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This work proves a regret bound of order $\tilde{O}(\sqrt T)$, significantly improving over the previous $\tilde{O}(T^{2/3})$ guarantee, and is the first $\tilde{O}(\sqrt T)$ regret guarantee for latent linear-dynamics bandits with bilinear reward observations and an open-loop action-sequence benchmark.
A UCB-based algorithm that constructs assortments item-wise by maximizing optimistic marginal gains, avoids black-box optimization oracles, and offers a statistically and computationally efficient solution for diversity-aware assortment optimization under uncertainty is proposed.
This analysis provides a unified treatment of memory-induced non-stationarity and nonlinear link functions, while ensuring that the leading regret term is independent of the curvature of the link function.
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