  Existing frameworks for evaluating and comparing generative models typically
target an offline setting, where the evaluator has access to full batches of
data produced by the models. However, in many practical scenarios, the goal is
to identify the best model using the fewest generated samples to minimize the
costs of querying data from the models. Such an online comparison is
challenging with current offline assessment methods. In this work, we propose
an online evaluation framework to find the generative model that maximizes a
standard assessment score among a group of available models. Our method uses an
optimism-based multi-armed bandit framework to identify the model producing
data with the highest evaluation score, quantifying the quality and diversity
of generated data. Specifically, we study the online assessment of generative
models based on the Fr\'echet Inception Distance (FID) and Inception Score (IS)
metrics and propose the FID-UCB and IS-UCB algorithms leveraging the upper
confidence bound approach in online learning. We prove sub-linear regret bounds
for these algorithms and present numerical results on standard image datasets,
demonstrating their effectiveness in identifying the score-maximizing
generative model.
