11,553 research outputs found
A Finite Time Analysis of Two Time-Scale Actor Critic Methods
Actor-critic (AC) methods have exhibited great empirical success compared
with other reinforcement learning algorithms, where the actor uses the policy
gradient to improve the learning policy and the critic uses temporal difference
learning to estimate the policy gradient. Under the two time-scale learning
rate schedule, the asymptotic convergence of AC has been well studied in the
literature. However, the non-asymptotic convergence and finite sample
complexity of actor-critic methods are largely open. In this work, we provide a
non-asymptotic analysis for two time-scale actor-critic methods under
non-i.i.d. setting. We prove that the actor-critic method is guaranteed to find
a first-order stationary point (i.e., ) of the non-concave performance function
, with sample
complexity. To the best of our knowledge, this is the first work providing
finite-time analysis and sample complexity bound for two time-scale
actor-critic methods.Comment: 45 page
Spin tunneling properties in mesoscopic magnets: effects of a magnetic field
The tunneling of a giant spin at excited levels is studied theoretically in
mesoscopic magnets with a magnetic field at an arbitrary angle in the easy
plane. Different structures of the tunneling barriers can be generated by the
magnetocrystalline anisotropy, the magnitude and the orientation of the field.
By calculating the nonvacuum instanton solution explicitly, we obtain the
tunnel splittings and the tunneling rates for different angle ranges of the
external magnetic field ( and ). The
temperature dependences of the decay rates are clearly shown for each case. It
is found that the tunneling rate and the crossover temperature depend on the
orientation of the external magnetic field. This feature can be tested with the
use of existing experimental techniques.Comment: 27 pages, 4 figures, accepted by Euro. Phys. J.
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