Two-Stage ML-Guided Decision Rules for Sequential Decision Making under Uncertainty

Sequential Decision Making under Uncertainty (SDMU) is ubiquitous in many domains such as energy, finance, and supply chains. Some SDMU applications are naturally modeled as Multistage Stochastic Optimization Problems (MSPs), but the resulting optimizations are notoriously challenging from a computational standpoint. Under assumptions of convexity and stage-wise independence of the uncertainty, the resulting optimization can be solved efficiently using Stochastic Dual Dynamic Programming (SDDP). Two-stage Linear Decision Rules (TS-LDRs) have been proposed to solve MSPs without the stage-wise independence assumption. TS-LDRs are computationally tractable, but using a policy that is a linear function of past observations is typically not suitable for non-convex environments arising, for example, in energy systems. This paper introduces a novel approach, Two-Stage General Decision Rules (TS-GDR), to generalize the policy space beyond linear functions, making them suitable for non-convex environments. TS-GDR is a self-supervised learning algorithm that trains the nonlinear decision rules using stochastic gradient descent (SGD); its forward passes solve the policy implementation optimization problems, and the backward passes leverage duality theory to obtain closed-form gradients. The effectiveness of TS-GDR is demonstrated through an instantiation using Deep Recurrent Neural Networks named Two-Stage Deep Decision Rules (TS-DDR). The method inherits the flexibility and computational performance of Deep Learning methodologies to solve SDMU problems generally tackled through large-scale optimization techniques. Applied to the Long-Term Hydrothermal Dispatch (LTHD) problem using actual power system data from Bolivia, the TS-DDR not only enhances solution quality but also significantly reduces computation times by several orders of magnitude.

Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks

The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they involve intricate, non-convex considerations related to Alternating Current (AC) power flow, which are essential for the safety and practicality of electrical grids. However, solving the OPF problem for varying conditions within stringent time frames poses practical challenges. To address this, operators resort to model simplifications of varying accuracy. Unfortunately, better approximations (tight convex relaxations) are often computationally intractable. This research explores machine learning (ML) to learn convex approximate solutions for faster analysis in the online setting while still allowing for coupling into other convex dependent decision problems. By trading off a small amount of accuracy for substantial gains in speed, they enable the efficient exploration of vast solution spaces in these complex problems.