The Multi-Armed Bandit (MAB) problem is challenging in non-stationary environments where reward distributions evolve dynamically. We introduce RAVEN-UCB, a novel algorithm that combines theoretical rigor with practical efficiency via variance-aware adaptation. It achieves tighter regret bounds than UCB1 and UCB-V, with gap-dependent regret of order $K σ_{\max}^2 \log T / Δ$ and gap-independent regret of order $\sqrt{K T \log T}$. RAVEN-UCB incorporates three innovations: (1) variance-driven exploration using $\sqrt{\hatσ_k^2 / (N_k + 1)}$ in confidence bounds, (2) adaptive control via $α_t = α_0 / \log(t + ε)$, and (3) constant-time recursive updates for efficiency. Experiments across non-stationary patterns - distributional changes, periodic shifts, and temporary fluctuations - in synthetic and logistics scenarios demonstrate its superiority over state-of-the-art baselines, confirming theoretical and practical robustness.