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Recent years have seen increasing employment of decision intelligence in electronic design automation (EDA), which aims to reduce the manual efforts and boost the design closure process in modern toolflows. However, existing approaches either require a large number of labeled data and expensive training efforts, or are limited in practical EDA toolflow integration due to computation overhead. This paper presents a generic end-to-end sequential decision making framework FlowTune for synthesis tooflow optimization, with a novel high-performance domain-specific, multi-stage multi-armed bandit (MAB) approach. This framework addresses optimization problems on Boolean optimization problems such as a) And-Inv-Graphs (# nodes), b) Conjunction Normal Form (CNF) minimization (# clauses) for Boolean Satisfiability; logic synthesis and technology mapping problems such as c) post static timing analysis (STA) delay and area optimization for standard-cell technology mapping, and d) FPGA technology mapping for 6-in LUT architectures. Moreover, we demonstrate the high extnsibility and generalizability of the proposed domain-specific MAB approach with end-to-end FPGA design flow, evaluated at post-routing stage, with two different FPGA backend tools (OpenFPGA and VPR) and two different logic synthesis representations (AIGs and MIGs). FlowTune is fully integrated with ABC [1], Yosys [2], VTR [3], LSOracle [4], OpenFPGA [5], and industrial tools, and is released publicly. The experimental results conducted on various design stages in the flow all demonstrate that our framework outperforms both hand-crafted flows [1] and ML explored flows [6], [7] in quality of results, and is orders of magnitude faster compared to ML-based approaches.