Reinforcement learning has shown strong performance in robotic manipulation, but learned policies often degrade in performance when test conditions differ from the training distribution. This limitation is especially important for reliable robot planning and control in contact-rich tasks such as pushing and pick-and-place, where changes in goals, contact conditions, or robot dynamics can drive the system out-of-distribution at inference time. In this paper, we investigate a hybrid controller that combines reinforcement learning with bounded extremum seeking (ES) to improve robustness under such conditions. In the proposed approach, deep deterministic policy gradient (DDPG) policies are trained under standard conditions on the robotic pushing and pick-and-place tasks, and are then combined with bounded ES during deployment. The RL policy provides fast manipulation behavior, while bounded ES ensures robustness of the overall controller to time variations when operating conditions depart from those seen during training. The resulting controller is evaluated under several out-of-distribution settings, including time-varying goals and spatially varying friction patches. Crucially, under reasonable assumptions, we prove finite time RL-based convergence of a robotic arm to an object after which bounded ES achieves finite-time convergence to a bounded velocity moving target. We provide analytic formulas for both convergence times, and an ability to tune the convergence times by our choice of gains.

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