Was Residual Penalty and Neural Operators All We Needed for Solving Optimal Control Problems?

Neural networks have been used to solve optimal control problems, typically by training neural networks using a combined loss function that considers data, differential equation residuals, and objective costs. We show that including cost functions in the training process is unnecessary, advocating for a simpler architecture and streamlined approach by decoupling the optimal control problem from the training process. Thus, our work shows that a simple neural operator architecture, such as DeepONet, coupled with an unconstrained optimization routine, can solve multiple optimal control problems with a single physics-informed training phase and a subsequent optimization phase. We achieve this by adding a penalty term based on the differential equation residual to the cost function and computing gradients with respect to the control using automatic differentiation through the trained neural operator within an iterative optimization routine. We showcase our method on nine distinct optimal control problems by training three separate DeepONet models, each corresponding to a different differential equation. For each model, we solve three problems with varying cost functions, demonstrating accurate and consistent performance across all cases.

ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming

Two-stage stochastic programming (2SP) offers a basic framework for modelling decision-making under uncertainty, yet scalability remains a challenge due to the computational complexity of recourse function evaluation. Existing learning-based methods like Neural Two-Stage Stochastic Programming (Neur2SP) employ neural networks (NNs) as recourse function surrogates but rely on computationally intensive mixed-integer programming (MIP) formulations. We propose ICNN-enhanced 2SP, a method that leverages Input Convex Neural Networks (ICNNs) to exploit linear programming (LP) representability in convex 2SP problems. By architecturally enforcing convexity and enabling exact inference through LP, our approach eliminates the need for integer variables inherent to the conventional MIP-based formulation while retaining an exact embedding of the ICNN surrogate within the 2SP framework. This results in a more computationally efficient alternative that maintains solution quality. Comprehensive experiments reveal that ICNNs incur only marginally longer training times while achieving validation accuracy on par with their MIP-based counterparts. Across benchmark problems, ICNN-enhanced 2SP often exhibits considerably faster solution times than the MIP-based formulations while preserving solution quality, with these advantages becoming significantly more pronounced as problem scale increases. For the most challenging instances, the method achieves speedups of up to 100$\times$ and solution quality superior to MIP-based formulations.

Employing Federated Learning for Training Autonomous HVAC Systems

Buildings account for 40 % of global energy consumption. A considerable portion of building energy consumption stems from heating, ventilation, and air conditioning (HVAC), and thus implementing smart, energy-efficient HVAC systems has the potential to significantly impact the course of climate change. In recent years, model-free reinforcement learning algorithms have been increasingly assessed for this purpose due to their ability to learn and adapt purely from experience. They have been shown to outperform classical controllers in terms of energy cost and consumption, as well as thermal comfort. However, their weakness lies in their relatively poor data efficiency, requiring long periods of training to reach acceptable policies, making them inapplicable to real-world controllers directly. Hence, common research goals are to improve the learning speed, as well as to improve their ability to generalize, in order to facilitate transfer learning to unseen building environments. In this paper, we take a federated learning approach to training the reinforcement learning controller of an HVAC system. A global control policy is learned by aggregating local policies trained on multiple data centers located in different climate zones. The goal of the policy is to simultaneously minimize energy consumption and maximize thermal comfort. The federated optimization strategy indirectly increases both the rate at which experience data is collected and the variation in the data. We demonstrate through experimental evaluation that these effects lead to a faster learning speed, as well as greater generalization capabilities in the federated policy compared to any individually trained policy.