32,794 research outputs found
State-Augmentation Transformations for Risk-Sensitive Reinforcement Learning
In the framework of MDP, although the general reward function takes three
arguments-current state, action, and successor state; it is often simplified to
a function of two arguments-current state and action. The former is called a
transition-based reward function, whereas the latter is called a state-based
reward function. When the objective involves the expected cumulative reward
only, this simplification works perfectly. However, when the objective is
risk-sensitive, this simplification leads to an incorrect value. We present
state-augmentation transformations (SATs), which preserve the reward sequences
as well as the reward distributions and the optimal policy in risk-sensitive
reinforcement learning. In risk-sensitive scenarios, firstly we prove that, for
every MDP with a stochastic transition-based reward function, there exists an
MDP with a deterministic state-based reward function, such that for any given
(randomized) policy for the first MDP, there exists a corresponding policy for
the second MDP, such that both Markov reward processes share the same reward
sequence. Secondly we illustrate that two situations require the proposed SATs
in an inventory control problem. One could be using Q-learning (or other
learning methods) on MDPs with transition-based reward functions, and the other
could be using methods, which are for the Markov processes with a deterministic
state-based reward functions, on the Markov processes with general reward
functions. We show the advantage of the SATs by considering Value-at-Risk as an
example, which is a risk measure on the reward distribution instead of the
measures (such as mean and variance) of the distribution. We illustrate the
error in the reward distribution estimation from the direct use of Q-learning,
and show how the SATs enable a variance formula to work on Markov processes
with general reward functions
Triple Derivations and Triple Homomorphisms of Perfect Lie Superalgebras
In this paper, we study triple derivations and triple homomorphisms of
perfect Lie superalgebras over a commutative ring . It is proved that, if
the base ring contains , is a perfect Lie superalgebra with
zero center, then every triple derivation of is a derivation, and every
triple derivation of the derivation algebra is an inner derivation.
Let be Lie superalgebras over a commutative ring , the notion of
triple homomorphism from to is introduced. We proved that, under
certain assumptions, homomorphisms, anti-homomorphisms, and sums of
homomorphisms and anti-homomorphisms are all triple homomorphisms.Comment: 12pages in Indagationes Mathematicae, 201
Exclusive Decay of Quarkonia and Meson into a Lepton Pair Combined with Two Pions
We study the exclusive decay of , and into a lepton
pair combined with two pions in the two kinematic regions. One is specified by
the two pions having large momenta, but a small invariant mass. The other is
specified by the two pions having small momenta. In both cases we find that in
the heavy quark limit the decay amplitude takes a factorized form, in which the
nonperturbative effect related to heavy meson is represented by a NRQCD matrix
element. The nonperturbative effects related to the two pions are represented
by some universal functions characterizing the conversion of gluons into the
pions. Using models for these universal functions and chiral perturbative
theory we are able to obtain numerical predictions for the decay widths. Our
numerical results show that the decay of \jpsi is at order of with
reasonable cuts and can be observed at BES II and the proposed BES III and
CLEO-C. For other decays the branching ratio may be too small to be measured.Comment: 19 pages, Latex 2e file, 12 EPS figures (included). Replaced with
version to appear in Eur. Phys. J. C,published online: 8 May 200
Invariants and K-spectrums of local theta lifts
Let be a type I irreducible reductive dual pair in
. We assume that is in the stable range
where is the smaller member. Let and be maximal compact subgroups
of and respectively. Let and be the
complexified Cartan decompositions of the Lie algebras of and
respectively. Let and be the inverse
images of and in the metaplectic double cover
of . Let
be a genuine irreducible -module. Our
first main result is that if is unitarizable, then except for one
special case, the full local theta lift is equal to the
local theta lift . Thus excluding the special case, the full
theta lift is an irreducible and unitarizable
-module. Our second main result is that the
associated variety and the associated cycle of are the theta lifts of
the associated variety and the associated cycle of the contragredient
representation respectively. Finally we obtain some interesting
-modules whose -spectrums are
isomorphic to the spaces of global sections of some vector bundles on some
nilpotent -orbits in
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