798 research outputs found
Distributed Nash Equilibrium Seeking with Limited Cost Function Knowledge via A Consensus-Based Gradient-Free Method
This paper considers a distributed Nash equilibrium seeking problem, where
the players only have partial access to other players' actions, such as their
neighbors' actions. Thus, the players are supposed to communicate with each
other to estimate other players' actions. To solve the problem, a
leader-following consensus gradient-free distributed Nash equilibrium seeking
algorithm is proposed. This algorithm utilizes only the measurements of the
player's local cost function without the knowledge of its explicit expression
or the requirement on its smoothness. Hence, the algorithm is gradient-free
during the entire updating process. Moreover, the analysis on the convergence
of the Nash equilibrium is studied for the algorithm with both diminishing and
constant step-sizes, respectively. Specifically, in the case of diminishing
step-size, it is shown that the players' actions converge to the Nash
equilibrium almost surely, while in the case of fixed step-size, the
convergence to the neighborhood of the Nash equilibrium is achieved. The
performance of the proposed algorithm is verified through numerical
simulations
Fully Distributed Nash Equilibrium Seeking in N-Cluster Games
Distributed optimization and Nash equilibrium (NE) seeking problems have
drawn much attention in the control community recently. This paper studies a
class of non-cooperative games, known as -cluster game, which subsumes both
cooperative and non-cooperative nature among multiple agents in the two
problems: solving distributed optimization problem within the cluster, while
playing a non-cooperative game across the clusters. Moreover, we consider a
partial-decision information game setup, i.e., the agents do not have direct
access to other agents' decisions, and hence need to communicate with each
other through a directed graph whose associated adjacency matrix is assumed to
be non-doubly stochastic. To solve the -cluster game problem, we propose a
fully distributed NE seeking algorithm by a synthesis of leader-following
consensus and gradient tracking, where the leader-following consensus protocol
is adopted to estimate the other agents' decisions and the gradient tracking
method is employed to trace some weighted average of the gradient. Furthermore,
the algorithm is equipped with uncoordinated constant step-sizes, which allows
the agents to choose their own preferred step-sizes, instead of a uniform
coordinated step-size. We prove that all agents' decisions converge linearly to
their corresponding NE so long as the largest step-size and the heterogeneity
of the step-size are small. We verify the derived results through a numerical
example in a Cournot competition game
Nash Equilibrium Seeking in N-Coalition Games via a Gradient-Free Method
This paper studies an -coalition non-cooperative game problem, where the
players in the same coalition cooperatively minimize the sum of their local
cost functions under a directed communication graph, while collectively acting
as a virtual player to play a non-cooperative game with other coalitions.
Moreover, it is assumed that the players have no access to the explicit
functional form but only the function value of their local costs. To solve the
problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based
on the gradient tracking method, is proposed. Specifically, a gradient
estimator is developed locally based on Gaussian smoothing to estimate the
partial gradients, and a gradient tracker is constructed locally to trace the
average sum of the partial gradients among the players within the coalition.
With a sufficiently small constant step-size, we show that all players' actions
approximately converge to the Nash equilibrium at a geometric rate under a
strongly monotone game mapping condition. Numerical simulations are conducted
to verify the effectiveness of the proposed algorithm
Gradient-Free Distributed Optimization with Exact Convergence
In this paper, a gradient-free distributed algorithm is introduced to solve a
set constrained optimization problem under a directed communication network.
