Peer review at AI conferences is stressed by rapidly rising submission volumes, leading to deteriorating review quality and increased author dissatisfaction. To address these issues, we developed Review Feedback Agent, a system leveraging multiple large language models (LLMs) to improve review clarity and actionability by providing automated feedback on vague comments, content misunderstandings, and unprofessional remarks to reviewers. Implemented at ICLR 2025 as a large randomized control study, our system provided optional feedback to more than 20,000 randomly selected reviews. To ensure high-quality feedback for reviewers at this scale, we also developed a suite of automated reliability tests powered by LLMs that acted as guardrails to ensure feedback quality, with feedback only being sent to reviewers if it passed all the tests. The results show that 27% of reviewers who received feedback updated their reviews, and over 12,000 feedback suggestions from the agent were incorporated by those reviewers. This suggests that many reviewers found the AI-generated feedback sufficiently helpful to merit updating their reviews. Incorporating AI feedback led to significantly longer reviews (an average increase of 80 words among those who updated after receiving feedback) and more informative reviews, as evaluated by blinded researchers. Moreover, reviewers who were selected to receive AI feedback were also more engaged during paper rebuttals, as seen in longer author-reviewer discussions. This work demonstrates that carefully designed LLM-generated review feedback can enhance peer review quality by making reviews more specific and actionable while increasing engagement between reviewers and authors. The Review Feedback Agent is publicly available at https://github.com/zou-group/review_feedback_agent.