Related papers: Lattice Theory in Multi-Agent Systems
Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information…
We introduce a categorical framework for diffusion on network-structured data valued in weighted lattices, extending the Laplacian paradigm beyond the category of Hilbert spaces. Central to our approach is the Lawvere Laplacian, an…
We compute the lattice operations for the (pairwise) stable set in many-to-many matching markets when only path-independence on agents' choice functions is imposed. To do this, we first show that the sets of firm-quasi-stable and…
This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an endomorphism on the cochain complex whose fixed points yield a…
Since the complexity of the practical environment, many distributed networked systems can not be illustrated with the integer-order dynamics and only be described as the fractional-order dynamics. Suppose multi-agent systems will show the…
Turing's model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the…
In this paper, we propose several consensus protocols of the first and second order for networked multi-agent systems and provide explicit representations for their asymptotic states. These representations involve the eigenprojection of the…
We introduce a $\phi^{4}$ lattice field theory with frustrated dynamics as a multi-agent system to reproduce stylized facts of financial markets such as fat-tailed distributions of returns and clustered volatility. Each lattice site,…
We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lagrangian multiforms" and "Pluri-Lagrangian systems", which…
Traditional measures based solely on pairwise associations often fail to capture the complex statistical structure of multivariate data. Existing approaches for identifying information shared among $d>3$ variables are frequently…
This study develops an original and innovative matrix representation with respect to the information flow for networked multi-agent system. To begin with, the general concepts of the edge Laplacian of digraph are proposed with its algebraic…
Lattice Conditional Independence models are a class of models developed first for the Gaussian case in which a distributive lattice classifies all the conditional independence statements. The main result is that these models can…
Multi-agent systems are increasingly widespread in a range of application domains, with optimization and learning underpinning many of the tasks that arise in this context. Different approaches have been proposed to enable the cooperative…
Multi-agent target tracking in the presence of nonlinear dynamics and agent heterogeneity, where state-space dimensions may differ, is a challenging problem that traditional graph Laplacian methods cannot easily address. This work leverages…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
We consider a one-dimensional infinite lattice where at each site there sits an agent carrying a velocity, which is drawn initially for each agent independently from a common distribution. This system evolves as a Markov process where a…
The existing results on controllability of multi-agents networks are mostly based on homogeneous nodes. This paper focuses on controllability of heterogeneous multi-agent networks, where the agents are modeled as two types. One type is that…
This work explores the edge agreement problem of second-order multi-agent system with dynamic quantization under directed communication. To begin with, by virtue of the directed edge laplacian, we derive a model reduction representation of…
Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we…
Most previous studies on multi-agent reinforcement learning focus on deriving decentralized and cooperative policies to maximize a common reward and rarely consider the transferability of trained policies to new tasks. This prevents such…