Distributed Exploration in Multi-Armed Bandits
This addresses the challenge of scaling bandit algorithms for computationally intensive, large-scale applications, offering a tradeoff between communication and speed-up.
The paper tackles the problem of distributed exploration in multi-armed bandits with k players collaborating to identify an ε-optimal arm, showing that with one communication round, players learn √k times faster than a single player, and with logarithmic communication, they achieve an ideal k speed-up.
We study exploration in Multi-Armed Bandits in a setting where $k$ players collaborate in order to identify an $ε$-optimal arm. Our motivation comes from recent employment of bandit algorithms in computationally intensive, large-scale applications. Our results demonstrate a non-trivial tradeoff between the number of arm pulls required by each of the players, and the amount of communication between them. In particular, our main result shows that by allowing the $k$ players to communicate only once, they are able to learn $\sqrt{k}$ times faster than a single player. That is, distributing learning to $k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement this result with a lower bound showing this is in general the best possible. On the other extreme, we present an algorithm that achieves the ideal factor $k$ speed-up in learning performance, with communication only logarithmic in $1/ε$.