Robot Design With Neural Networks, MILP Solvers and Active Learning

TL;DR

This paper introduces CNMA, a novel constrained blackbox optimization method using neural networks and MILP solvers, which reduces evaluation costs and handles complex constraints effectively in robotic system design.

Contribution

CNMA combines neural network approximation with MILP solvers and active learning to efficiently solve constrained blackbox optimization problems in robotics.

Findings

CNMA outperforms Nelder-Mead, Gaussian, and Random Search in evaluation efficiency.

It handles complex, recursive constraints directly without penalty functions.

Demonstrated on diverse robotic systems from 6 to 36 dimensions.

Abstract

Central to the design of many robot systems and their controllers is solving a constrained blackbox optimization problem. This paper presents CNMA, a new method of solving this problem that is conservative in the number of potentially expensive blackbox function evaluations; allows specifying complex, even recursive constraints directly rather than as hard-to-design penalty or barrier functions; and is resilient to the non-termination of function evaluations. CNMA leverages the ability of neural networks to approximate any continuous function, their transformation into equivalent mixed integer linear programs (MILPs) and their optimization subject to constraints with industrial strength MILP solvers. A new learning-from-failure step guides the learning to be relevant to solving the constrained optimization problem. Thus, the amount of learning is orders of magnitude smaller than that needed to learn functions over their entire domains. CNMA is illustrated with the design of several robotic systems: wave-energy propelled boat, lunar lander, hexapod, cartpole, acrobot and parallel parking. These range from 6 real-valued dimensions to 36. We show that CNMA surpasses the Nelder-Mead, Gaussian and Random Search optimization methods against the metric of number of function evaluations.