Feature-Based Online Bilateral Trade
Solenne Gaucher, Martino Bernasconi, Matteo Castiglioni, Andrea Celli,, Vianney Perchet
TL;DR
This paper develops online algorithms for bilateral trade with feature-based valuations, achieving low regret under various feedback and budget constraints, advancing understanding of dynamic pricing with private information.
Contribution
It introduces novel algorithms for online bilateral trade with feature-based valuations, characterizing regret bounds under different feedback and budget constraints.
Findings
Achieves $O(\log T)$ regret with two-bit feedback and strong budget balance.
Provides tight $ ilde{O}(T^{2/3})$ regret bounds with noisy valuations.
Shows how to reduce one-bit feedback scenarios to two-bit setups, highlighting feedback-budget trade-offs.
Abstract
Bilateral trade models the problem of facilitating trades between a seller and a buyer having private valuations for the item being sold. In the online version of the problem, the learner faces a new seller and buyer at each time step, and has to post a price for each of the two parties without any knowledge of their valuations. We consider a scenario where, at each time step, before posting prices the learner observes a context vector containing information about the features of the item for sale. The valuations of both the seller and the buyer follow an unknown linear function of the context. In this setting, the learner could leverage previous transactions in an attempt to estimate private valuations. We characterize the regret regimes of different settings, taking as a baseline the best context-dependent prices in hindsight. First, in the setting in which the learner has two-bit…
Peer Reviews
Decision·ICLR 2025 Poster
The authors propose a very reasonable contextual model of online bilateral trade. I find the new model to be well motivated and combines two natural areas of study namely bilateral trade and online contextual regret minimization. The algorithms themselves seem interesting and are fairly natural. The reduction from the two bit strong budget balanced case to the one bit global budget balanced case is perhaps the most interesting to me. Essentially it is a general recipe where by one can exploit
Although the algorithms are natural and interesting, I am unable to distinguish where the new ideas are and how much of the paper is using known tools to a new setting. I would appreciate more explanation on what the new ideas are in both the two bit setting and the one-bit setting. \o
The paper is well-written and analyzes a very interesting theoretical problem. The authors did a good job to describe the problem and how the algorithm handles the challenges. The theoretical guarantee of the paper is sound. The authors provide a complete story for the setting with two-bit feedback model. In addition, the reduction from one-bit to two-bit by sacrificing budget balance constraint is very interesting and elegant.
There is no matching lower bound for the one-bit feedback setting. I also have some questions regarding this setting.
1. The paper derives strong $O(\log T)$ regret, though under stronger conditions. 2. The paper derives $O(T^{2/3})$ regret upper bound for their algorithm and shows that there exists a matching lower bound.
1. The main results of the paper rely on the two-bid feedback setting, where both the seller and the buyer reveal to the decision maker whether they want to sell the product or buy the product. This is quite a strong condition, and the paper would benefit from a more detailed discussion on whether this condition happens or not in reality. 2. Though the theoretical guarantee is provided, there are not numerical experiments in the paper showing the empirical performances. Also, the computation co
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Taxonomy
TopicsAuction Theory and Applications · Advanced Bandit Algorithms Research · Optimization and Search Problems