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There have been several recent works proposed to utilize model-based optimization methods to improve the productivity of using high-level synthesis (HLS) to design domain-specific architectures. They would replace the time-consuming performance estimation or simulation of design with a proxy model, and automatically insert pragmas to guide hardware optimizations. In this work, we address the challenges associated with high-level synthesis (HLS) design space exploration (DSE) through the evolving landscape of HLS tools. As these tools develop, the quality of results (QoR) from synthesis can vary significantly, complicating the maintenance of optimal design strategies across different toolchains. We introduce Active-CEM, a task transfer learning scheme that leverages a model-based explorer designed to adapt efficiently to changes in toolchains. This approach optimizes sample efficiency by identifying high-quality design configurations under a new toolchain without requiring extensive re-evaluation. We further refine our methodology by incorporating toolchain-invariant modeling. This allows us to predict QoR changes more accurately despite shifts in the black-box implementation of the toolchains. Experiment results on the HLSyn benchmark transitioning to new toolchain show an average performance improvement of 2.38× compared to AutoDSE and a 1.2× improvement over HARP, while also increasing the sample efficiency by 5.75×, and reducing the runtime by 2.7×.