Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approach

A new study addresses the max-min and min-max problems involving non-smooth, submodular-concave functions, utilizing a zeroth-order method that leverages the subgradient of the Lovász extension and Gaussian smoothing techniques. The research demonstrates the algorithm's convergence to an ε-saddle point in offline scenarios and achieves an O(√(N P̄_N)) online duality gap, where N represents iterations and P̄_N indicates the path length of optimal decisions.

This development is significant as it enhances the understanding of optimization techniques in artificial intelligence, particularly in scenarios where traditional smoothness assumptions do not hold, potentially leading to more robust algorithms in various applications.