Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approach
arXiv:2601.21243v2 Announce Type: replace-cross Abstract: We consider max-min and min-max problems with objective functions that are possibly non-smooth, submodular with respect to the minimiser and concave with respect to the maximiser. We investigate the performance of a zeroth-order method applied to this problem. The method is based on the subgradient of the Lov\'asz extension of the objective function with respect to the minimiser and based on Gaussian smoothing to estimate the smoothed function gradient with respect to the maximiser. In expectation sense, we prove the convergence of the
The continuous advancements in AI research, particularly in optimization theory, drive the exploration of new methods for complex problem-solving, making this development timely.
This research provides a more robust and efficient mathematical framework for optimizing non-smooth, non-convex functions, which could enhance the performance of advanced AI algorithms and agentic systems.
The ability to solve complex min-max problems more effectively could lead to more stable and powerful machine learning models and autonomous AI agents, improving their real-world applicability.
- · AI researchers
- · Machine learning industry
- · Companies developing AI agents
- · Inefficient optimization methodologies
Improved performance and stability in various machine learning applications, particularly those involving adversarial or game-theoretic scenarios.
Faster development and deployment of sophisticated AI agents capable of higher-level decision-making in complex environments.
Enhanced automation and the collapsing of white-collar workflows by more capable and reliable AI agentic systems.
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