The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits

Ronshee Chawla, Abishek Sankararaman, Ayalvadi Ganesh, Sanjay Shakkottai
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3471-3481, 2020.

Abstract

We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\Omega(\log(T))$ times through any connected pairwise gossip mechanism, then every agent’s regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents.

Cite this Paper


BibTeX
@InProceedings{pmlr-v108-chawla20a, title = {The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits}, author = {Chawla, Ronshee and Sankararaman, Abishek and Ganesh, Ayalvadi and Shakkottai, Sanjay}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3471--3481}, year = {2020}, editor = {Silvia Chiappa and Roberto Calandra}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/chawla20a/chawla20a.pdf}, url = { http://proceedings.mlr.press/v108/chawla20a.html }, abstract = {We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\Omega(\log(T))$ times through any connected pairwise gossip mechanism, then every agent’s regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents.} }
Endnote
%0 Conference Paper %T The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits %A Ronshee Chawla %A Abishek Sankararaman %A Ayalvadi Ganesh %A Sanjay Shakkottai %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-chawla20a %I PMLR %P 3471--3481 %U http://proceedings.mlr.press/v108/chawla20a.html %V 108 %X We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\Omega(\log(T))$ times through any connected pairwise gossip mechanism, then every agent’s regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents.
APA
Chawla, R., Sankararaman, A., Ganesh, A. & Shakkottai, S.. (2020). The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3471-3481 Available from http://proceedings.mlr.press/v108/chawla20a.html .

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