Multi-ResNets for Subspace Preconditioning in Constrained Optimization

We propose MResOpt, a staged residual neural network architecture for constrained optimization problems. Our architecture fits within predict-complete-correct pipelines and decomposes constraint satisfaction by priority through intermediate re-completion and stage-aware losses. The framework enables domain-informed ordered constraint satisfaction which allows the network to utilize ordinal structure when present. Under an idealized infinite-width regime, we show that our design behaves as sequential Gaussian Process regression. On synthetic QP, QCQP, and SOCP benchmarks, the staged architecture improves high-priority constraint satisfaction across convex and non-convex settings. On line-flow-constrained AC optimal power flow, we introduce a physics-motivated constraint ordering and show that MResOpt supports a learned division of labor that keeps iterates on the equality manifold, achieving substantially lower high-priority violation than reprojected baselines while remaining computationally efficient.

Fill-and-Spill: Deep Reinforcement Learning Policy Gradient Methods for Reservoir Operation Decision and Control

Changes in demand, various hydrological inputs, and environmental stressors are among the issues that water managers and policymakers face on a regular basis. These concerns have sparked interest in applying different techniques to determine reservoir operation policy decisions. As the resolution of the analysis increases, it becomes more difficult to effectively represent a real-world system using traditional methods such as Dynamic Programming (DP) and Stochastic Dynamic Programming (SDP) for determining the best reservoir operation policy. One of the challenges is the "curse of dimensionality," which means the number of samples needed to estimate an arbitrary function with a given level of accuracy grows exponentially with respect to the number of input variables (i.e., dimensionality) of the function. Deep Reinforcement Learning (DRL) is an intelligent approach to overcome the curses of stochastic optimization problems for reservoir operation policy decisions. To our knowledge, this study is the first attempt that examine various novel DRL continuous-action policy gradient methods (PGMs), including Deep Deterministic Policy Gradients (DDPG), Twin Delayed DDPG (TD3), and two different versions of Soft Actor-Critic (SAC18 and SAC19) for optimizing reservoir operation policy. In this study, multiple DRL techniques were implemented in order to find the optimal operation policy of Folsom Reservoir in California, USA. The reservoir system supplies agricultural, municipal, hydropower, and environmental flow demands and flood control operations to the City of Sacramento. Analysis suggests that the TD3 and SAC are robust to meet the Folsom Reservoir's demands and optimize reservoir operation policies.