This paper revisits the problem of rate distortion optimization (RDO) with focus on inter-picture dependence. A joint RDO framework which incorporates the Lagrange multiplier as one of parameters to be optimized is proposed. Simpliﬁcation strategies are demonstrated for practical applications. To make the problem tractable, we consider an approach where prediction residuals of pictures in a video sequence are assumed to be emitted from a ﬁnite set of sources. Consequently the RDO problem is formulated as ﬁnding optimal coding parameters for a ﬁnite number of sources, regardless of the length of the video sequence. Speciﬁcally, in cases where a hierarchical prediction structure is used, prediction residuals of pictures at the same prediction layer are assumed to be emitted from a common source. Following this approach, we propose an iterative algorithm to alternatively optimize the selections of quantization parameters (QPs) and the corresponding Lagrange multipliers. Based on the results of the iterative algorithm, we further propose two practical algorithms to compute QPs and the Lagrange multipliers for the RA(random access) hierarchical video coding: the ﬁrst practical algorithm uses a ﬁxed formula to compute QPs and the Lagrange multipliers, and the second practical algorithm adaptively adjusts both QPs and the Lagrange multipliers. Experimental results show that these three algorithms, integrated into the HM 16.20 reference software of HEVC, can achieve considerable RD improvements over the standard HM 16.20 encoder, in the common RA test conﬁguration.