168 research outputs found
Facets of a mixed-integer bilinear covering set with bounds on variables
We derive a closed form description of the convex hull of mixed-integer
bilinear covering set with bounds on the integer variables. This convex hull
description is determined by considering some orthogonal disjunctive sets
defined in a certain way. This description does not introduce any new
variables, but consists of exponentially many inequalities. An extended
formulation with a few extra variables and much smaller number of constraints
is presented. We also derive a linear time separation algorithm for finding the
facet defining inequalities of this convex hull. We study the effectiveness of
the new inequalities and the extended formulation using some examples
Optimal Control Strategies in Delayed Sharing Information Structures
The -step delayed sharing information structure is investigated. This
information structure comprises of controllers that share their information
with a delay of time steps. This information structure is a link between
the classical information structure, where information is shared perfectly
between the controllers, and a non-classical information structure, where there
is no "lateral" sharing of information among the controllers. Structural
results for optimal control strategies for systems with such information
structures are presented. A sequential methodology for finding the optimal
strategies is also derived. The solution approach provides an insight for
identifying structural results and sequential decomposition for general
decentralized stochastic control problems.Comment: Sumbitted to IEEE Transactions on automatic contro
Critical Collapse of Einstein Cluster
We observe critical phenomena in spherically symmetric gravitational collapse
of Einstein Cluster. We show analytically that the collapse evolution ends
either in formation of a black hole or in dispersal depending on the values of
initial parameters which characterize initial density and angular momentum of
the collapsing cloud. Near the threshold of black hole formation, we obtain
scaling relation for the mass of the black hole and find the critical exponent
value to be 3/2. We numerically confirm that there exist wide ranges of initial
parameter values around the critical configuration for which the model remains
shell-crossing free.Comment: Accepted for publication in Prog. Theor. Phy
A relaxed technical assumption for posterior sampling-based reinforcement learning for control of unknown linear systems
We revisit the Thompson sampling algorithm to control an unknown linear
quadratic (LQ) system recently proposed by Ouyang et al (arXiv:1709.04047). The
regret bound of the algorithm was derived under a technical assumption on the
induced norm of the closed loop system. In this technical note, we show that by
making a minor modification in the algorithm (in particular, ensuring that an
episode does not end too soon), this technical assumption on the induced norm
can be replaced by a milder assumption in terms of the spectral radius of the
closed loop system. The modified algorithm has the same Bayesian regret of
, where is the time-horizon and the
notation hides logarithmic terms in~
A Structural Result for Delayed Sharing Information Structures
Abstract-The n-step delayed sharing information structure is investigated. This information structure is a link between the classical information structure, where information is shared perfectly among the controllers, and a non-classical information structure, where there is no "lateral" sharing of information among the controllers. A structural result for optimal control policies in systems with such information structures is presented. A methodology for sequentially finding optimal policies is also established. The solution approach provides an insight for identifying structural results for general decentralized stochastic control problems
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