Inference-time alignment methods, such as Best-of-
N, offer a flexible alternative to training-based alignment by using reward models to select high-quality responses generated by a reference LLM. However, the efficacy of these methods is inherently limited by the response quality: if the reference LLM assigns negligible probability to high-reward responses, no selection strategy will succeed in finding aligned outputs. In this work, we propose Best-of-Better-
N (BoBN), an in context learning-based generation framework to address this challenge. Our method utilizes retrieval from high-reward examples relevant to the input query and task. Crucially, we introduce a restyling step where retrieved responses are rewritten by the reference LLM to align with the target task's format and style. These restyled examples are used in-context to shift the sampling distribution toward the high-reward region. We analytically characterize how in-context learning shifts the output distribution of pretrained transformers toward the high-reward region, resulting in provable benefits on the target task. We then evaluate BoBN on safety alignment and mathematical reasoning benchmarks across several reference LLMs. BoBN's higher-quality responses enable better performance to be achieved when the number of responses
N is fixed, and smaller
N required to achieve a target performance.