LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization

• URL: http://arxiv.org/abs/2408.06297v1
• Date: Mon, 12 Aug 2024 17:08:31 GMT
• Title: LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization
• Authors: Adarsh Barik, Anand Krishna, Vincent Y. F. Tan,
• Abstract summary: An adversary can introduce outliers by corrupting loss functions in an arbitrary number of k, unknown to the learner. We present a robust online rounds optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of k, unknown.
• Score: 56.67706781191521
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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