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Nash Social Welfare for Multi Armed Bandits: Trajectory-wise Expected and High Probability Regret
We study fair multi-armed bandits under the Nash Social Welfare (NSW) objective, which measures performance via the geometric mean of accumulated rewards. Existing work defines Nash regret as $\mathrm{NR}_T = μ^\star - (\prod_{t=1}^T \mathbb{E}μ_{I_t})^{1/T}$, where $μ_{I_t}$ is the mean reward of t
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