Learning the Switching Rate by Discretising Bernoulli Sources Online

Steven Rooij, Tim Erven
; Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:432-439, 2009.

Abstract

The expert tracking algorithm Fixed-Share depends on a parameter alpha, called the switching rate. If the final number of outcomes T is known in advance, then the switching rate can be learned with regret 1/2 log T + O(1) bits. The current fastest method that achieves this, Learn-alpha, is based on optimal discretisation of the Bernoulli distributions into O(√T) bins and runs in O(T√T) time; however the exact locations of these points have to be determined algorithmically. This paper introduces a new discretisation scheme with the same regret bound for known T, that specifies the number and positions of the discretisation points explicitly. The scheme is especially useful when T is not known in advance: a new fully on-line algorithm, Refine-Online, is presented, which runs in O(T√T log T) time and achieves a regret of 1/2 log 3 log T + O(log log T) bits.

Cite this Paper


BibTeX
@InProceedings{pmlr-v5-rooij09a, title = {Learning the Switching Rate by Discretising Bernoulli Sources Online}, author = {Steven Rooij and Tim Erven}, booktitle = {Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics}, pages = {432--439}, year = {2009}, editor = {David van Dyk and Max Welling}, volume = {5}, series = {Proceedings of Machine Learning Research}, address = {Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v5/rooij09a/rooij09a.pdf}, url = {http://proceedings.mlr.press/v5/rooij09a.html}, abstract = {The expert tracking algorithm Fixed-Share depends on a parameter alpha, called the switching rate. If the final number of outcomes T is known in advance, then the switching rate can be learned with regret 1/2 log T + O(1) bits. The current fastest method that achieves this, Learn-alpha, is based on optimal discretisation of the Bernoulli distributions into O(√T) bins and runs in O(T√T) time; however the exact locations of these points have to be determined algorithmically. This paper introduces a new discretisation scheme with the same regret bound for known T, that specifies the number and positions of the discretisation points explicitly. The scheme is especially useful when T is not known in advance: a new fully on-line algorithm, Refine-Online, is presented, which runs in O(T√T log T) time and achieves a regret of 1/2 log 3 log T + O(log log T) bits.} }
Endnote
%0 Conference Paper %T Learning the Switching Rate by Discretising Bernoulli Sources Online %A Steven Rooij %A Tim Erven %B Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2009 %E David van Dyk %E Max Welling %F pmlr-v5-rooij09a %I PMLR %J Proceedings of Machine Learning Research %P 432--439 %U http://proceedings.mlr.press %V 5 %W PMLR %X The expert tracking algorithm Fixed-Share depends on a parameter alpha, called the switching rate. If the final number of outcomes T is known in advance, then the switching rate can be learned with regret 1/2 log T + O(1) bits. The current fastest method that achieves this, Learn-alpha, is based on optimal discretisation of the Bernoulli distributions into O(√T) bins and runs in O(T√T) time; however the exact locations of these points have to be determined algorithmically. This paper introduces a new discretisation scheme with the same regret bound for known T, that specifies the number and positions of the discretisation points explicitly. The scheme is especially useful when T is not known in advance: a new fully on-line algorithm, Refine-Online, is presented, which runs in O(T√T log T) time and achieves a regret of 1/2 log 3 log T + O(log log T) bits.
RIS
TY - CPAPER TI - Learning the Switching Rate by Discretising Bernoulli Sources Online AU - Steven Rooij AU - Tim Erven BT - Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics PY - 2009/04/15 DA - 2009/04/15 ED - David van Dyk ED - Max Welling ID - pmlr-v5-rooij09a PB - PMLR SP - 432 DP - PMLR EP - 439 L1 - http://proceedings.mlr.press/v5/rooij09a/rooij09a.pdf UR - http://proceedings.mlr.press/v5/rooij09a.html AB - The expert tracking algorithm Fixed-Share depends on a parameter alpha, called the switching rate. If the final number of outcomes T is known in advance, then the switching rate can be learned with regret 1/2 log T + O(1) bits. The current fastest method that achieves this, Learn-alpha, is based on optimal discretisation of the Bernoulli distributions into O(√T) bins and runs in O(T√T) time; however the exact locations of these points have to be determined algorithmically. This paper introduces a new discretisation scheme with the same regret bound for known T, that specifies the number and positions of the discretisation points explicitly. The scheme is especially useful when T is not known in advance: a new fully on-line algorithm, Refine-Online, is presented, which runs in O(T√T log T) time and achieves a regret of 1/2 log 3 log T + O(log log T) bits. ER -
APA
Rooij, S. & Erven, T.. (2009). Learning the Switching Rate by Discretising Bernoulli Sources Online. Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, in PMLR 5:432-439

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