Specifically, at each time-step, the agents locally compute a so-called
pseudo-gradient to guide the updates of the decision variables, which can be
applied in the fields where the gradient information is unknown, not available
or non-existent. A surplus-based method is adopted to remove the doubly
stochastic requirement on the weighting matrix, which enables the
implementation of the algorithm in graphs having no associated doubly
stochastic weighting matrix. For the convergence results, the proposed
algorithm is able to obtain the exact convergence to the optimal value with any
positive, non-summable and non-increasing step-sizes. Furthermore, when the
step-size is also square-summable, the proposed algorithm is guaranteed to
achieve the exact convergence to an optimal solution. In addition to the
standard convergence analysis, the convergence rate of the proposed algorithm
with respect to different cases of step-sizes is investigated. Finally, the
effectiveness of the proposed algorithm is verified through numerical
simulations
Gradient-Free Nash Equilibrium Seeking in N-Cluster Games with Uncoordinated Constant Step-Sizes
In this paper, we consider a problem of simultaneous global cost minimization
and Nash equilibrium seeking, which commonly exists in -cluster
non-cooperative games. Specifically, the agents in the same cluster collaborate
to minimize a global cost function, being a summation of their individual cost
functions, and jointly play a non-cooperative game with other clusters as
players. For the problem settings, we suppose that the explicit analytical
expressions of the agents' local cost functions are unknown, but the function
values can be measured. We propose a gradient-free Nash equilibrium seeking
algorithm by a synthesis of Gaussian smoothing techniques and gradient
tracking. Furthermore, instead of using the uniform coordinated step-size, we
allow the agents across different clusters to choose different constant
step-sizes. When the largest step-size is sufficiently small, we prove a linear
convergence of the agents' actions to a neighborhood of the unique Nash
equilibrium under a strongly monotone game mapping condition, with the error
gap being propotional to the largest step-size and the smoothing parameter. The
performance of the proposed algorithm is validated by numerical simulations
Social Profit Optimization with Demand Response Management in Electricity Market: A Multi-timescale Leader-following Approach
In the electricity market, it is quite common that the market participants
make "selfish" strategies to harvest the maximum profits for themselves, which
may cause the social benefit loss and impair the sustainability of the society
in the long term. Regarding this issue, in this work, we will discuss how the
social profit can be improved through strategic demand response (DR)
management. Specifically, we explore two interaction mechanisms in the market:
Nash equilibrium (NE) and Stackelberg equilibrium (SE) among utility companies
(UCs) and user-UC interactions, respectively. At the user side, each user
determines the optimal energy-purchasing strategy to maximize its own profit.
At the UC side, a governmental UC (g-UC) is considered, who aims to optimize
the social profit of the market. Meanwhile, normal UCs play games to maximize
their own profits. As a result, a basic leader-following problem among the UCs
is formulated under the coordination of the independent system operator (ISO).
Moreover, by using our proposed demand function amelioration (DFA) strategy, a
multi-timescale leader-following problem is formulated. In this case, the
maximal market efficiency can be achieved without changing the "selfish
instinct" of normal UCs. In addition, by considering the local constraints for
the UCs, two projection-based pricing algorithms are proposed for UCs, which
can provide approximate optimal solutions for the resulting non-convex social
profit optimization problems. The feasibility of the proposed algorithms is
verified by using the concept of price of anarchy (PoA) in a multi-UC
multi-user market model in the simulation.Comment: 33 pages, 15 figure
An Unsupervised Approach to Ultrasound Elastography with End-to-end Strain Regularisation
Quasi-static ultrasound elastography (USE) is an imaging modality that
consists of determining a measure of deformation (i.e.strain) of soft tissue in
response to an applied mechanical force. The strain is generally determined by
estimating the displacement between successive ultrasound frames acquired
before and after applying manual compression. The computational efficiency and
accuracy of the displacement prediction, also known as time-delay estimation,
are key challenges for real-time USE applications. In this paper, we present a
novel deep-learning method for efficient time-delay estimation between
ultrasound radio-frequency (RF) data. The proposed method consists of a
convolutional neural network (CNN) that predicts a displacement field between a
pair of pre- and post-compression ultrasound RF frames. The network is trained
in an unsupervised way, by optimizing a similarity metric be-tween the
reference and compressed image. We also introduce a new regularization term
that preserves displacement continuity by directly optimizing the strain
smoothness. We validated the performance of our method by using both ultrasound
simulation and in vivo data on healthy volunteers. We also compared the
performance of our method with a state-of-the-art method called OVERWIND [17].
Average contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) of our
method in 30 simulation and 3 in vivo image pairs are 7.70 and 6.95, 7 and
0.31, respectively. Our results suggest that our approach can effectively
predict accurate strain images. The unsupervised aspect of our approach
represents a great potential for the use of deep learning application for the
analysis of clinical ultrasound data.Comment: Accepted at MICCAI 202
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