  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.
