Mobile devices such as smartphones, laptops, and tablets can often connect to multiple access networks (e.g., Wi-Fi, LTE, and 5G) simultaneously.Recent advancements facilitate seamless integration of these connections below the transport layer, enhancing the experience for apps that lack inherent multi-path support.This optimization hinges on dynamically determining the traffic distribution across networks for each device, a process referred to as multi-access traffic splitting.This paper introduces NetworkGym, a high-fidelity network environment simulator that facilitates generating multiple network traffic flows and multi-access traffic splitting.This simulator facilitates training and evaluating different RL-based solutions for the multi-access traffic splitting problem.Our initial explorations demonstrate that the majority of existing state-of-the-art offline RL algorithms (e.g. CQL) fail to outperform certain hand-crafted heuristic policies on average.This illustrates the urgent need to evaluate offline RL algorithms against a broader range of benchmarks, rather than relying solely on popular ones such as D4RL.We also propose an extension to the TD3+BC algorithm, named Pessimistic TD3 (PTD3), and demonstrate that it outperforms many state-of-the-art offline RL algorithms.PTD3's behavioral constraint mechanism, which relies on value-function pessimism, is theoretically motivated and relatively simple to implement.We open source our code and offline datasets at github.com/hmomin/networkgym.