Optimization is a time-consuming part of radiation treatment planning. We propose to reduce the optimization problem by only using a representative subset of informative voxels. This way, we improve planning efficiency while maintaining or enhancing the plan quality. To reduce the computational complexity of the optimization problem, we propose to subsample the set of voxels via importance sampling. We derive a sampling distribution based on an importance score that we obtain from pre-solving an easy optimization problem involving a simplified probing objective. By solving a reduced version of the original optimization problem using this subset, we effectively reduce the problem's size and computational demands while accounting for regions in which satisfactory dose deliveries are challenging. In contrast to other stochastic (sub-)sampling methods, our technique only requires a single sampling step to define a reduced optimization problem. This problem can be efficiently solved using established solvers. Empirical experiments on open benchmark data highlight substantially reduced optimization times, up to 50 times faster than the original ones, for intensity-modulated radiation therapy (IMRT), all while upholding plan quality comparable to traditional methods. Our approach has the potential to significantly accelerate radiation treatment planning by addressing its inherent computational challenges. We reduce the treatment planning time by reducing the size of the optimization problem rather than improving the optimization method. Our efforts are thus complementary to much of the previous developments.