  Non-stationary parametric bandits have attracted much attention recently.
There are three principled ways to deal with non-stationarity, including
sliding-window, weighted, and restart strategies. As many non-stationary
environments exhibit gradual drifting patterns, the weighted strategy is
commonly adopted in real-world applications. However, previous theoretical
studies show that its analysis is more involved and the algorithms are either
computationally less efficient or statistically suboptimal. This paper revisits
the weighted strategy for non-stationary parametric bandits. In linear bandits
(LB), we discover that this undesirable feature is due to an inadequate regret
analysis, which results in an overly complex algorithm design. We propose a
refined analysis framework, which simplifies the derivation and importantly
produces a simpler weight-based algorithm that is as efficient as
window/restart-based algorithms while retaining the same regret as previous
studies. Furthermore, our new framework can be used to improve regret bounds of
other parametric bandits, including Generalized Linear Bandits (GLB) and
Self-Concordant Bandits (SCB). For example, we develop a simple weighted GLB
algorithm with an $\widetilde{O}(k_\mu^{\frac{5}{4}} c_\mu^{-\frac{3}{4}}
d^{\frac{3}{4}} P_T^{\frac{1}{4}}T^{\frac{3}{4}})$ regret, improving the
$\widetilde{O}(k_\mu^{2} c_\mu^{-1}d^{\frac{9}{10}}
P_T^{\frac{1}{5}}T^{\frac{4}{5}})$ bound in prior work, where $k_\mu$ and
$c_\mu$ characterize the reward model's nonlinearity, $P_T$ measures the
non-stationarity, $d$ and $T$ denote the dimension and time horizon.
