Search

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., Comment: 10 Main Pages, 6 Appendices, 6 Figures

The sustainable utilization of hydro energy relies on accurate estimates of the opportunity cost of the water. This value is calculated through long-term hydrothermal dispatch problems (LTHDP), and the recent literature has raised awareness about the consequences of modeling simplifications in these problems. The inaccurate representation of Kirchhoff's voltage law under the premise of a DC power flow is an example. Under a non-linear AC model, however, the LTHDP becomes intractable, and the literature lacks an accurate evaluation method of different modeling alternatives. In this paper, we extend the state-of-the-art cost-assessment framework of network approximations for LTHDP and bring relevant and practical new insights. First, we increase the quality of the assessment by using an AC power flow to simulate and compare the performance of five policies based on different network approximations. Second, we find that the tightest network relaxation (based on semidefinite programming) is not the one exhibiting the best performance. Results show that the DC {power flow} with quadratic losses approximation exhibits the lowest expected cost and inconsistency gaps. Finally, its computational burden is lower than that exhibited by the semidefinite relaxation, whereas market distortions are significantly reduced in comparison to previously published benchmarks based on DC power flow.