The paper introduces a method for online conformal prediction with decaying step sizes, which simultaneously provides both worst-case and best-case guarantees. The method is designed to handle arbitrary sequences of data points and independent and identically distributed (I.I.D.) sequences. In the adversarial setting, the method ensures that the coverage rate converges to the desired level for every time point, not just on average over the observed sequence. In the I.I.D. setting, the method guarantees convergence of the coverage rate to the nominal level. The key innovation is the use of decaying step sizes, which improve the stability and practical performance of the method compared to previous approaches. The paper also includes theoretical guarantees and experimental results demonstrating the effectiveness of the proposed method.The paper introduces a method for online conformal prediction with decaying step sizes, which simultaneously provides both worst-case and best-case guarantees. The method is designed to handle arbitrary sequences of data points and independent and identically distributed (I.I.D.) sequences. In the adversarial setting, the method ensures that the coverage rate converges to the desired level for every time point, not just on average over the observed sequence. In the I.I.D. setting, the method guarantees convergence of the coverage rate to the nominal level. The key innovation is the use of decaying step sizes, which improve the stability and practical performance of the method compared to previous approaches. The paper also includes theoretical guarantees and experimental results demonstrating the effectiveness of the proposed method.