Learning to Restart: Differentiable Restart Policies for Optimization Dynamics

arXiv:2611.08883v1 Announce Type: new Abstract: Adaptive restart mechanisms, which reset the momentum or other auxiliary state of an iterative optimizer, play a central role in the empirical performance of accelerated first-order methods, yet existing restart rules remain almost entirely hand-designed. The obstruction to learning restart policies is that, unlike the typical Learning to Optimize (L2O) setting, the discrete restart events make the resulting trajectory non-differentiable in the algorithm parameters and thus block gradient-based optimization of the restart policy. We resolve this obstruction by developing a differentiable framework for restart policies through their continuous-time limit.