Self-evaluation, a model's ability to assess the correctness of its own output, is crucial for Large Multimodal Models (LMMs) to achieve self-improvement in multi-turn conversations, yet largely absent in foundation models. Recent work has employed reinforcement learning (RL) to enhance self-evaluation; however, its fixed reward mechanism suffers from reward hacking when optimizing multiple training objectives, leading to model collapse. In this paper we propose AdaPO, an online reinforcement learning framework capable of adaptively adjusting training objective in real time according to the current training state for each task. Specifically, to mitigate reward hacking , AdaPO introduces an Adaptive Reward Model (ARM) and a Reward Aware Dynamic KL Regularization mechanism. ARM assesses the task's training state from the distribution of model generated multi-turn trajectories' performance. Reward Aware Dynamic KL replaces a fixed penalty with dynamic coefficients which is modulated by the reward gap between different multi-turn situations. Notably, our method automatically and smoothly adjusts its learning focus based on sub-tasks' training progress without manual intervention. Extensive experiments over 8 benchmarks and various models show that our method significantly enhances both direct reasoning and self-evaluation capability. We will release our code to contribute to the community.