ODDO: Online Duality-Driven Optimization

TL;DR

ODDO is a novel online optimization framework for energy management in micro-grids that predicts optimal dual variables to efficiently solve convex problems under uncertainty without relying on detailed data assumptions.

Contribution

The paper introduces ODDO, a new duality-driven online optimization method that is simple, efficient, and robust to prediction errors, applicable to uncertain convex problems.

Findings

ODDO achieves near-optimal solutions in real and synthetic data scenarios.

The framework is robust against prediction errors in Lagrange multipliers.

ODDO does not require detailed probabilistic assumptions on data.

Abstract

Motivated by energy management for micro-grids, we study convex optimization problems with uncertainty in the objective function and sequential decision making. To solve these problems, we propose a new framework called ``Online Duality-Driven Optimization'' (ODDO). This framework distinguishes itself from existing paradigms for optimization under uncertainty in its efficiency, simplicity, and ability to solve problems without any quantitative assumptions on the uncertain data. The key idea in this framework is that we predict, instead of the actual uncertain data, the optimal Lagrange multipliers. Subsequently, we use these predictions to construct an online primal solution by exploiting strong duality of the problem. We show that the framework is robust against prediction errors in the optimal Lagrange multipliers both theoretically and in practice. In fact, evaluations of the framework on problems with both real and randomly generated input data show that ODDO can achieve near-optimal online solutions, even when we use only elementary statistics to predict the optimal Lagrange multipliers.