Deep Reinforcement Learning for Sequential Combinatorial Auctions

Authors: Sai Srivatsa Ravindranath, Zhe Feng, Di Wang, Manzil Zaheer, Aranyak Mehta, David C. Parkes
Primary area: other topics in machine learning (i.e., none of the above)
Keywords: Mechanism Design, Auctions, Game Theory, Differential Economics, Reinforcement Learning, Deep Learning, Market Design, AI for Economics

Abstract:
Revenue-optimal auction design is a challenging problem with significant theoretical and practical implications. Sequential auction mechanisms, known for their simplicity and strong strategyproofness guarantees, are often limited by theoretical results that are largely existential, except for certain restrictive settings. Although traditional reinforcement learning methods such as Proximal Policy Optimization (PPO) and Soft Actor-Critic (SAC) are applicable in this domain, they struggle with computational demands and convergence issues when dealing with large and continuous action spaces. In light of this and recognizing that we can model transitions differentiable for our settings, we propose using a new reinforcement learning framework tailored for sequential combinatorial auctions that leverages first-order gradients.  Our extensive evaluations show that our approach achieves significant improvement in revenue over both analytical baselines and standard reinforcement learning algorithms. Furthermore, we scale our approach to scenarios involving up to 50 agents and 50 items, demonstrating its applicability in complex, real-world auction settings. As such, this work advances the computational tools available for auction design and contributes to bridging the gap between theoretical results and practical implementations in sequential auction design.

Decision: reject
Reviewer scores: 5, 6, 6, 6

Reviews and discussion:
<thread>
creation date:
1730472150545

thread_type:
official_review

<thread_object>
creator: reviewer_zdta

<content>
summary:
This paper introduces a new approach that uses fitted policy iteration and analytical gradients for learning revenue-maximizing sequential combinatorial auctions. Using twofold manner: initially refining the value function to align with the policy function and subsequently adjusting the policy function to maximize rewards. This method also can used in continuous action spaces via gradient descent.

strengths:
This paper introduces a new approach that uses fitted policy iteration and analytical gradients for learning revenue-maximizing sequential combinatorial auctions. Using twofold manner: initially refining the value function to align with the policy function and subsequently adjusting the policy function to maximize rewards. This method also can used in continuous action spaces via gradient descent.

weaknesses:
No

questions:
No
</content>
</thread_object>

</thread>
<thread>
creation date:
1730608818003

thread_type:
official_review

<thread_object>
creator: reviewer_hp6c

<content>
summary:
The paper explores designing revenue-maximizing mechanisms in sequential combinatorial auctions (SCAs) using deep reinforcement learning (DRL). SCAs present auction items sequentially, allowing bidders to make strategic choices at each stage. Although traditional sequential auctions have theoretical guarantees, they lack mechanisms to maximize revenue in complex environments. This paper addresses these limitations by proposing a deep reinforcement learning framework that leverages analytical gradients to optimize auctions involving multiple agents and items efficiently.

strengths:
1. The paper provides theoretical foundations for its policy optimization approach and demonstrates its effectiveness through extensive experiments. 
2. The paper introduces a new way to handle DRL in SCAs, particularly in combinatorial and high-dimensional settings.

weaknesses:
* The method involves fitted policy iterations and analytical gradients. The complexity can be increased and needs to be measured.
* The framework assumes knowledge of agents' valuation distributions, which may not always be accessible or accurate in practice.

questions:
1. What is the complexity of the new proposed method?
2. How to reduce the reliance on agents' valuation distributions?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730695826387

thread_type:
official_review

<thread_object>
creator: reviewer_pq2q

<content>
summary:
This paper proposed a method on designing revenue-optimal mechanisms for sequential combinatorial auctions to allocate items to multiple agents in stages where the agents place bids on bundles of items based on their preferences using DRL with designs like analytical gradients.

strengths:
- The paper is generally well-written and easy to follow, the motivation on solving limitations from RL on sample inefficiency and issues with convergence in large, continuous action spaces is valid
- Use of Analytical Gradients seems to be effective in enhancing sample efficiency and convergence.
- The approach demonstrates scalability to scenarios with empirical results.

weaknesses:
-  Despite improvements, the method may still face computational challenges in extremely large-scale auctions, similar to issues noted in Pieroth et al. (2023). 
- The reliance on known valuation distributions may limit applicability in settings where such information is unavailable which limits the use cases of this method, more explanation on this would be good
- The baseline selection needs to be justified, why not also compare with more state-of-the-art algorithms?
- This approach uses a fixed order of agent visits, which can limit its optimality in situations where the order of bidding impacts the auction’s overall revenue.
- Whether and how much this work is sensitive to hyperparameters is not explained.

questions:
Please see weakness.
</content>
</thread_object>

</thread>
<thread>
creation date:
1731441644018

thread_type:
official_review

<thread_object>
creator: reviewer_w499

<content>
summary:
This work investigates sequential combinatorial auctions, an instance of auction where the bidders arrive in a sequence and place bids on bundles (combinations) of items. Sequential combinatorial auctions is relevant due to its simplicity, its strategyproofness, and its generality. This work aims on numerically finding the optimal solution. Previously, this was achieved by formulating the problem into an MDP, and then running PPO on it. But the previous work was under the additive assumption so it did not really tackle the combinatorial nature of the problem. This obviously skipped the exponential action space brought by the bundles.

