Reinforcement Learning (RL) is a powerful method for controlling dynamic systems, but its learning mechanism can lead to unpredictable actions that undermine the safety of critical systems. Here, we propose RL with Adaptive Control Regularization (RL-ACR), an algorithm that enables safe RL exploration by combining the RL policy with a policy regularizer that hard-codes safety constraints. We perform policy combination via a "focus network," which determines the appropriate combination depending on the state—relying more on the safe policy regularizer for less-exploited states while allowing unbiased convergence for well-exploited states. In a series of critical control applications, we demonstrate that RL-ACR ensures safety during training while achieving the performance standards of model-free RL approaches that disregard safety.