On the convergence of no-regret learning in selfish routing

Walid Krichene, Benjamin Drighès, Alexandre Bayen
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):163-171, 2014.

Abstract

We study the repeated, non-atomic routing game, in which selfish players make a sequence of routing decisions. We consider a model in which players use regret-minimizing algorithms as the learning mechanism, and study the resulting dynamics. We are concerned in particular with the convergence to the set of Nash equilibria of the routing game. No-regret learning algorithms are known to guarantee convergence of a subsequence of population strategies. We are concerned with convergence of the actual sequence. We show that convergence holds for a large class of online learning algorithms, inspired from the continuous-time replicator dynamics. In particular, the discounted Hedge algorithm is proved to belong to this class, which guarantees its convergence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-krichene14, title = {On the convergence of no-regret learning in selfish routing}, author = {Krichene, Walid and Drighès, Benjamin and Bayen, Alexandre}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {163--171}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/krichene14.pdf}, url = {https://proceedings.mlr.press/v32/krichene14.html}, abstract = {We study the repeated, non-atomic routing game, in which selfish players make a sequence of routing decisions. We consider a model in which players use regret-minimizing algorithms as the learning mechanism, and study the resulting dynamics. We are concerned in particular with the convergence to the set of Nash equilibria of the routing game. No-regret learning algorithms are known to guarantee convergence of a subsequence of population strategies. We are concerned with convergence of the actual sequence. We show that convergence holds for a large class of online learning algorithms, inspired from the continuous-time replicator dynamics. In particular, the discounted Hedge algorithm is proved to belong to this class, which guarantees its convergence.} }
Endnote
%0 Conference Paper %T On the convergence of no-regret learning in selfish routing %A Walid Krichene %A Benjamin Drighès %A Alexandre Bayen %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-krichene14 %I PMLR %P 163--171 %U https://proceedings.mlr.press/v32/krichene14.html %V 32 %N 2 %X We study the repeated, non-atomic routing game, in which selfish players make a sequence of routing decisions. We consider a model in which players use regret-minimizing algorithms as the learning mechanism, and study the resulting dynamics. We are concerned in particular with the convergence to the set of Nash equilibria of the routing game. No-regret learning algorithms are known to guarantee convergence of a subsequence of population strategies. We are concerned with convergence of the actual sequence. We show that convergence holds for a large class of online learning algorithms, inspired from the continuous-time replicator dynamics. In particular, the discounted Hedge algorithm is proved to belong to this class, which guarantees its convergence.
RIS
TY - CPAPER TI - On the convergence of no-regret learning in selfish routing AU - Walid Krichene AU - Benjamin Drighès AU - Alexandre Bayen BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-krichene14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 163 EP - 171 L1 - http://proceedings.mlr.press/v32/krichene14.pdf UR - https://proceedings.mlr.press/v32/krichene14.html AB - We study the repeated, non-atomic routing game, in which selfish players make a sequence of routing decisions. We consider a model in which players use regret-minimizing algorithms as the learning mechanism, and study the resulting dynamics. We are concerned in particular with the convergence to the set of Nash equilibria of the routing game. No-regret learning algorithms are known to guarantee convergence of a subsequence of population strategies. We are concerned with convergence of the actual sequence. We show that convergence holds for a large class of online learning algorithms, inspired from the continuous-time replicator dynamics. In particular, the discounted Hedge algorithm is proved to belong to this class, which guarantees its convergence. ER -
APA
Krichene, W., Drighès, B. & Bayen, A.. (2014). On the convergence of no-regret learning in selfish routing. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):163-171 Available from https://proceedings.mlr.press/v32/krichene14.html.

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