Abstract
In this paper, we study the stochastic version of the one-sided full information bandit problem, where we have K arms \([K] = \{1, 2, \ldots , K\}\), and playing arm i would gain reward from an unknown distribution for arm i while obtaining reward feedback for all arms \(j \ge i\). One-sided full information bandit can model the online repeated second-price auctions, where the auctioneer could select the reserved price in each round and the bidders only reveal their bids when their bids are higher than the reserved price. In this paper, we present an elimination-based algorithm to solve the problem. Our elimination based algorithm achieves distribution independent regret upper bound \(O(\sqrt{T\cdot \log (TK)})\), and distribution dependent bound \(O((\log T + \log K)f(\varDelta ))\), where T is the time horizon, \(\varDelta \) is a vector of gaps between the mean reward of arms and the mean reward of the best arm, and \(f(\varDelta )\) is a formula depending on the gap vector that we will specify in detail. Our algorithm has the best theoretical regret upper bound so far. We also validate our algorithm empirically against other possible alternatives.
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Notes
- 1.
Note that the second-price auction is truthful in a single round, but in multi-rounds, it may not be truthful since the bidders may want to lower their bids first so that the seller would learn a lower reserve price. The truthfulness is not the main concern of this paper and its discussion is beyond the scope of this paper.
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Acknowledgement
Wei Chen is partially supported by the National Natural Science Foundation of China (Grant No. 61433014).
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Zhao, H., Chen, W. (2020). Stochastic One-Sided Full-Information Bandit. In: Brefeld, U., Fromont, E., Hotho, A., Knobbe, A., Maathuis, M., Robardet, C. (eds) Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2019. Lecture Notes in Computer Science(), vol 11908. Springer, Cham. https://doi.org/10.1007/978-3-030-46133-1_10
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