This work leverages the particular structure of auction, and proposes a gradient that uses the knowledge of the world model. This allows a first-order gradient feedback of the update. The work is inspired by fitted policy iteration (which I'm not sure why the manuscript did not cite any previous work) and the policy improvement step of which could benefit from the gradient derived.

With some additional techniques and tricks, the work is capable of hosting a decent size (at most 50 items) problem. Experiments are conducted on both additive and combinatorial settings against baselines including mechanism design methods and the previous RL approach. The proposed method seems to work well on the experiments.

strengths:
1. This work numerically solves sequential auctions with combinatorial action space. The solution is through an organic synergy between policy gradient and the auction process.
2. It scales to an action space with as many as 50 items.
3. Experiments show that it outperforms previous baselines.

weaknesses:
1. The topic (sequential auction + combinatorial + numerical solution) is a bit limited to the specific sub-community. I'm not seeing the method/techniques to be of a general interest.
2. The experiments are conducted only on toy examples. Given the numerical nature of the work, I was expecting some real data, or even real system, experiments.

questions:
Isn't FTI an existing algorithm? I don't see a citation on that.
</content>
</thread_object>

</thread>
<thread>
creation date:
1732222836242

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Reliance on Samples from Valuation Distribution

comment:
The reliance on samples from valuation distributions is a standard assumption in the automated mechanism design literature, both in deep learning-based approaches [1] and traditional methods [2]. In the context of independent private value auctions, as considered in this paper, the auctioneer only has access to valuation distributions or samples derived from them, with the objective of designing a mechanism that maximizes expected revenue while maintaining incentive compatibility and individual rationality. For a comprehensive discussion on the sample complexity required to ensure, with high probability, that the average revenue over the sample approximates the expected revenue with respect to the underlying unknown distribution, we refer the reviewers to [3]. However, it is worth noting that these results are specific to AMA auctions and do not readily extend to deep learning methods.

To address this, we aim to empirically evaluate the reliance on samples through an additional experiment. Specifically, we train both PPO and our approach using a fixed number of samples (s = {2, 5, 10, ..., 10000}) drawn from the valuation distribution, instead of sampling online, and report their performance on the same test set used originally. This provides an empirical perspective on the sample complexity requirements of our method and PPO. The results are in Tables 1 and 2.

| **Num Samples** | **PPO (rev)** | **FPI (rev)** |
|:--------------------:|:-------:|:-------:|
|          2           |   2.43  |   2.01  |
|          5           |   2.60  |   2.68  |
|         10           |   2.88  |   2.66  |
|        100           |   3.04  |   3.06  |
|       1000           |   3.08  |   3.12  |
|      10000           |   3.08  |   3.12  |
| online                | 3.09 | 3.12 |

**Table 1:**  Performance with varying number of samples for Setting A with 5 agents and 5 items

| **Num Samples** | **PPO (rev)** | **FPI (rev)** |
|:--------------------:|:-------:|:-------:|
|          2           |  5.85  |   5.33  |
|          5           |   5.45  |   6.25  |
|         10           |   5.37  |   6.80  |
|        100           |   6.51  |   7.42  |
|       1000           |   6.61  |   7.56  |
|      10000           |   6.68  |   7.58  |
| online                | 6.68 | 7.59 |

**Table 2:**  Performance with varying number of samples for Setting A with 10 agents and 10 items

---

**Reference**  
[1] Dütting, P., Feng, Z., Narasimhan, H., Parkes, D. C., & Ravindranath, S. S. (2024). Optimal auctions through deep learning: Advances in differentiable economics. Journal of the ACM, 71(1), 1-53.

[2] Sandholm, Tuomas. "Automated mechanism design: A new application area for search algorithms." International Conference on Principles and Practice of Constraint Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003.  

[3] Balcan, M. F. F., Sandholm, T., & Vitercik, E. (NeurIPS 2016).  
Sample complexity of automated mechanism design
</content>
</thread_object>

</thread>


Metareview:
metareview:
This paper applies deep reinforcement learning (DRL) to the problem of revenue-maximizing sequential combinatorial auctions (SCAs), leveraging analytical gradients and fitted policy iteration to address sample efficiency and scalability. However, the approach appears to be a direct application of standard DRL techniques tailored to the auction setting by exploiting specific transition structures, raising concerns about its broader contribution to DRL literature and real-world applicability. While the authors addressed scalability and baseline selection, the relevance to real-world systems remains unclear, and the work does not convincingly demonstrate novel contributions to the DRL community beyond applying existing methods to a specific problem.