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Distributionally Robust Optimization for Sequential Decision Making
The distributionally robust Markov Decision Process (MDP) approach asks for a
distributionally robust policy that achieves the maximal expected total reward
under the most adversarial distribution of uncertain parameters. In this paper,
we study distributionally robust MDPs where ambiguity sets for the uncertain
parameters are of a format that can easily incorporate in its description the
uncertainty's generalized moment as well as statistical distance information.
In this way, we generalize existing works on distributionally robust MDP with
generalized-moment-based and statistical-distance-based ambiguity sets to
incorporate information from the former class such as moments and dispersions
to the latter class that critically depends on empirical observations of the
uncertain parameters. We show that, under this format of ambiguity sets, the
resulting distributionally robust MDP remains tractable under mild technical
conditions. To be more specific, a distributionally robust policy can be
constructed by solving a sequence of one-stage convex optimization subproblems
Noise spectra of stochastic pulse sequences: application to large scale magnetization flips in the finite size 2D Ising model
We provide a general scheme to predict and derive the contribution to the
noise spectrum of a stochastic sequence of pulses from the distribution of
pulse parameters. An example is the magnetization noise spectra of a 2D Ising
system near its phase transition. At , the low frequency spectra is
dominated by magnetization flips of nearly the entire system. We find that both
the predicted and the analytically derived spectra fit those produced from
simulations. Subtracting this contribution leaves the high frequency spectra
which follow a power law set by the critical exponents.Comment: 4 pages, 5 figures. We improved text and included a predicted noise
curve in Figure 4. 2 examples from Figure 3 are remove
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