{"id":1140741,"date":"2026-09-15T16:20:13","date_gmt":"2026-09-15T23:20:13","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/?post_type=msr-research-item&p=1140741"},"modified":"2026-09-15T16:20:15","modified_gmt":"2026-09-15T23:20:15","slug":"is-best-of-n-the-best-of-them-coverage-scaling-and-optimality-in-inference-time-alignment","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/is-best-of-n-the-best-of-them-coverage-scaling-and-optimality-in-inference-time-alignment\/","title":{"rendered":"Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment"},"content":{"rendered":"\n\n\n

Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking. Toward a theoretical understanding of how to best leverage additional computation, we focus on inference-time alignment, which we formalize as the problem of improving the quality of responses drawn from a pre-trained policy, given a prompt of interest and access to an imperfect reward model. We analyze the performance of inference-time alignment algorithms in terms of (i) response quality, and (ii) compute, and provide new results that highlight the importance of the pre-trained policy’s coverage over high-quality responses for performance and compute scaling:<\/p>\n\n\n\n

    \n
  1. We show that Best-of-N alignment with an ideal choice for N can achieve optimal performance under stringent notions of coverage, but provably suffers from reward hacking when N is large, and fails to achieve tight guarantees under more realistic coverage conditions.<\/li>\n\n\n\n
  2. We introduce InferenceTimePessimism, a new algorithm which mitigates reward hacking through deliberate use of inference-time compute, implementing the principle of pessimism in the face of uncertainty via rejection sampling; we prove that its performance is optimal and does not degrade with N, meaning it is scaling-monotonic.<\/li>\n\n\n\n
  3. We complement our theoretical results with an experimental evaluation that demonstrate the benefits of InferenceTimePessimism across a variety of tasks and models.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking. Toward a theoretical understanding of how to best leverage additional computation, we focus on inference-time alignment, which we formalize as the problem of improving […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Audrey Huang","user_id":0},{"type":"user_nicename","value":"Adam Block","user_id":"43395"},{"type":"user_nicename","value":"Qinghua Liu","user_id":"43554"},{"type":"user_nicename","value":"Nan Jiang","user_id":"36614"},{"type":"user_nicename","value":"Akshay Krishnamurthy","user_id":"30913"},{"type":"user_nicename","value":"Dylan 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