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Contextual Bandits with Cross-Learning

In the classic contextual bandits problem, in each round t, a learner observes some context c, chooses some action i to perform, and receives some reward ri,t(c)
. We consider the variant of this problem in which in addition to receiving the reward ri,t(c)
, the learner also learns the values of ri,t(c′)
for some other contexts c′
in set Oi(c)
, that is, the rewards that would be achieved by performing that action under different contexts c′∈Oi(c)
. This variant arises in several strategic settings, such as learning how to bid in nontruthful repeated auctions, which has gained a lot of attention lately as many platforms have switched to running first price auctions. We call this problem the contextual bandits problem with cross-learning. The best algorithms for the classic contextual bandits problem achieve O˜(CKT−−−−√)
regret against all stationary policies, in which C is the number of contexts, K the number of actions, and T the number of rounds. We design and analyze new algorithms for the contextual bandits problem with cross-learning and show that their regret has better dependence on the number of contexts. Under complete cross-learning in which the rewards for all contexts are learned when choosing an action, that is, set Oi(c)
contains all contexts, we show that our algorithms achieve regret O˜(KT−−−√)
, removing the dependence on C. For any other cases, that is, under partial cross-learning in which |Oi(c)|

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Informasi Detail
Judul Seri
No. Panggil
-
Penerbit
: .,
Deskripsi Fisik
p. 1607-1629
Bahasa
English
ISBN/ISSN
-
Klasifikasi
NONE
Tipe Isi
-
Tipe Media
-
Tipe Pembawa
-
Edisi
-
Subjek
BIDDING
FIRST PRICE AUCTIONS
CONTEXTUAL BANDITS
CROSS-LEARNING
Info Detail Spesifik
https://doi.org/10.1287/moor.2022.1313
Pernyataan Tanggungjawab
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