Online nonconvex optimization addresses dynamic and complex decision-making problems arising in real-world decision-making tasks where the optimizer’s objective evolves with the intricate and changing nature of the underlying system.
This paper studies an online nonconvex composite optimization model with limited first-order access, encompassing a wide range of practical scenarios.
We define local regret using a proximal gradient mapping-based measure, overcoming limitations in existing local regret metrics and demonstrating its soundness through connections to the best action in hindsight and other measures.
To tackle the model, we propose a general stochastic nested optimization framework and provide a specific stochastic proximal gradient implementation.
We establish the general framework’s local regret guarantees, and the complexity guarantees when employed with the stochastic proximal gradient update.
Additionally, specific guarantees are proved for stochastic nonconvex multiplayer games and the offline stochastic proximal gradient method under bounded first-moment assumption.
Our approach’s applicability and potential use is demonstrated through practical examples.
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