Global Random Maximization of Piecewise Linear Neural Network
Year: 2026
Type: preprint
Abstract: This paper addresses the problem of maximizing functions defined on a polytope domain in $\mathbb{R}^{d_0}$ that are expensive to evaluate, such as conditional expectations arising in stochastic control. We consider a neural network surrogate of the target function and propose a simple random maximization strategy based on evaluating the network at independent uniformly distributed inputs and taking the sample maximum. Leveraging the structure of neural network outputs, we derive explicit convergence rates for both the asymptotic distribution and the non-asymptotic mean-square error of the sample maximum, showing that they are governed by a parameter $\alpha$ reflecting the local geometry of the network near its maximum. This provides tractable guarantees under mild assumptions, in contrast to generic black-box optimization settings. Motivated by this geometric dependence, we introduce a multi-surrogate strategy in which several diverse neural network approximations are constructed and maximized independently. Empirical results demonstrate that this approach significantly accelerates convergence, especially in higher-dimensional settings.
Source: HAL
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7163782317