Contextual Online Bilateral Trade
Romain Cosson, Federico Fusco, Anupam Gupta, Stefano Leonardi, Renato Paes Leme, and Matteo Russo

TL;DR
This paper develops algorithms for repeated bilateral trade with contextual valuations, achieving near-optimal regret bounds under different feedback models while maintaining budget balance and addressing both gain from trade and profit maximization.
Contribution
It introduces regret-minimizing algorithms for contextual bilateral trade with two feedback models, achieving tight bounds and ensuring budget balance.
Findings
Achieves $O(d ext{log}d)$ regret for gain from trade with two-bit feedback.
Attains $O(d ext{log} ext{log} T + d ext{log}d)$ regret for profit maximization.
Extends results to one-bit feedback with small profit loss and explores exponential dependence on dimension.
Abstract
We study repeated bilateral trade when the valuations of the sellers and the buyers are contextual. More precisely, the agents' valuations are given by the inner product of a context vector with two unknown -dimensional vectors -- one for the buyers and one for the sellers. At each time step , the learner receives a context and posts two prices, one for the seller and one for the buyer, and the trade happens if both agents accept their price. We study two objectives for this problem, gain from trade and profit, proving no-regret with respect to a surprisingly strong benchmark: the best omniscient dynamic strategy. In the natural scenario where the learner observes \emph{separately} whether the agents accept their price -- the so-called \emph{two-bit} feedback -- we design algorithms that achieve regret for gain from trade, and regret…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Machine Learning and Algorithms · Game Theory and Applications
