Coordination without communication: optimal regret in two players multi-armed bandits

TL;DR

This paper introduces a communication-free coordination strategy for two cooperating agents in a stochastic multi-armed bandit setting, achieving near-optimal regret and minimal collisions, with theoretical bounds supporting its effectiveness.

Contribution

It presents a novel no-communication coordination strategy for two agents in multi-armed bandits with proven near-optimal regret bounds and collision avoidance.

Findings

Achieves near-optimal regret of O(√T log T)

Ensures no collisions with high probability

Provides a lower bound indicating the necessity of the logarithmic term

Abstract

We consider two agents playing simultaneously the same stochastic three-armed bandit problem. The two agents are cooperating but they cannot communicate. We propose a strategy with no collisions at all between the players (with very high probability), and with near-optimal regret $O(\sqrt{T \log(T)})$. We also argue that the extra logarithmic term $\sqrt{\log(T)}$ should be necessary by proving a lower bound for a full information variant of the problem.