[Paper Review] Differentially Private Combinatorial Cloud Auction

Tianjiao Ni, Zhili Chen+4 more|arXiv (Cornell University)|Jan 3, 2020

Privacy-Preserving Technologies in Data26 references4 citations

TL;DR

This paper proposes Differentially Private Combinatorial Cloud Auction (DPCA), a mechanism that ensures differential privacy, approximate truthfulness, and high revenue in cloud resource allocation by using the exponential mechanism to select clearing unit prices based on revenue-proportional probabilities. The improved variants DPCA-S and DPCA-M reduce running time by selecting unit prices sequentially or in groups, achieving a tunable trade-off between efficiency and revenue while preserving privacy guarantees.

ABSTRACT

Cloud service providers typically provide different types of virtual machines (VMs) to cloud users with various requirements. Thanks to its effectiveness and fairness, auction has been widely applied in this heterogeneous resource allocation. Recently, several strategy-proof combinatorial cloud auction mechanisms have been proposed. However, they fail to protect the bid privacy of users from being inferred from the auction results. In this paper, we design a differentially private combinatorial cloud auction mechanism (DPCA) to address this privacy issue. Technically, we employ the exponential mechanism to compute a clearing unit price vector with a probability proportional to the corresponding revenue. We further improve the mechanism to reduce the running time while maintaining high revenues, by computing a single clearing unit price, or a subgroup of clearing unit prices at a time, resulting in the improved mechanisms DPCA-S and its generalized version DPCA-M, respectively. We theoretically prove that our mechanisms can guarantee differential privacy, approximate truthfulness and high revenue. Extensive experimental results demonstrate that DPCA can generate near-optimal revenues at the price of relatively high time complexity, while the improved mechanisms achieve a tunable trade-off between auction revenue and running time.

Motivation & Objective

• To address the lack of bid privacy protection in existing truthful combinatorial cloud auction mechanisms, where bid information can be inferred from auction outcomes.
• To design a mechanism that guarantees differential privacy without compromising revenue or truthfulness in combinatorial cloud auctions.
• To reduce the high computational complexity of the baseline DPCA mechanism while maintaining high revenue, enabling practical deployment.
• To provide a tunable trade-off between auction running time and revenue through modularized price selection strategies.

Proposed method

• The DPCA mechanism uses the exponential mechanism to select a clearing unit price vector with probability proportional to the revenue it generates, ensuring differential privacy.
• DPCA-S improves efficiency by selecting one unit price per iteration, reducing noise injection and computational load.
• DPCA-M generalizes the approach by selecting a group of unit prices simultaneously, balancing revenue and performance.
• The mechanisms are designed to satisfy approximate truthfulness by aligning incentives with truthful bidding under privacy constraints.
• Theoretical analysis proves that DPCA, DPCA-S, and DPCA-M achieve differential privacy, approximate truthfulness, and high revenue.
• The mechanisms are evaluated using simulations with varying numbers of VM types, users, and privacy budgets to assess trade-offs between revenue, time, and user satisfaction.

Experimental results

Research questions

• RQ1 Can a combinatorial cloud auction mechanism guarantee differential privacy while maintaining high revenue and approximate truthfulness?
• RQ2 How can the computational complexity of differentially private auction mechanisms be reduced without significantly degrading revenue?
• RQ3 What is the trade-off between running time and auction revenue when selecting unit prices sequentially versus in groups?
• RQ4 How does the privacy budget ε affect the performance of the proposed mechanisms in terms of revenue and user satisfaction?
• RQ5 Can the proposed mechanisms outperform non-private auction mechanisms in revenue when privacy is a constraint?

Key findings

• DPCA achieves near-optimal revenue but has high running time, making it suitable only for small-scale cloud auctions.
• DPCA-S achieves the lowest running time (under 200 ms) but yields the worst revenue due to increased noise from multiple exponential mechanism applications.
• DPCA-M achieves a balanced trade-off, with higher revenue than DPCA-S and lower running time than DPCA, especially when selecting multiple prices per group (T=3).
• As the privacy budget ε increases from 0.2 to 1.0, both revenue and user satisfaction across all mechanisms increase, confirming the positive impact of higher privacy budgets.
• In practical scenarios with 350 users and 20 VM types, DPCA-M with T=3 outperforms DPCA-S and Basic in revenue, while maintaining acceptable running times under 5 seconds.
• When VM supply exceeds demand, the proposed private mechanisms generate higher revenue than the non-private baseline, demonstrating the value of privacy-preserving design even under surplus conditions.