Reinforcement learning (RL) for large language models (LLMs) is highly sensitive to hyperparameter configurations, making hyperparameter optimization (HPO) essential yet computationally expensive. Existing multi-fidelity HPO methods remain inefficient for LLM RL due to the massive model scale and resource-intensive training cycles. In this paper, we propose Joint Fidelity Hyperparameter Optimization (JF-HPO), which simultaneously adapts both model size and training budget as fidelity. JF-HPO is empowered by: (i) it leverages a small proxy model of the target LLM for efficient training and evaluation in each HPO trial; (ii) it integrates carefully designed early-stopping strategies based on training dynamics; (iii) it introduces an efficient checkpointing mechanism to eliminate redundant computations. Compared with existing HPO methods, JF-HPO significantly improves the computational efficiency of each trial (up to 14.9 times), while achieving better or competitive predictive accuracy under the same time budget. Notably, compared with utilizing hyperparameter configurations from the VeRL Recipe, JF-HPO delivers performance improvements ranging from 5.8% to 111.6%.