LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization
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| Format: | Preprint |
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2024
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| author | Barik, Adarsh Krishna, Anand Tan, Vincent Y. F. |
| author_facet | Barik, Adarsh Krishna, Anand Tan, Vincent Y. F. |
| contents | We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds k, unknown to the learner. Our focus is on a novel setting allowing unbounded domains and large gradients for the losses without relying on a Lipschitz assumption. We introduce the Log Exponential Adjusted Robust and iNvex (LEARN) loss, a non-convex (invex) robust loss function to mitigate the effects of outliers and develop a robust variant of the online gradient descent algorithm by leveraging the LEARN loss. We establish tight regret guarantees (up to constants), in a dynamic setting, with respect to the uncorrupted rounds and conduct experiments to validate our theory. Furthermore, we present a unified analysis framework for developing online optimization algorithms for non-convex (invex) losses, utilizing it to provide regret bounds with respect to the LEARN loss, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06297 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization Barik, Adarsh Krishna, Anand Tan, Vincent Y. F. Machine Learning Optimization and Control We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds k, unknown to the learner. Our focus is on a novel setting allowing unbounded domains and large gradients for the losses without relying on a Lipschitz assumption. We introduce the Log Exponential Adjusted Robust and iNvex (LEARN) loss, a non-convex (invex) robust loss function to mitigate the effects of outliers and develop a robust variant of the online gradient descent algorithm by leveraging the LEARN loss. We establish tight regret guarantees (up to constants), in a dynamic setting, with respect to the uncorrupted rounds and conduct experiments to validate our theory. Furthermore, we present a unified analysis framework for developing online optimization algorithms for non-convex (invex) losses, utilizing it to provide regret bounds with respect to the LEARN loss, which may be of independent interest. |
| title | LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2408.06297 |