

In a multi-party machine learning system, different parties cooperate on optimizing towards better models by sharing data in a privacy-preserving way. A major challenge in learning is the incentive issue. For example, if there is competition among the parties, one may strategically hide his data to prevent other parties from getting better models. In this paper, we study the problem through the lens of mechanism design and incorporate the features of multi-party learning in our setting. First, each agent's valuation has externalities that depend on others' types and actions. Second, each agent can only misreport a type lower than his true type, but not the other way round. We call this setting interdependent value with type-dependent action spaces. We provide the optimal truthful mechanism in the quasi-monotone utility setting. We also provide necessary and sufficient conditions for truthful mechanisms in the most general case. Finally, we show the existence of such mechanisms is highly affected by the market growth rate and provide empirical analysis.

Motivation & Objective

• Address incentive issues in multi-party machine learning where competing parties may strategically withhold data.
• Model a novel setting with interdependent values and type-dependent action spaces, where agents cannot over-report their true data quality.
• Provide a mechanism that ensures individual rationality, incentive compatibility, and weak budget balance under general valuation functions.
• Analyze the impact of market growth rate on the existence of desirable mechanisms.
• Design an algorithm to compute optimal payments using shortest-path constraints derived from utility gaps.

Proposed method

• Formulate the problem as a mechanism design setting with interdependent values and restricted action spaces (agents can only under-report).
• Define utility gaps $Gap_i(t_i', t_i, t_{-i})$ to capture the difference in agent $i$'s utility when misreporting $t_i'$ versus truthfully reporting $t_i$.
• Construct a payment system based on shortest-path computation in a graph where nodes represent type profiles and edges encode utility constraints.
• Use a single-source shortest-path algorithm to compute the maximum feasible payments $p_i^{max}(t_i, t_{-i})$ that satisfy individual rationality and incentive compatibility.
• Introduce a decision algorithm that checks whether a weakly budget-balanced, efficient, and truthful mechanism exists by verifying if total payments sum to less than zero.
• Discretize the type space into intervals of size $\epsilon$ to handle continuous data sizes, assuming all valuation functions are common knowledge.

Experimental results

Research questions

• RQ1 Under what conditions does a truthful, individually rational, and weakly budget-balanced mechanism exist in multi-party machine learning with interdependent values and restricted reporting?
• RQ2 How does the market growth rate affect the existence of mechanisms that satisfy all desirable properties?
• RQ3 What is the optimal payment rule that maximizes revenue while ensuring incentive compatibility in the quasi-monotone utility setting?
• RQ4 Can a mechanism be constructed that guarantees efficiency and truthfulness when agents cannot over-report their data quality?
• RQ5 What algorithmic techniques can be used to compute the maximal feasible payments under complex interdependent valuation functions?

Key findings

• The proposed mechanism is revenue-optimal and truthful in the quasi-monotone utility setting, with payments computed via shortest-path constraints.
• A necessary and sufficient condition for truthful and individually rational mechanisms is derived, based on utility gap constraints and payment feasibility.
• The existence of a desirable mechanism is highly sensitive to the market growth rate; slow growth may preclude the existence of such mechanisms.
• The algorithmic approach reduces the mechanism design problem to a system of difference constraints, solvable via shortest-path computation.
• The maximum payment for each agent is determined by the shortest path from a base node to the corresponding type profile, ensuring all incentive constraints are satisfied.
• If the sum of maximum payments across all agents is negative, no mechanism can simultaneously satisfy individual rationality, incentive compatibility, and weak budget balance.