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Effective decision-making in autonomous driving relies on accurate inference of other traffic agents' future behaviors. To achieve this, we propose an online learning-based behavior prediction model and an efficient planner for Partially Observable Markov Decision Processes (POMDPs). We develop a learning-based prediction model, enhanced with a recurrent neural memory network, to dynamically update latent belief states and infer the intentions of other agents. The model can also integrate the ego vehicle's intentions to reflect closed-loop interactions among agents, and it learns from both offline data and online interactions. For planning, we employ an option-based Monte-Carlo Tree Search (MCTS) planner, which reduces computational complexity by searching over action sequences. Inside the MCTS planner, we use predicted long-term multi-modal trajectories to approximate future updates, which eliminates iterative belief updating and improves the running efficiency. Our approach also incorporates deep Q-learning (DQN) as a search prior, which significantly improves the performance of the MCTS planner. Experimental results from simulated environments validate the effectiveness of our proposed method. The online belief update model can significantly enhance the accuracy and temporal consistency of predictions, leading to improved decision-making performance. Employing DQN as a search prior in the MCTS planner considerably boosts its performance and outperforms an imitation learning-based prior. Additionally, we show that the option-based MCTS substantially outperforms the vanilla method in terms of performance and …