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Efficient regret bounds for online bid optimisation in budget-limited sponsored search auctions

Efficient regret bounds for online bid optimisation in budget-limited sponsored search auctions
Efficient regret bounds for online bid optimisation in budget-limited sponsored search auctions
We study the problem of an advertising agent who needs to intelligently distribute her budget across a sequence of online keyword bidding auctions. We assume the closing price of each auction is governed by the same unknown distribution, and study the problem of making provably optimal bidding decisions. Learning the distribution is done under censored observations, i.e. the closing price of an auction is revealed only if the bid we place is above it. We consider three algorithms, namely ε-First, Greedy Product-Limit (GPL) and LuekerLearn, respectively, and we show that these algorithms provably achieve Hannan-consistency. In particular, we show that the regret bound of epsilon-FIrst is at most O(T2\3) with high probability. For the other two algorithms, we first prove that, by using a censored data distribution estimator proposed by Zeng[19], the empirical distribution of the closing market price converges in probability to its true distribution with a O(1/√ t) rate, where t is the number of updates. Based on this result, we prove that both GPL and LuekerLearn achieve O(√ T) regret bound with high probability. This in fact provides an affirmative answer to the research question raised in [1]. We also evaluate the above mentioned algorithms using real bidding data, and show that although GPL achieves the best performance on average (up to 90% of the optimal solution), its long running time may limit its suitability in practice. By contrast, LuekerLearn and ε-First proposed in this paper achieve up to 85% of the optimal, but with an exponential reduction in computational complexity (a saving up to 95%, compared to GPL).
809-818
Tran-Thanh, Long
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Stavrogiannis, Lampros C.
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Naroditskiy, Victor
8881263c-ee85-49f2-b658-99c31b490e1d
Robu, Valentin
36b30550-208e-48d4-8f0e-8ff6976cf566
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Key, Peter
512c3cbe-f4ee-4c1b-a334-2b141d980527
Tran-Thanh, Long
e0666669-d34b-460e-950d-e8b139fab16c
Stavrogiannis, Lampros C.
08655c3e-a334-4bec-a8a6-3acce9d6ee5b
Naroditskiy, Victor
8881263c-ee85-49f2-b658-99c31b490e1d
Robu, Valentin
36b30550-208e-48d4-8f0e-8ff6976cf566
Jennings, Nicholas R.
ab3d94cc-247c-4545-9d1e-65873d6cdb30
Key, Peter
512c3cbe-f4ee-4c1b-a334-2b141d980527

Tran-Thanh, Long, Stavrogiannis, Lampros C., Naroditskiy, Victor, Robu, Valentin, Jennings, Nicholas R. and Key, Peter (2014) Efficient regret bounds for online bid optimisation in budget-limited sponsored search auctions. 30th Conference on Uncertainty in Artificial Intelligence, Canada. 23 - 27 Jul 2014. pp. 809-818 .

Record type: Conference or Workshop Item (Paper)

Abstract

We study the problem of an advertising agent who needs to intelligently distribute her budget across a sequence of online keyword bidding auctions. We assume the closing price of each auction is governed by the same unknown distribution, and study the problem of making provably optimal bidding decisions. Learning the distribution is done under censored observations, i.e. the closing price of an auction is revealed only if the bid we place is above it. We consider three algorithms, namely ε-First, Greedy Product-Limit (GPL) and LuekerLearn, respectively, and we show that these algorithms provably achieve Hannan-consistency. In particular, we show that the regret bound of epsilon-FIrst is at most O(T2\3) with high probability. For the other two algorithms, we first prove that, by using a censored data distribution estimator proposed by Zeng[19], the empirical distribution of the closing market price converges in probability to its true distribution with a O(1/√ t) rate, where t is the number of updates. Based on this result, we prove that both GPL and LuekerLearn achieve O(√ T) regret bound with high probability. This in fact provides an affirmative answer to the research question raised in [1]. We also evaluate the above mentioned algorithms using real bidding data, and show that although GPL achieves the best performance on average (up to 90% of the optimal solution), its long running time may limit its suitability in practice. By contrast, LuekerLearn and ε-First proposed in this paper achieve up to 85% of the optimal, but with an exponential reduction in computational complexity (a saving up to 95%, compared to GPL).

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More information

e-pub ahead of print date: 9 June 2014
Published date: 9 June 2014
Venue - Dates: 30th Conference on Uncertainty in Artificial Intelligence, Canada, 2014-07-23 - 2014-07-27
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 365566
URI: https://eprints.soton.ac.uk/id/eprint/365566
PURE UUID: 17eac920-889f-4177-8d44-59a62246cac0
ORCID for Long Tran-Thanh: ORCID iD orcid.org/0000-0003-1617-8316

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Date deposited: 10 Jun 2014 14:05
Last modified: 02 Aug 2018 00:30

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