Neural network output optimization using interval analysis.

Area of Science:

• Artificial Intelligence
• Computational Mathematics

Background:

• Neural networks (NNs) with fixed weights present a nonlinear output optimization challenge within specific input spaces.
• This global optimization problem is frequently encountered in reinforcement learning (RL).

Purpose of the Study:

• To address the limitations of interval analysis (IA) and Taylor models (TMs) in NN output optimization.
• To introduce and evaluate a novel method, the polynomial set (PS) method, for more accurate and efficient NN output optimization.

Main Methods:

• Applying interval analysis to guarantee complete solution finding with bounded accuracy.
• Utilizing Taylor models to mitigate IA drawbacks, noting their limitations with large input domains.
• Introducing the polynomial set (PS) method as an alternative to TMs for polynomial inclusion functions.

Main Results:

• IA suffers from dependency effects and high computational load in NN output optimization.
• TMs show good convergence for small intervals but worsen the dependency effect for large domains.
• The PS method provides bounds on network output that are tighter or equal to standard IA, outperforming other methods in experiments.

Conclusions:

• The polynomial set method is a superior alternative for neural network output optimization.
• PS method effectively reduces the drawbacks of IA and TMs, offering improved accuracy and efficiency.
• This research advances global optimization techniques for NNs, particularly relevant for reinforcement learning applications.