523 research outputs found
A McKean-Vlasov approach to distributed electricity generation development
This paper analyses the interaction between centralised carbon emissive
technologies and distributed intermittent non-emissive technologies. In our
model, there is a representative consumer who can satisfy her electricity
demand by investing in distributed generation (solar panels) and by buying
power from a centralised firm at a price the firm sets. Distributed generation
is intermittent and induces an externality cost to the consumer. The firm
provides non-random electricity generation subject to a carbon tax and to
transmission costs. The objective of the consumer is to satisfy her demand
while mini\-mising investment costs, payments to the firm and intermittency
costs. The objective of the firm is to satisfy the consumer's residual demand
while minimising investment costs, demand deviation costs, and maximising the
payments from the consumer. We formulate the investment decisions as
McKean-Vlasov control problems with stochastic coefficients. We provide
explicit, price model-free solutions to the optimal decision problems faced by
each player, the solution of the Pareto optimum, and the Stackelberg
equilibrium where the firm is the leader. We find that, from the social
planner's point of view, the carbon tax or transmission costs are necessary to
justify a positive share of distributed capacity in the long-term, whatever the
respective investment costs of both technologies are. The Stackelberg
equilibrium is far from the Pareto equilibrium and leads to an over-investment
in distributed energy and to a much higher price for centralised energy
Algebra in teacher training in the normal school of São Paulo: the first teaching programs of this discipline
This text presents partial results of a research in development that aims to identify the purposes of Algebra in the formation of teachers in the Normal School of São Paulo, from 1880 to 1930. In this text, in particular, it is considered a specific period of time frame of research: mid-1890s; and, in order to analyse the first programs of this discipline for the training of primary teachers, documents such as legislation, a compendium of Algebra and programs of teaching of the normal and secondary course are mobilized. It was found that, in this period, the teaching of Algebra for the future teachers was more restricted than that offered in the secondary course. This reduced format of the Normal School program may be associated with the duration of normal course studies, shorter than the secondary course, but mainly, for the different purposes of the courses
Linear Quadratic Reinforcement Learning: Sublinear Regret in the Episodic Continuous-Time Framework
In this paper we study a continuous-time linear quadratic reinforcement
learning problem in an episodic setting. We first show that na\"ive
discretization and piecewise approximation with discrete-time RL algorithms
yields a linear regret with respect to the number of learning episodes . We
then propose an algorithm with continuous-time controls based on a regularized
least-squares estimation, and establish a sublinear regret bound in the order
of . The analysis consists of two parts: parameter
estimation error, which relies on properties of sub-exponential random
variables and double stochastic integrals; and perturbation analysis, which
establishes the robustness of the associated continuous-time Riccati equation
by exploiting its regularity property.Comment: 25 page
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