We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in generative AI, reinforcement learning, and computational biology. We consider the common learning scenario where the data set consists of unlabeled data along with a smaller set of data with noisy reward labels. Our approach leverages a learned reward function on the smaller data set as a pseudolabeler. From a theoretical standpoint, we show that this directed generator can effectively learn and sample from the reward-conditioned data distribution. Additionally, our model is capable of recovering the latent subspace representation of data. Moreover, we establish that the model generates a new population that moves closer to a user-specified target reward value, where the optimality gap aligns with the off-policy bandit regret in the feature subspace. The improvement in rewards obtained is influenced by the interplay between the strength of the reward signal, the distribution shift, and the cost of off-support extrapolation. We provide empirical results to validate our theory and highlight the relationship between the strength of extrapolation and the quality of generated samples.

翻译：本文探索了通过条件扩散模型实现奖励引导生成的方理论与方法。导向生成旨在生成具有由奖励函数衡量的期望属性的样本，这在生成式人工智能、强化学习和计算生物学领域具有广泛应用。我们考虑常见的学习场景：数据集包含无标签数据以及少量带有噪声奖励标签的数据。我们的方法利用在小数据集上学习的奖励函数作为伪标签器。从理论角度，我们证明了这种导向生成器能够有效学习并采样奖励条件分布。此外，我们的模型能够恢复数据的潜在子空间表示。进一步地，我们证明该模型生成的新群体将向用户指定的目标奖励值移动，其最优性差距对应于特征子空间中的离策略臂后悔值。获得的奖励提升受奖励信号强度、分布偏移以及支持外推代价三者相互作用的共同影响。我们通过实证结果验证了理论，并揭示了外推强度与生成样本质量之间的关系。