Robust scaling in fusion science: case study for the L-H power threshold

In regression analysis for deriving scaling laws in the context of fusion studies, standard regression methods are usually applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to fusion data. More sophisticated statistical techniques are available, but they are not widely used in the fusion community and, moreover, the predictions by scaling laws may vary significantly depending on the particular regression technique. Therefore we have developed a new regression method, which we call geodesic least squares regression (GLS), that is robust in the presence of significant uncertainty on both the data and the regression model. The method is based on probabilistic modeling of all variables involved in the scaling expression, using adequate probability distributions and a natural similarity measure between them (geodesic distance). In this work we revisit the scaling law for the power threshold for the L-to-H transition in tokamaks, using data from the multi-machine ITPA databases. Depending on model assumptions, OLS can yield different predictions of the power threshold for ITER. In contrast, GLS regression delivers consistent results. Consequently, given the ubiquity and importance of scaling laws and parametric dependence studies in fusion research, GLS regression is proposed as a robust and easily implemented alternative to classic regression techniques

Load Forecasting Based Distribution System Network Reconfiguration-A Distributed Data-Driven Approach

In this paper, a short-term load forecasting approach based network reconfiguration is proposed in a parallel manner. Specifically, a support vector regression (SVR) based short-term load forecasting approach is designed to provide an accurate load prediction and benefit the network reconfiguration. Because of the nonconvexity of the three-phase balanced optimal power flow, a second-order cone program (SOCP) based approach is used to relax the optimal power flow problem. Then, the alternating direction method of multipliers (ADMM) is used to compute the optimal power flow in distributed manner. Considering the limited number of the switches and the increasing computation capability, the proposed network reconfiguration is solved in a parallel way. The numerical results demonstrate the feasible and effectiveness of the proposed approach.Comment: 5 pages, preprint for Asilomar Conference on Signals, Systems, and Computers 201

Sequential Design for Optimal Stopping Problems

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids anchoring the simulated sample paths of the underlying state process. This allows for active learning of the classifiers partitioning the state space into the continuation and stopping regions. To this end, we examine sequential design schemes that adaptively place new design points close to the stopping boundaries. We then discuss dynamic regression algorithms that can implement such recursive estimation and local refinement of the classifiers. The new algorithm is illustrated with a variety of numerical experiments, showing that an order of magnitude savings in terms of design size can be achieved. We also compare with existing benchmarks in the context of pricing multi-dimensional Bermudan options.Comment: 24 page

Distributed stochastic optimization via matrix exponential learning

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.Comment: 31 pages, 3 figure