Learnability in Online Kernel Selection with Memory Constraint via Data-dependent Regret Analysis
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| Format: | Preprint |
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2024
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| _version_ | 1866915210291314688 |
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| author | Li, Junfan Liao, Shizhong |
| author_facet | Li, Junfan Liao, Shizhong |
| contents | Online kernel selection is a fundamental problem of online kernel methods.In this paper,we study online kernel selection with memory constraint in which the memory of kernel selection and online prediction procedures is limited to a fixed budget. An essential question is what is the intrinsic relationship among online learnability, memory constraint, and data complexity? To answer the question,it is necessary to show the trade-offs between regret and memory constraint.Previous work gives a worst-case lower bound depending on the data size,and shows learning is impossible within a small memory constraint.In contrast, we present distinct results by offering data-dependent upper bounds that rely on two data complexities:kernel alignment and the cumulative losses of competitive hypothesis.We propose an algorithmic framework giving data-dependent upper bounds for two types of loss functions.For the hinge loss function,our algorithm achieves an expected upper bound depending on kernel alignment.For smooth loss functions,our algorithm achieves a high-probability upper bound depending on the cumulative losses of competitive hypothesis.We also prove a matching lower bound for smooth loss functions.Our results show that if the two data complexities are sub-linear,then learning is possible within a small memory constraint.Our algorithmic framework depends on a new buffer maintaining framework and a reduction from online kernel selection to prediction with expert advice. Finally,we empirically verify the prediction performance of our algorithms on benchmark datasets. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_00916 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learnability in Online Kernel Selection with Memory Constraint via Data-dependent Regret Analysis Li, Junfan Liao, Shizhong Machine Learning Online kernel selection is a fundamental problem of online kernel methods.In this paper,we study online kernel selection with memory constraint in which the memory of kernel selection and online prediction procedures is limited to a fixed budget. An essential question is what is the intrinsic relationship among online learnability, memory constraint, and data complexity? To answer the question,it is necessary to show the trade-offs between regret and memory constraint.Previous work gives a worst-case lower bound depending on the data size,and shows learning is impossible within a small memory constraint.In contrast, we present distinct results by offering data-dependent upper bounds that rely on two data complexities:kernel alignment and the cumulative losses of competitive hypothesis.We propose an algorithmic framework giving data-dependent upper bounds for two types of loss functions.For the hinge loss function,our algorithm achieves an expected upper bound depending on kernel alignment.For smooth loss functions,our algorithm achieves a high-probability upper bound depending on the cumulative losses of competitive hypothesis.We also prove a matching lower bound for smooth loss functions.Our results show that if the two data complexities are sub-linear,then learning is possible within a small memory constraint.Our algorithmic framework depends on a new buffer maintaining framework and a reduction from online kernel selection to prediction with expert advice. Finally,we empirically verify the prediction performance of our algorithms on benchmark datasets. |
| title | Learnability in Online Kernel Selection with Memory Constraint via Data-dependent Regret Analysis |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2407.00916 |