# Model-Free Unsupervised Learning for Optimization Problems with Constraints

## TL;DR

This paper introduces a model-free neural network-based framework for solving constrained optimization problems in wireless communications without requiring explicit models or optimal solutions, demonstrating efficiency through power control simulations.

## Contribution

It presents a novel, model-free learning approach that uses neural networks to optimize functions and Lagrange multipliers without supervision, applicable to complex wireless problems.

## Key findings

- Framework effectively solves power control problems.
- Neural networks learn constraints and objectives simultaneously.
- Demonstrates efficiency over traditional methods.

## Abstract

In many optimization problems in wireless communications, the expressions of objective function or constraints are hard or even impossible to derive, which makes the solutions difficult to find. In this paper, we propose a model-free learning framework to solve constrained optimization problems without the supervision of the optimal solution. Neural networks are used respectively for parameterizing the function to be optimized, parameterizing the Lagrange multiplier associated with instantaneous constraints, and approximating the unknown objective function or constraints. We provide learning algorithms to train all the neural networks simultaneously, and reveal the connections of the proposed framework with reinforcement learning. Numerical and simulation results validate the proposed framework and demonstrate the efficiency of model-free learning by taking power control problem as an example.