Automated Deterministic Auction Design with Objective Decomposition

TL;DR

This work tackles the challenge of designing high-revenue, DSIC and IR deterministic auctions for general multi-item settings. It introduces OD-VVCA, which constrains mechanisms to deterministic Virtual Valuations Combinatorial Auctions and uses a parallelizable dynamic programming solver to compute allocations/payments efficiently, enabling scalable optimization. The revenue objective is decomposed into a differentiable component $Z(V, \mathbf{w}, \boldsymbol{\lambda})$ and a discontinuous component $F(V, \mathbf{w}, \boldsymbol{\lambda})$, with $\mathbf{w}=e^{\boldsymbol{\alpha}}$ and Gaussian smoothing applied to $Z$ to facilitate gradient-based optimization. Empirical results show that OD-VVCA delivers higher revenue than both deterministic baselines and randomized AMA-based methods, particularly in large-scale asymmetric auctions, demonstrating practical applicability and scalability for automated deterministic mechanism design in multi-item auctions.

Abstract

Identifying high-revenue mechanisms that are both dominant strategy incentive compatible (DSIC) and individually rational (IR) is a fundamental challenge in auction design. While theoretical approaches have encountered bottlenecks in multi-item auctions, there has been much empirical progress in automated designing such mechanisms using machine learning. However, existing research primarily focuses on randomized auctions, with less attention given to the more practical deterministic auctions. Therefore, this paper investigates the automated design of deterministic auctions and introduces OD-VVCA, an objective decomposition approach for automated designing Virtual Valuations Combinatorial Auctions (VVCAs). Firstly, we restrict our mechanism to deterministic VVCAs, which are inherently DSIC and IR. Afterward, we utilize a parallelizable dynamic programming algorithm to compute the allocation and revenue outcomes of a VVCA efficiently. We then decompose the revenue objective function into continuous and piecewise constant discontinuous components, optimizing each using distinct methods. Extensive experiments show that OD-VVCA achieves high revenue in multi-item auctions, especially in large-scale settings where it outperforms both randomized and deterministic baselines, indicating its efficacy and scalability.

Figures (4)

• Figure 1: Overview of OD-VVCA for automated design of deterministic auctions. We constrain the mechanism to VVCAs with $n + n \times 2^m$ parameters, introducing $\bm\alpha \in \mathbb{R}^n$ such that ${\bm{w}} = e^{\bm\alpha} \in \mathbb{R}_+^n$ to accommodate the positive range of ${\bm{w}}$. A parallelizable dynamic programming algorithm is employed to compute the allocations and payments for a batch of valuations. Afterward, the average revenue objective is decomposed into two components, and their gradients are estimated or computed directly. By integrating these gradients, we update the VVCA parameters through gradient ascent.
• Figure 2: Training curves for OD-VVCA, BBBVVCA, and FO-VVCA under $5 \times 10$\ref{['settingA']}, $5 \times 10$\ref{['settingB']} and $5\times 3$\ref{['settingB']}. The plots depict average results across $5$ runs and the $95\%$
• Figure 3: Training dynamics of OD-VVCA over $2000$ iterations in $2\times 2$ (\ref{['settingA']}). The trajectory of $(x, y)$ is simultaneously plotted on $R(x, y)$, $F(x, y)$, and $Z(x, y)$. The trajectory converges at a point balancing the values of both $F(x, y)$ and $Z(x, y)$, illustrating the effectiveness of optimizing $R(x, y)$ through objective decomposition.
• Figure 4: Visualization of $Z_{\mathcal{S}}(e^{\bm\alpha}, {\bm\lambda})$, $\tilde{Z}^\sigma_{\mathcal{S}}(e^{\bm\alpha}, {\bm\lambda})$, and the corresponding estimated gradient $\tilde{\nabla} \tilde{Z}_{\mathcal{S}}(e^{\bm\alpha}, {\bm\lambda})$ in $2\times 2$\ref{['settingA']} with respect to one parameter.

Theorems & Definitions (8)

• Proposition 4.0
• Remark 4.1
• Proposition A.1
• proof
• Proposition B.0
• Lemma B.1
• proof
• proof : Proof of \ref{['proposition:Z:smooth']}