Optimal Information Blending with Measurements in the L2 Sphere

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Density estimation with ensembles of randomized poly-trees

International audienceIn this work we explore the Perturb and Combine idea celebrated in supervised learning in the context of probability density estimation in high-dimensional spaces. We propose a new family of unsupervised learning methods of mixtures of large ensembles of randomly generated poly-trees. The specific feature of these methods is their scalability to very large numbers of variables and training instances. We explore various variants of these methods empirically on a set of discrete test problems of growing complexity

Scenario trees and policy selection for multistage stochastic programming using machine learning

We propose a hybrid algorithmic strategy for complex stochastic optimization problems, which combines the use of scenario trees from multistage stochastic programming with machine learning techniques for learning a policy in the form of a statistical model, in the context of constrained vector-valued decisions. Such a policy allows one to run out-of-sample simulations over a large number of independent scenarios, and obtain a signal on the quality of the approximation scheme used to solve the multistage stochastic program. We propose to apply this fast simulation technique to choose the best tree from a set of scenario trees. A solution scheme is introduced, where several scenario trees with random branching structure are solved in parallel, and where the tree from which the best policy for the true problem could be learned is ultimately retained. Numerical tests show that excellent trade-offs can be achieved between run times and solution quality

Large Margin Classification with the Progressive Hedging Algorithm

Several learning algorithms in classification and structured prediction are formulated as large scale optimization problems. We show that a generic iterative reformulation and resolving strategy based on the progressive hedging algorithm from stochastic programming results in a highly parallel algorithm when applied to the large margin classification problem with nonlinear kernels. We also underline promising aspects of the available analysis of progressive hedging strategies

Projecting Generation Decisions Induced by a Stochastic Program on a Family of Supply Curve Functions

We propose to post-process the results of a scenario based stochastic program by projecting its decisions on a parameterized space of policies. By doing so the risk of overfitting to the set of scenarios used in the stochastic program is reduced. A proper choice of the structure of the space of policies allows one to exploit them in the context of novel scenarios, be it for Monte-Carlo based value estimation or for use in real-life conditions. These ideas are presented in the context of planning the exploitation of electric energy resources or for evaluating the economic value of a portfolio of assets

Risk-aware decision making and dynamic programming

This paper considers sequential decision making problems under uncertainty, the tradeoff between the expected return and the risk of high loss, and methods that use dynamic programming to find optimal policies. It is argued that using Bellman's Principle determines how risk considerations on the return can be incorporated. The discussion centers around returns generated by Markov Decision Processes and conclusions concern a large class of methods in Reinforcement Learning

Multistage stochastic programming: A scenario tree based approach to planning under uncertainty

peer reviewedIn this chapter, we present the multistage stochastic programming framework for sequential decision making under uncertainty. We discuss its differences with Markov Decision Processes, from the point of view of decision models and solution algorithms. We describe the standard technique for solving approximately multistage stochastic problems, which is based on a discretization of the disturbance space called scenario tree. We insist on a critical issue of the approach: the decisions can be very sensitive to the parameters of the scenario tree, whereas no efficient tool for checking the quality of approximate solutions exists. In this chapter, we show how supervised learning techniques can be used to evaluate reliably the quality of an approximation, and thus facilitate the selection of a good scenario tree. The framework and solution techniques presented in the chapter are explained and detailed on several examples. Along the way, we define notions from decision theory that can be used to quantify, for a particular problem, the advantage of switching to a more sophisticated decision model

Planning under uncertainty, ensembles of disturbance trees and kernelized discrete action spaces

peer reviewedOptimizing decisions on an ensemble of incomplete disturbance trees and aggregating their first stage decisions has been shown as a promising approach to (model-based) planning under uncertainty in large continuous action spaces and in small discrete ones. The present paper extends this approach and deals with large but highly structured action spaces, through a kernel-based aggregation scheme. The technique is applied to a test problem with a discrete action space of 6561 elements adapted from the NIPS 2005 SensorNetwork benchmark

Machine Learning Solution Methods for Multistage Stochastic Programming

This thesis investigates the following question: Can supervised learning techniques be successfully used for finding better solutions to multistage stochastic programs? A similar question had already been posed in the context of reinforcement learning, and had led to algorithmic and conceptual advances in the field of approximate value function methods over the years. This thesis identifies several ways to exploit the combination "multistage stochastic programming/supervised learning" for sequential decision making under uncertainty. Multistage stochastic programming is essentially the extension of stochastic programming to several recourse stages. After an introduction to multistage stochastic programming and a summary of existing approximation approaches based on scenario trees, this thesis mainly focusses on the use of supervised learning for building decision policies from scenario-tree approximations. Two ways of exploiting learned policies in the context of the practical issues posed by the multistage stochastic programming framework are explored: the fast evaluation of performance guarantees for a given approximation, and the selection of good scenario trees. The computational efficiency of the approach allows novel investigations relative to the construction of scenario trees, from which novel insights, solution approaches and algorithms are derived. For instance, we generate and select scenario trees with random branching structures for problems over large planning horizons. Our experiments on the empirical performances of learned policies, compared to golden-standard policies, suggest that the combination of stochastic programming and machine learning techniques could also constitute a method per se for sequential decision making under uncertainty, inasmuch as learned policies are simple to use, and come with performance guarantees that can actually be quite good. Finally, limitations of approaches that build an explicit model to represent an optimal solution mapping are studied in a simple parametric programming setting, and various insights regarding this issue are obtained

High-dimensional probability density estimation with randomized ensembles of tree structured bayesian networks

peer reviewe