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In this paper, we consider a general task of jumping varying distances and heights for a quadrupedal robot in noisy environments, such as off of uneven terrain and with variable robot dynamics parameters. To accurately jump in such conditions, we propose a framework using deep reinforcement learning that leverages and augments the complex solution of nonlinear trajectory optimization for quadrupedal jumping. While the standalone optimization limits jumping to take-off from flat ground and requires accurate assumptions of robot dynamics, our proposed approach improves the robustness to allow jumping off of significantly uneven terrain with variable robot dynamical parameters and environmental conditions. Compared with walking and running, the realization of aggressive jumping on hardware necessitates accounting for the motors' torque-speed relationship as well as the robot's total power limits. By incorporating these constraints into our learning framework, we successfully deploy our policy sim-to-real without further tuning, fully exploiting the available onboard power supply and motors. We demonstrate robustness to environment noise of foot disturbances of up to 6 cm in height, or 33% of the robot's nominal standing height, while jumping 2x the body length in distance.