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Machine learning force fields (MLFFs) are an attractive alternative to ab-initio methods for molecular dynamics (MD) simulations. However, they can produce unstable simulations, limiting their ability to model phenomena occurring over…
We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…
As evaluation designs of large language models may shape our trajectory toward artificial general intelligence, comprehensive and forward-looking assessment is essential. Existing benchmarks primarily assess static knowledge, while…
Solving control tasks in complex environments automatically through learning offers great potential. While contemporary techniques from deep reinforcement learning (DRL) provide effective solutions, their decision-making is not transparent.…
In many reinforcement learning (RL) applications, we want policies that reach desired states and then keep the controlled system within an acceptable region around the desired states over an indefinite period of time. This latter objective…
Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic…
The wide availability of data coupled with the computational advances in artificial intelligence and machine learning promise to enable many future technologies such as autonomous driving. While there has been a variety of successful…
Except for special classes of games, there is no systematic framework for analyzing the dynamical properties of multi-agent strategic interactions. Potential games are one such special but restrictive class of games that allow for tractable…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a…
Learning in zero-sum games studies a situation where multiple agents competitively learn their strategy. In such multi-agent learning, we often see that the strategies cycle around their optimum, i.e., Nash equilibrium. When a game…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
Motivated by applications in job scheduling, queuing networks, and load balancing in cyber-physical systems, we develop and analyze a game-theoretic framework to balance the load among servers in static and dynamic settings. In these…
This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and…
In this technical note, we study the mean square stability-based analysis of stochastic continuous-time linear networked systems. The stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output…
Static reduction of information structures (ISs) is a method that is commonly adopted in stochastic control, team theory, and game theory. One approach entails change of measure arguments, which has been crucial for stochastic analysis and…
A central problem in the theory of multi-agent reinforcement learning (MARL) is to understand what structural conditions and algorithmic principles lead to sample-efficient learning guarantees, and how these considerations change as we move…
Electrical grids are now much more complex due to the rapid integration of distributed generation and alternative energy sources, which makes forecasting grid stability with optimized control a crucial task for operators. Traditional…
With multiple carriers in a logistics market, customers can choose the best carrier to deliver their products and packages. In this paper, we present a novel approach of using the stochastic evolutionary game to analyze the decision-making…
Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics…