588 research outputs found
Topics in inference and decision-making with partial knowledge
Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data
Maximizing Social Welfare Subject to Network Externalities: A Unifying Submodular Optimization Approach
We consider the problem of allocating multiple indivisible items to a set of
networked agents to maximize the social welfare subject to network
externalities. Here, the social welfare is given by the sum of agents'
utilities and externalities capture the effect that one user of an item has on
the item's value to others. We first provide a general formulation that
captures some of the existing models as a special case. We then show that the
social welfare maximization problem benefits some nice diminishing or
increasing marginal return properties. That allows us to devise polynomial-time
approximation algorithms using the Lovasz extension and multilinear extension
of the objective functions. Our principled approach recovers or improves some
of the existing algorithms and provides a simple and unifying framework for
maximizing social welfare subject to network externalities
All-dielectric reciprocal bianisotropic nanoparticles
The study of high-index dielectric nanoparticles currently attracts a lot of
attention. They do not suffer from absorption but promise to provide control on
the properties of light comparable to plasmonic nanoparticles. To further
advance the field, it is important to identify versatile dielectric
nanoparticles with unconventional properties. Here, we show that breaking the
symmetry of an all-dielectric nanoparticle leads to a geometrically tunable
magneto-electric coupling, i.e. an omega-type bianisotropy. The suggested
nanoparticle exhibits different backscatterings and, as an interesting
consequence, different optical scattering forces for opposite illumination
directions. An array of such nanoparticles provides different reflection phases
when illuminated from opposite directions. With a proper geometrical tuning,
this bianisotropic nanoparticle is capable of providing a phase change
in the reflection spectrum while possessing a rather large and constant
amplitude. This allows creating reflectarrays with near-perfect transmission
out of the resonance band due to the absence of an usually employed metallic
screen.Comment: 7 pages, 6 figure
Managing Price Uncertainty in Prosumer-Centric Energy Trading: A Prospect-Theoretic Stackelberg Game Approach
In this paper, the problem of energy trading between smart grid prosumers,
who can simultaneously consume and produce energy, and a grid power company is
studied. The problem is formulated as a single-leader, multiple-follower
Stackelberg game between the power company and multiple prosumers. In this
game, the power company acts as a leader who determines the pricing strategy
that maximizes its profits, while the prosumers act as followers who react by
choosing the amount of energy to buy or sell so as to optimize their current
and future profits. The proposed game accounts for each prosumer's subjective
decision when faced with the uncertainty of profits, induced by the random
future price. In particular, the framing effect, from the framework of prospect
theory (PT), is used to account for each prosumer's valuation of its gains and
losses with respect to an individual utility reference point. The reference
point changes between prosumers and stems from their past experience and future
aspirations of profits. The followers' noncooperative game is shown to admit a
unique pure-strategy Nash equilibrium (NE) under classical game theory (CGT)
which is obtained using a fully distributed algorithm. The results are extended
to account for the case of PT using algorithmic solutions that can achieve an
NE under certain conditions. Simulation results show that the total grid load
varies significantly with the prosumers' reference point and their
loss-aversion level. In addition, it is shown that the power company's profits
considerably decrease when it fails to account for the prosumers' subjective
perceptions under PT
Bandit Learning for Dynamic Colonel Blotto Game with a Budget Constraint
We consider a dynamic Colonel Blotto game (CBG) in which one of the players
is the learner and has limited troops (budget) to allocate over a finite time
horizon. At each stage, the learner strategically determines the budget
distribution among the battlefields based on past observations. The other
player is the adversary, who chooses its budget allocation strategies randomly
from some fixed unknown distribution. The learner's objective is to minimize
its regret, which is the difference between the payoff of the best mixed
strategy and the realized payoff by following a learning algorithm. The dynamic
CBG is analyzed under the framework of combinatorial bandit and bandit with
knapsacks. We first convert the dynamic CBG with budget constraint to a path
planning problem on a graph. We then devise an efficient dynamic policy for the
learner that uses a combinatorial bandit algorithm Edge on the path planning
graph as a subroutine for another algorithm LagrangeBwK. It is shown that under
the proposed policy, the learner's regret is bounded with high probability by a
term sublinear in time horizon and polynomial with respect to other
parameters
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