LLMs have made significant progress in complex but easy-to-verify problems, yet they still struggle with discovering the unknown. In this paper, we present \textbf{AlphaResearch}, an autonomous research agent designed to discover new algorithms on open-ended problems by iteratively running the following steps: (1) propose new ideas (2) program to verify (3) optimize the research proposals. To synergize the feasibility and innovation of the discovery process, we construct a novel dual environment by combining the execution-based verifiable reward and reward from simulated real-world peer review environment in AlphaResearch. We construct \textbf{\dataset}, a set of questions that includes an eight open-ended algorithmic problems competition to benchmark AlphaResearch. Experimental results show that AlphaResearch achieves stronger discovery performance than other agentic discovery systems on six open-ended problems. Notably, the algorithm discovered by AlphaResearch on the \emph{``packing circles''} problem achieves the best-of-known performance, surpassing the results of human researchers and strong baselines from recent work (e.g., AlphaEvolve). Additionally, we conduct a comprehensive analysis of the benefits and remaining challenges of autonomous research agent, providing valuable insights for future research.