Although chain-of-thought (CoT) prompting combined with language models has achieved encouraging results on complex reasoning tasks, the naive greedy decoding used in CoT prompting usually causes the repetitiveness and local optimality. To address this shortcoming, ensemble-optimization tries to obtain multiple reasoning paths to get the final answer assembly. However, current ensemble-optimization methods either simply employ rule-based post-processing such as self-consistency, or train an additional model based on several task-related human annotations to select the best one among multiple reasoning paths, yet fail to generalize to realistic settings where the type of input questions is unknown or the answer format of reasoning paths is unknown. To avoid their limitations, we propose Self-Agreement, a generalizable ensemble-optimization method applying in almost all scenarios where the type of input questions and the answer format of reasoning paths may be known or unknown. Self-agreement firstly samples from language model’s decoder to generate a diverse set of reasoning paths, and subsequently prompts the language model one more time to determine the optimal answer by selecting the most agreed answer among the sampled reasoning paths. Self-agreement simultaneously achieves remarkable performance on six public reasoning benchmarks and superior generalization capabilities.

Reinforcement learning (RL) has been widely used in training large language models (LLMs) for preventing unexpected outputs, e.g., reducing harmfulness and errors. However, existing RL methods mainly adopt instance-level reward, which cannot provide fine-grained supervision for complex reasoning tasks. As a result, the RL training cannot be fully aware of the specific part or step that actually leads to the incorrectness in model response. To address it, we propose a new RL method named RLMEC that incorporates a generative model as the reward model, which is trained by the erroneous solution rewriting task under the minimum editing constraint, which can produce token-level supervision for RL training. Based 0on the generative reward model, we design the token-level RL objective for training and an imitation-based regularization for stabilizing RL process. And these two objectives focus on the revision of the key tokens for the erroneous solution, reducing the effect of other unimportant tokens. Experiment results on 8 tasks have demonstrated the effectiveness of our approach. Our code and data will be publicly released.