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We present a careful comparison of two model-free control algorithms,Evolution Strategies (ES) and Proximal Policy Optimization (PPO), with recedinghorizon model predictive control (MPC) for operating simulated, priceresponsive water heaters. Four MPC variants are considered: a one-shotcontroller with perfect forecasting yielding optimal control; a limited-horizoncontroller with perfect forecasting; a mean forecasting-based controller; and atwo-stage stochastic programming controller using historical scenarios. In allcases, the MPC model for water temperature and electricity price are exact;only water demand is uncertain. For comparison, both ES and PPO learn neuralnetwork-based policies by directly interacting with the simulated environmentunder the same scenarios used by MPC. All methods are then evaluated on aseparate one-week continuation of the demand time series. We demonstrate thatoptimal control for this problem is challenging, requiring more than 8-hourlookahead for MPC with perfect forecasting to attain the minimum cost. Despitethis challenge, both ES and PPO learn good general purpose policies thatoutperform mean forecast and two-stage stochastic MPC controllers in terms ofaverage cost and are more than two orders of magnitude faster at computingactions. We show that ES in particular can leverage parallelism to learn apolicy in under 90 seconds using 1150 CPU cores.

A Comparison of Model-Free and Model Predictive Control for Price Responsive Water Heaters