We propose a novel model for learned query optimization which provides query hints leading to better execution plans. The model addresses the three key challenges in learned hint-based query optimization: reliable hint recommendation (ensuring non-degradation of query latency), efficient hint exploration, and fast inference. We provide an in-depth analysis of existing NN-based approaches to hint-based optimization and experimentally confirm the named challenges for them. Our alternative solution consists of a new inference schema based on an ensemble of context-aware models and a graph storage for reliable hint suggestion and fast inference, and a budget-controlled training procedure with a local search algorithm that solves the issue of exponential search space exploration. In experiments on standard benchmarks, our model demonstrates optimization capability close to the best achievable with coarse-grained hints. Controlling the degree of parallelism (query dop) in addition to operator-related hints enables our model to achieve 3x latency improvement on JOB benchmark which sets a new standard for optimization. Our model is interpretable and easy to debug, which is particularly important for deployment in production.