8,178 research outputs found

    An Efficient Maximization Algorithm With Implications in Min-Max Predictive Control

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    n this technical note, an algorithm for binary quadratic programs defined by matrices with band structure is proposed. It was shown in the article by T. Alamo, D. M. de la Pentildea, D. Limon, and E. F. Camacho, ldquoConstrained min-max predictive control: modifications of the objective function leading to polynomial complexity,rdquo IEEE Tran. Autom. Control , vol. 50, pp. 710-714, May 2005, that this class of problems arise in robust model predictive control when min-max techniques are applied. Although binary quadratic problems belongs to a class of NP-complete problems, the computational burden of the proposed maximization algorithm for band matrices is polynomial with the dimension of the optimization variable and exponential with the band size. Computational results and comparisons on several hundred test problems demonstrate the efficiency of the algorithm

    Min-max regret versus gross margin maximization in arable sector modeling

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    "A sector model presented in this article, uses about 200 representative French cereal-oriented farms to estimate policy impacts by means of mathematical modeling. Usually, such models suppose that farmers intend to maximize expected gross margin. This rationality hypothesis however seems hardly justifiable, especially these days, when gross margin variability due to European Common Agricultural Policy changes may become significant. Increasing uncertainty introduces bounded rationality to the decision problem so that crop gross margins may be better approximated by interval rather than by expected (precise) values. The initial LP problem is specified as an “Interval Linear Programming (ILP)”. We assume that farmers tend to decide upon their surface allocation prudently in order to get through with minimum loss, which is precisely the rationale underlying the minimization of maximum regret decision criterion. Recent advances in operations research, namely Mausser and Laguna algorithms, are exploited to implement the min-max regret criterion to arable agriculture ILP. The validation against observed crop mix proved that as uncertainty increases about 40% of the farmers adopt the min-max regret decision rule instead of the gross margin maximization."Interval Linear Programming, Min-Max Regret, Common Agricultural Policy, Arable cropping, France

    Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

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    The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

    Positive multi-criteria models in agriculture for energy and environmental policy analysis

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    Environmental consciousness and accompanying actions have been paralleled by the evolution of multi-criteria methods which have provided tools to assist policy makers in discovering compromises in order to muddle through. This paper recalls the development of multi-criteria methods in agriculture, focusing on their contribution to produce input or output functions useful for environmental and/or energy policy. Response curves generated by MC models can more accurately predict farmers’ response to market and policy parameters compared with classic profit maximizing behavior. Concrete examples from recent literature illustrate the above statements and ideas for further research are provided.multi-criteria models, interval programming, supply curves, bio-energy, policy analysis

    Online Learning and Profit Maximization from Revealed Preferences

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    We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices, subject to a budget constraint. The merchant observes only the purchased goods, and seeks to adapt prices to optimize his profits. We give an efficient algorithm for the merchant's problem that consists of a learning phase in which the consumer's utility function is (perhaps partially) inferred, followed by a price optimization step. We also consider an alternative online learning algorithm for the setting where prices are set exogenously, but the merchant would still like to predict the bundle that will be bought by the consumer for purposes of inventory or supply chain management. In contrast with most prior work on the revealed preferences problem, we demonstrate that by making stronger assumptions on the form of utility functions, efficient algorithms for both learning and profit maximization are possible, even in adaptive, online settings
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