Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866917434787627008 |
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| author | Tran-The, Hung Gupta, Sunil Rana, Santu Ha, Huong Venkatesh, Svetha |
| author_facet | Tran-The, Hung Gupta, Sunil Rana, Santu Ha, Huong Venkatesh, Svetha |
| contents | Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_02539 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces Tran-The, Hung Gupta, Sunil Rana, Santu Ha, Huong Venkatesh, Svetha Machine Learning Information Theory Bayesian optimisation is a popular method for efficient optimisation of expensive black-box functions. Traditionally, BO assumes that the search space is known. However, in many problems, this assumption does not hold. To this end, we propose a novel BO algorithm which expands (and shifts) the search space over iterations based on controlling the expansion rate thought a hyperharmonic series. Further, we propose another variant of our algorithm that scales to high dimensions. We show theoretically that for both our algorithms, the cumulative regret grows at sub-linear rates. Our experiments with synthetic and real-world optimisation tasks demonstrate the superiority of our algorithms over the current state-of-the-art methods for Bayesian optimisation in unknown search space. |
| title | Sub-linear Regret Bounds for Bayesian Optimisation in Unknown Search Spaces |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2009.02539 |