Nonparametric Bayesian Optimization for General Rewards
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915784067907584 |
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| author | Zhang, Zishi Ren, Tao Peng, Yijie |
| author_facet | Zhang, Zishi Ren, Tao Peng, Yijie |
| contents | This work focuses on Bayesian optimization (BO) under reward model uncertainty. We propose the first BO algorithm that achieves no-regret guarantee in a general reward setting, requiring only Lipschitz continuity of the objective function and accommodating a broad class of measurement noise. The core of our approach is a novel surrogate model, termed as infinite Gaussian process ($\infty$-GP). It is a Bayesian nonparametric model that places a prior on the space of reward distributions, enabling it to represent a substantially broader class of reward models than classical Gaussian process (GP). The $\infty$-GP is used in combination with Thompson Sampling (TS) to enable effective exploration and exploitation. Correspondingly, we develop a new TS regret analysis framework for general rewards, which relates the regret to the total variation distance between the surrogate model and the true reward distribution. Furthermore, with a truncated Gibbs sampling procedure, our method is computationally scalable, incurring minimal additional memory and computational complexities compared to classical GP. Empirical results demonstrate state-of-the-art performance, particularly in settings with non-stationary, heavy-tailed, or other ill-conditioned rewards. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07411 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonparametric Bayesian Optimization for General Rewards Zhang, Zishi Ren, Tao Peng, Yijie Machine Learning This work focuses on Bayesian optimization (BO) under reward model uncertainty. We propose the first BO algorithm that achieves no-regret guarantee in a general reward setting, requiring only Lipschitz continuity of the objective function and accommodating a broad class of measurement noise. The core of our approach is a novel surrogate model, termed as infinite Gaussian process ($\infty$-GP). It is a Bayesian nonparametric model that places a prior on the space of reward distributions, enabling it to represent a substantially broader class of reward models than classical Gaussian process (GP). The $\infty$-GP is used in combination with Thompson Sampling (TS) to enable effective exploration and exploitation. Correspondingly, we develop a new TS regret analysis framework for general rewards, which relates the regret to the total variation distance between the surrogate model and the true reward distribution. Furthermore, with a truncated Gibbs sampling procedure, our method is computationally scalable, incurring minimal additional memory and computational complexities compared to classical GP. Empirical results demonstrate state-of-the-art performance, particularly in settings with non-stationary, heavy-tailed, or other ill-conditioned rewards. |
| title | Nonparametric Bayesian Optimization for General Rewards |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.07411 |