480 research outputs found
An Efficient Distributed Nash Equilibrium Seeking with Compressed and Event-triggered Communication
Distributed Nash equilibrium (NE) seeking problems for networked games have
been widely investigated in recent years. Despite the increasing attention,
communication expenditure is becoming a major bottleneck for scaling up
distributed approaches within limited communication bandwidth between agents.
To reduce communication cost, an efficient distributed NE seeking (ETC-DNES)
algorithm is proposed to obtain an NE for games over directed graphs, where the
communication efficiency is improved by event-triggered exchanges of compressed
information among neighbors. ETC-DNES saves communication costs in both
transmitted bits and rounds of communication. Furthermore, our method only
requires the row-stochastic property of the adjacency matrix, unlike previous
approaches that hinged on doubly-stochastic communication matrices. We provide
convergence guarantees for ETC-DNES on games with restricted strongly monotone
mappings and testify its efficiency with no sacrifice on the accuracy. The
algorithm and analysis are extended to a compressed algorithm with stochastic
event-triggered mechanism (SETC-DNES). In SETC-DNES, we introduce a random
variable in the triggering condition to further enhance algorithm efficiency.
We demonstrate that SETC-DNES guarantees linear convergence to the NE while
achieving even greater reductions in communication costs compared to ETC-DNES.
Finally, numerical simulations illustrate the effectiveness of the proposed
algorithms
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
Privacy-Preserving Distributed Optimization and Learning
Distributed optimization and learning has recently garnered great attention
due to its wide applications in sensor networks, smart grids, machine learning,
and so forth. Despite rapid development, existing distributed optimization and
learning algorithms require each agent to exchange messages with its neighbors,
which may expose sensitive information and raise significant privacy concerns.
In this survey paper, we overview privacy-preserving distributed optimization
and learning methods. We first discuss cryptography, differential privacy, and
other techniques that can be used for privacy preservation and indicate their
pros and cons for privacy protection in distributed optimization and learning.
We believe that among these approaches, differential privacy is most promising
due to its low computational and communication complexities, which are
extremely appealing for modern learning based applications with high dimensions
of optimization variables. We then introduce several differential-privacy
algorithms that can simultaneously ensure privacy and optimization accuracy.
Moreover, we provide example applications in several machine learning problems
to confirm the real-world effectiveness of these algorithms. Finally, we
highlight some challenges in this research domain and discuss future
directions.Comment: Accepted as a chapter in the Encyclopedia of Systems and Control
Engineering published by Elsevie
Quantized distributed Nash equilibrium seeking under DoS attacks: A quantized consensus based approach
This paper studies distributed Nash equilibrium (NE) seeking under
Denial-of-Service (DoS) attacks and quantization. The players can only exchange
information with their own direct neighbors. The transmitted information is
subject to quantization and packet losses induced by malicious DoS attacks. We
propose a quantized distributed NE seeking strategy based on the approach of
dynamic quantized consensus. To solve the quantizer saturation problem caused
by DoS attacks, the quantization mechanism is equipped to have zooming-in and
holding capabilities, in which the holding capability is consistent with the
results in quantized consensus under DoS. A sufficient condition on the number
of quantizer levels is provided, under which the quantizers are free from
saturation under DoS attacks. The proposed distributed quantized NE seeking
strategy is shown to have the so-called maximum resilience to DoS attacks.
Namely, if the bound characterizing the maximum resilience is violated, an
attacker can deny all the transmissions and hence distributed NE seeking is
impossible
Distributed Nash equilibrium tracking via the alternating direction method of multipliers
summary:Nash equilibrium is recognized as an important solution concept in non-cooperative game theory due to its broad applicability to economics, social sciences, computer science, and engineering. In view of its importance, substantial progress has been made to seek a static Nash equilibrium using distributed methods. However, these approaches are inapplicable in dynamic environments because, in this setting, the Nash equilibrium constantly changes over time. In this paper, we propose a dynamic algorithm that can track the time-varying Nash equilibrium in a non-cooperative game. Our approach enables each player to update its action using an alternating direction method of multipliers while ensuring this estimated action of each player always converges to a neighborhood of the Nash equilibrium at each sampling instant. We prove that the final tracking error is linearly proportional to the sampling interval, which implies that the tracking error can be sufficiently close to zero when the sampling interval is small enough. Finally, numerical simulations are conducted to verify the correctness of our theoretical results
Differentially-private Distributed Algorithms for Aggregative Games with Guaranteed Convergence
The distributed computation of a Nash equilibrium in aggregative games is
gaining increased traction in recent years. Of particular interest is the
mediator-free scenario where individual players only access or observe the
decisions of their neighbors due to practical constraints. Given the
competitive rivalry among participating players, protecting the privacy of
individual players becomes imperative when sensitive information is involved.
We propose a fully distributed equilibrium-computation approach for aggregative
games that can achieve both rigorous differential privacy and guaranteed
computation accuracy of the Nash equilibrium. This is in sharp contrast to
existing differential-privacy solutions for aggregative games that have to
either sacrifice the accuracy of equilibrium computation to gain rigorous
privacy guarantees, or allow the cumulative privacy budget to grow unbounded,
hence losing privacy guarantees, as iteration proceeds. Our approach uses
independent noises across players, thus making it effective even when
adversaries have access to all shared messages as well as the underlying
algorithm structure. The encryption-free nature of the proposed approach, also
ensures efficiency in computation and communication. The approach is also
applicable in stochastic aggregative games, able to ensure both rigorous
differential privacy and guaranteed computation accuracy of the Nash
equilibrium when individual players only have stochastic estimates of their
pseudo-gradient mappings. Numerical comparisons with existing counterparts
confirm the effectiveness of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:2202.0111
Distributed Delay-Tolerant Strategies for Equality-Constraint Sum-Preserving Resource Allocation
This paper proposes two nonlinear dynamics to solve constrained distributed
optimization problem for resource allocation over a multi-agent network. In
this setup, coupling constraint refers to resource-demand balance which is
preserved at all-times. The proposed solutions can address various model
nonlinearities, for example, due to quantization and/or saturation. Further, it
allows to reach faster convergence or to robustify the solution against
impulsive noise or uncertainties. We prove convergence over weakly connected
networks using convex analysis and Lyapunov theory. Our findings show that
convergence can be reached for general sign-preserving odd nonlinearity. We
further propose delay-tolerant mechanisms to handle general bounded
heterogeneous time-varying delays over the communication network of agents
while preserving all-time feasibility. This work finds application in CPU
scheduling and coverage control among others. This paper advances the
state-of-the-art by addressing (i) possible nonlinearity on the agents/links,
meanwhile handling (ii) resource-demand feasibility at all times, (iii)
uniform-connectivity instead of all-time connectivity, and (iv) possible
heterogeneous and time-varying delays. To our best knowledge, no existing work
addresses contributions (i)-(iv) altogether. Simulations and comparative
analysis are provided to corroborate our contributions
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