In recommendation systems, users interact with only a small fraction of a vast item catalog, producing feedback that is both sparse and noisy. This challenges post-training generative recommenders: reward models trained from logged interactions often fail to generalize, while directly optimizing imperfect rewards can lead to reward over-optimization. We propose Exponential reward-weighted fine-tuning (Exp-RSFT), where each logged interaction is weighted by $\exp(r/λ)$, avoids this failure by optimizing directly on the logged rewards, with the temperature $λ$ regularizing against their noise. We theoretically show that Exp-RSFT's suboptimality decomposes into two costs: a coverage cost arising from limitations of the logging policy and a noise cost from imperfect feedback. The temperature $λ$ balances these competing effects, yielding an optimal tradeoff between exploiting high-reward behavior and robustness to noise. Across three public benchmarks and a large-scale industrial dataset, we verify this theoretical prediction: performance follows an inverted-U trend as a function of $λ$, while PPO and DPO often over-optimize unreliable reward models and degrade recommendation quality. Exp-RSFT consistently improves ranking performance without requiring online exploration or preference data.

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