Title: Iterative Relaxing Gradient Projection for Continual Learning. Abstract: A critical capability for intelligent systems is to continually learn given a sequence of tasks. An ideal continual learner should be able to avoid catastrophic forgetting and effectively leverage past learned experiences to master new knowledge. Among different continual learning algorithms, gradient projection approaches impose hard constraints on the optimization space for new tasks to minimize task interference, yet hinder forward knowledge transfer at the same time. Recent methods use expansion-based techniques to relax the constraints, but a growing network can be computationally expensive. Therefore, it remains a challenge whether we can improve forward knowledge transfer for gradient projection approaches \textit{using a fixed network architecture}. In this work, we propose the Iterative Relaxing Gradient Projection (IRGP) framework. The basic idea is to iteratively search for the parameter subspaces most related to the current task and relax these parameters, then reuse the frozen spaces to facilitate forward knowledge transfer while consolidating previous knowledge. Our framework requires neither memory buffers nor extra parameters. Extensive experiments have demonstrated the superiority of our framework over several strong baselines. We also provide theoretical guarantees for our iterative relaxing strategies. 