807 research outputs found
Regret Bounds for Reinforcement Learning with Policy Advice
In some reinforcement learning problems an agent may be provided with a set
of input policies, perhaps learned from prior experience or provided by
advisors. We present a reinforcement learning with policy advice (RLPA)
algorithm which leverages this input set and learns to use the best policy in
the set for the reinforcement learning task at hand. We prove that RLPA has a
sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and
that both this regret and its computational complexity are independent of the
size of the state and action space. Our empirical simulations support our
theoretical analysis. This suggests RLPA may offer significant advantages in
large domains where some prior good policies are provided
An Efficient Mechanism for Cross-border Support of Renewable Electricity in the European Union
The ability to exchange renewable electricity (RES-e) capacity between EU member states improves the welfare of all member states since potentials and demands for RES-e capacity vary across the EU. This notion is reflected in the promotion of so-called cooperation mechanisms by the European Commission. The existing mechanisms appear, unfortunately, to be insufficient to facilitate an efficient level of trade in capacity across the EU; only a small quantity of energy is expected to be subject to cooperation mechanisms (Klessmann et al. 2010). In order to address these challenges, in this paper we propose a new mechanism for cross-border support of renewable electricity in EU. The guiding idea is that the cross-border mechanism allocates new RES-e generating capacity across EU Member States to where it is most valuable. This can, but need not, coincide with the most cost efficient allocation. The mechanism consists of two main elements. Firstly, a cross-border impact matrix that indicates the spill-over of benefits between member states induced from the power injection of additional RES-e generating capacity. Secondly, an EU wide auction in which member states and generators of RES-e bid prices indicating their willingness to pay for additional RES-e generating capacity. Then for given parameters the auctioneer selects the set of bids that maximizes an EU-wide surplus. We find that the mechanism leads to a decentralized optimization of RES-e support in the EU, by matching high willingness to pay of member states with low cost potentials of RES-e generation, but only if the benefits of RES-e are actually delivered for the member state paying for it. Moreover, the mechanism offers the potential to significantly reduce the barriers of the current cooperation mechanism, such as transaction costs or uncertainty about costs and benefits
Relativistic photoelectron spectra in the ionization of atoms by elliptically polarized light
Relativistic tunnel ionization of atoms by intense, elliptically polarized
light is considered. The relativistic version of the Landau-Dykhne formula is
employed. The general analytical expression is obtained for the relativistic
photoelectron spectra. The most probable angle of electron emission, the
angular distribution near this angle, the position of the maximum and the width
of the energy spectrum are calculated. In the weak field limit we obtain the
familiar non-relativistic results. For the case of circular polarization our
analytical results are in agreement with recent derivations of Krainov [V.P.
Krainov, J. Phys. B, {\bf 32}, 1607 (1999)].Comment: 8 pages, 2 figures, accepted for publication in Journal of Physics
A geometrical angle on Feynman integrals
A direct link between a one-loop N-point Feynman diagram and a geometrical
representation based on the N-dimensional simplex is established by relating
the Feynman parametric representations to the integrals over contents of
(N-1)-dimensional simplices in non-Euclidean geometry of constant curvature. In
particular, the four-point function in four dimensions is proportional to the
volume of a three-dimensional spherical (or hyperbolic) tetrahedron which can
be calculated by splitting into birectangular ones. It is also shown that the
known formula of reduction of the N-point function in (N-1) dimensions
corresponds to splitting the related N-dimensional simplex into N rectangular
ones.Comment: 47 pages, including 42 pages of the text (in plain Latex) and 5 pages
with the figures (in a separate Latex file, requires axodraw.sty) a note and
three references added, minor problem with notation fixe
Relativistic semiclassical approach in strong-field nonlinear photoionization
Nonlinear relativistic ionization phenomena induced by a strong laser
radiation with elliptically polarization are considered. The starting point is
the classical relativistic action for a free electron moving in the
electromagnetic field created by a strong laser beam. The application of the
relativistic action to the classical barrier-suppression ionization is briefly
discussed. Further the relativistic version of the Landau-Dykhne formula is
employed to consider the semiclassical sub-barrier ionization. Simple
analytical expressions have been found for: (i) the rates of the strong-field
nonlinear ionization including relativistic initial and final state effects;
(ii) the most probable value of the components of the photoelectron final state
momentum; (iii) the most probable direction of photoelectron emission and (iv)
the distribution of the photoelectron momentum near its maximum value.Comment: 13 pages, 3 figures, to be published in Phys. Rev.
Gauge Independence of IR singularities in Non-Commutative QFT - and Interpolating Gauges
IR divergences of a non-commutative U(1) Maxwell theory are discussed at the
one-loop level using an interpolating gauge to show that quadratic IR
divergences are independent not only from a covariant gauge fixing but also
independent from an axial gauge fixing.Comment: 11 pages, 2 figures, v1 minor correction
Correlation energy of an electron gas in strong magnetic fields at high densities
The high-density electron gas in a strong magnetic field B and at zero
temperature is investigated. The quantum strong-field limit is considered in
which only the lowest Landau level is occupied. It is shown that the
perturbation series of the ground-state energy can be represented in analogy to
the Gell-Mann Brueckner expression of the ground-state energy of the field-free
electron gas. The role of the expansion parameter is taken by r_B= (2/3 \pi^2)
(B/m^2) (\hbar r_s /e)^3 instead of the field-free Gell-Mann Brueckner
parameter r_s. The perturbation series is given exactly up to o(r_B) for the
case of a small filling factor for the lowest Landau level.Comment: 10 pages, Accepted for publication in Phys.Rev.
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