Particle-in-cell simulations are among the most essential tools for the modeling and optimization of laser-plasma accelerators, since they reproduce the physics from first principles. However, the high computational cost associated with them can severely limit the scope of parameter and design optimization studies. Here, we show that a multitask Bayesian optimization algorithm can be used to mitigate the need for such high-fidelity simulations by incorporating information from inexpensive evaluations of reduced physical models. In a proof-of-principle study, where a high-fidelity optimization with fbpic is assisted by reduced-model simulations with wake-t, the algorithm demonstrates an order-of-magnitude speedup. This opens a path for the cost-effective optimization of laser-plasma accelerators in large parameter spaces, an important step toward fulfilling the high beam quality requirements of future applications.