We introduce EURUS, a suite of large language models (LLMs) optimized for reasoning. Finetuned from Mistral-7B, Llama-3-8B, and Mixtral-8x22B, EURUS models achieve state-of-the-art results among open-source models on a diverse set of benchmarks covering mathematics, code generation, and logical reasoning problems. Notably, EURUX-8X22B outperforms GPT-3.5 Turbo in reasoning through a comprehensive benchmarking across 12 test sets covering five tasks. The strong performance of EURUS can be primarily attributed to ULTRAINTERACT, our newly-curated large-scale, high-quality training data dataset specifically designed for complex reasoning tasks. ULTRAINTERACT can be used in both supervised fine-tuning, preference learning, and reward modeling. It pairs each instruction with a preference tree consisting of (1) reasoning chains with diverse planning strategies in a unified format, (2) multi-turn interaction trajectories with the environment and the critique, and (3) pairwise positive and negative responses to facilitate preference learning. ULTRAINTERACT allows us to conduct an in-depth exploration of preference learning for reasoning tasks. Our investigation reveals that some well-established preference learning algorithms may be less suitable for reasoning tasks compared to their effectiveness in general conversations. The hypothesis is that in reasoning tasks, the space of correct answers is much smaller than that of incorrect ones, so it is necessary to explicitly increase the reward of chosen data. Therefore, in addition to increasing the reward margin as many preference learning algorithms do, the absolute values of positive responses’ rewards should be positive and may serve as a proxy for performance. Inspired by this, we derive a novel reward modeling objective and empirically that it leads to a stable reward modeling curve and better performance. Together with ULTRAINTERACT, we obtain a strong reward model.