Beyond Grids: Multi-objective Bayesian Optimization With Adaptive Discretization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866915509845360640 |
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| author | Nika, Andi Elahi, Sepehr Ararat, Çağın Tekin, Cem |
| author_facet | Nika, Andi Elahi, Sepehr Ararat, Çağın Tekin, Cem |
| contents | We consider the problem of optimizing a vector-valued objective function $\boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({\cal X},d)$ of designs. We assume that $\boldsymbol{f}$ is not known beforehand and that evaluating $\boldsymbol{f}$ at design $x$ results in a noisy observation of $\boldsymbol{f}(x)$. Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of ${\cal X}$ is large, we propose an algorithm, called Adaptive $\boldsymbolε$-PAL, that exploits the smoothness of the GP-sampled function and the structure of $({\cal X},d)$ to learn fast. In essence, Adaptive $\boldsymbolε$-PAL employs a tree-based adaptive discretization technique to identify an $\boldsymbolε$-accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of $\boldsymbolε$-accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_14061 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Beyond Grids: Multi-objective Bayesian Optimization With Adaptive Discretization Nika, Andi Elahi, Sepehr Ararat, Çağın Tekin, Cem Machine Learning Applications We consider the problem of optimizing a vector-valued objective function $\boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({\cal X},d)$ of designs. We assume that $\boldsymbol{f}$ is not known beforehand and that evaluating $\boldsymbol{f}$ at design $x$ results in a noisy observation of $\boldsymbol{f}(x)$. Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of ${\cal X}$ is large, we propose an algorithm, called Adaptive $\boldsymbolε$-PAL, that exploits the smoothness of the GP-sampled function and the structure of $({\cal X},d)$ to learn fast. In essence, Adaptive $\boldsymbolε$-PAL employs a tree-based adaptive discretization technique to identify an $\boldsymbolε$-accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of $\boldsymbolε$-accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods. |
| title | Beyond Grids: Multi-objective Bayesian Optimization With Adaptive Discretization |
| topic | Machine Learning Applications |
| url | https://arxiv.org/abs/2006.14061 |