To address the issue where traditional impedance control struggles to meet compliance requirements during robot interactions with dynamic environments, an adaptive variable impedance control strategy based on an iterative learning control (ILC) framework is proposed to achieve the desired compliant robot-environment interaction behavior. This strategy integrates the Adam optimization algorithm with streaming sparse Gaussian processes (SSGP) on the basis of iterative learning, addressing the shortcomings of slow convergence of impedance parameters and weak generalization capability in traditional iterative learning control (ILC). First, by learning from the Adam optimization algorithm, an adaptive gradient learning (AGL) method is proposed to guide the learning rate setting in iterative learning, thereby accelerating the convergence speed of impedance parameters. Second, by employing streaming sparse Gaussian processes, data is sparsely processed in a streaming manner to retain key features, thereby enhancing the generalization ability of the variable impedance strategy for new tasks. Experimental results show that, compared with traditional iterative learning methods, the proposed method significantly improves the convergence speed of impedance parameters. It effectively addresses the issues of learning rate sensitivity and task-dependency in impedance learning, while enhancing the generalization capability of impedance learning, thereby verifying the effectiveness of the proposed method.