2,473 research outputs found
Stochastic Online Learning with Probabilistic Graph Feedback
We consider a problem of stochastic online learning with general
probabilistic graph feedback, where each directed edge in the feedback graph
has probability . Two cases are covered. (a) The one-step case, where
after playing arm the learner observes a sample reward feedback of arm
with independent probability . (b) The cascade case where after playing
arm the learner observes feedback of all arms in a probabilistic
cascade starting from -- for each with probability , if arm
is played or observed, then a reward sample of arm would be observed
with independent probability . Previous works mainly focus on
deterministic graphs which corresponds to one-step case with , an adversarial sequence of graphs with certain topology guarantees,
or a specific type of random graphs. We analyze the asymptotic lower bounds and
design algorithms in both cases. The regret upper bounds of the algorithms
match the lower bounds with high probability
Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz
The spin-1/2 XYZ model with both periodic and anti-periodic boundary
conditions is studied via the off-diagonal Bethe ansatz method. The exact
spectra of the Hamiltonians and the Bethe ansatz equations are derived by
constructing the inhomogeneous T-Q relations, which allow us to treat both the
even N (the number of lattice sites) and odd N cases simultaneously in an
unified approach.Comment: 20 pages, 3 tables, published version, numerical check is adde
Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
The off-diagonal Bethe ansatz method is generalized to the high spin
integrable systems associated with the su(2) algebra by employing the spin-s
isotropic Heisenberg chain model with generic integrable boundaries as an
example. With the fusion techniques, certain closed operator identities for
constructing the functional T-Q relations and the Bethe ansatz equations are
derived. It is found that a variety of inhomogeneous T-Q relations obeying the
operator product identities can be constructed. Numerical results for two-site
s=1 case indicate that an arbitrary choice of the derived T-Q relations is
enough to give the complete spectrum of the transfer matrix.Comment: 26 pages, 2 tables, 1 figure, published versio
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