Bandit algorithms: Letting go of logarithmic regret for statistical robustness

Kumar Ashutosh, Jayakrishnan Nair, Anmol Kagrecha, Krishna Jagannathan
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:622-630, 2021.

Abstract

We study regret minimization in a stochastic multi-armed bandit setting, and establish a fundamental trade-off between the regret suffered under an algorithm, and its statistical robustness. Considering broad classes of underlying arms’ distributions, we show that bandit learning algorithms with logarithmic regret are always inconsistent and that consistent learning algorithms always suffer a super-logarithmic regret. This result highlights the inevitable statistical fragility of all ‘logarithmic regret’ bandit algorithms available in the literature - for instance, if a UCB algorithm designed for 1-subGaussian distributions is used in a subGaussian setting with a mismatched variance parameter, the learning performance could be inconsistent. Next, we show a positive result: statistically robust and consistent learning performance is attainable if we allow the regret to be slightly worse than logarithmic. Specifically, we propose three classes of distribution oblivious algorithms that achieve an asymptotic regret that is arbitrarily close to logarithmic.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-ashutosh21a, title = { Bandit algorithms: Letting go of logarithmic regret for statistical robustness }, author = {Ashutosh, Kumar and Nair, Jayakrishnan and Kagrecha, Anmol and Jagannathan, Krishna}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {622--630}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/ashutosh21a/ashutosh21a.pdf}, url = {https://proceedings.mlr.press/v130/ashutosh21a.html}, abstract = { We study regret minimization in a stochastic multi-armed bandit setting, and establish a fundamental trade-off between the regret suffered under an algorithm, and its statistical robustness. Considering broad classes of underlying arms’ distributions, we show that bandit learning algorithms with logarithmic regret are always inconsistent and that consistent learning algorithms always suffer a super-logarithmic regret. This result highlights the inevitable statistical fragility of all ‘logarithmic regret’ bandit algorithms available in the literature - for instance, if a UCB algorithm designed for 1-subGaussian distributions is used in a subGaussian setting with a mismatched variance parameter, the learning performance could be inconsistent. Next, we show a positive result: statistically robust and consistent learning performance is attainable if we allow the regret to be slightly worse than logarithmic. Specifically, we propose three classes of distribution oblivious algorithms that achieve an asymptotic regret that is arbitrarily close to logarithmic. } }
Endnote
%0 Conference Paper %T Bandit algorithms: Letting go of logarithmic regret for statistical robustness %A Kumar Ashutosh %A Jayakrishnan Nair %A Anmol Kagrecha %A Krishna Jagannathan %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-ashutosh21a %I PMLR %P 622--630 %U https://proceedings.mlr.press/v130/ashutosh21a.html %V 130 %X We study regret minimization in a stochastic multi-armed bandit setting, and establish a fundamental trade-off between the regret suffered under an algorithm, and its statistical robustness. Considering broad classes of underlying arms’ distributions, we show that bandit learning algorithms with logarithmic regret are always inconsistent and that consistent learning algorithms always suffer a super-logarithmic regret. This result highlights the inevitable statistical fragility of all ‘logarithmic regret’ bandit algorithms available in the literature - for instance, if a UCB algorithm designed for 1-subGaussian distributions is used in a subGaussian setting with a mismatched variance parameter, the learning performance could be inconsistent. Next, we show a positive result: statistically robust and consistent learning performance is attainable if we allow the regret to be slightly worse than logarithmic. Specifically, we propose three classes of distribution oblivious algorithms that achieve an asymptotic regret that is arbitrarily close to logarithmic.
APA
Ashutosh, K., Nair, J., Kagrecha, A. & Jagannathan, K.. (2021). Bandit algorithms: Letting go of logarithmic regret for statistical robustness . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:622-630 Available from https://proceedings.mlr.press/v130/ashutosh21a.html.

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