Cost-based optimization is widely known to suffer from a major weakness: administrators spend a significant amount of time to tune the associated cost models. This problem only gets exacerbated in cross-platform settings as there are many more parameters that need to be tuned. In the era of machine learning (ML), the first step to remedy this problem is to replace the cost model of the optimizer with an ML model. However, such a solution brings in two major challenges. First, the optimizer has to transform a query plan to a vector million times during plan enumeration incurring a very high overhead. Second, a lot of training data is required to effectively train the ML model. We overcome these challenges in Robopt, a novel vector-based optimizer we have built for Rheem, a cross-platform system. Robopt not only uses an ML model to prune the search space but also bases the entire plan enumeration on a set of algebraic operations that operate on vectors, which are a natural fit to the ML model. This leads to both speed-up and scale-up of the enumeration process by exploiting modern CPUs via vectorization. We also accompany Robopt with a scalable training data generator for building its ML model. Our evaluation shows that (i) the vector-based approach is more efficient and scalable than simply using an ML model and (ii) Robopt matches and, in some cases, improves Rheem's cost-based optimizer in choosing good plans without requiring any tuning effort.