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1. Age-Dependent Distributed MAC for Ultra-Dense Wireless Networks

   https://doi.org/10.1109/INFOCOM42981.2021.9488674  

   Narasimha, Dheeraj ; Shakkottai, Srinivas ; Ying, Lei ( May 2021 , IEEE Conference on Computer Communications INFOCOM)

   null (Ed.)

   We consider an ultra-dense wireless network with N channels and M = N devices. Messages with fresh information are generated at each device according to a random process and need to be transmitted to an access point. The value of a message decreases as it ages, so each device searches for an idle channel to transmit the message as soon as it can. However, each channel probing is associated with a fixed cost (energy), so a device needs to adapt its probing rate based on the "age" of the message. At each device, the design of the optimal probing strategy can be formulated as an infinite horizon Markov Decision Process (MDP) where the devices compete with each other to find idle channels. While it is natural to view the system as a Bayesian game, it is often intractable to analyze such a system. Thus, we use the Mean Field Game (MFG) approach to analyze the system in a large-system regime, where the number of devices is very large, to understand the structure of the problem and to find efficient probing strategies. We present an analysis based on the MFG perspective. We begin by characterizing the space of valid policies and use this to show the existence of a Mean Field Nash Equilibrium (MFNE) in a constrained set for any general increasing cost functions with diminishing rewards. Further we provide an algorithm for computing the equilibrium for any given device, and the corresponding age-dependent channel probing policy. 

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2. Reinforcement Learning for Mean Field Games with Strategic Complementarities

   Lee, Kiyeob ; Rengarajan, Desik ; Kalathil, Dileep ; Shakkottai, Srinivas. ( January 2021 , Proceedings of Machine Learning Research)

   null (Ed.)

   Mean Field Games (MFG) are the class of games with a very large number of agents and the standard equilibrium concept is a Mean Field Equilibrium (MFE). Algorithms for learning MFE in dynamic MFGs are un- known in general. Our focus is on an important subclass that possess a monotonicity property called Strategic Complementarities (MFG-SC). We introduce a natural refinement to the equilibrium concept that we call Trembling-Hand-Perfect MFE (T-MFE), which allows agents to employ a measure of randomization while accounting for the impact of such randomization on their payoffs. We propose a simple algorithm for computing T-MFE under a known model. We also introduce a model-free and a model-based approach to learning T-MFE and provide sample complexities of both algorithms. We also develop a fully online learning scheme that obviates the need for a simulator. Finally, we empirically evaluate the performance of the proposed algorithms via examples motivated by real-world applications. 

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3. Reinforcement Learning for Mean Field Games with Strategic Complementarities (AISTATS 2021)

   https://doi.org/PMLR 130:2458-2466  

   Lee, Kiyeob ; Rengarajan, Desik ; Kalathil, Dileep ; Shakkottai, Srinivas ( January 2021 , Proceedings of Machine Learning Research)

   null (Ed.)

   Mean Field Games (MFG) are the class of games with a very large number of agents and the standard equilibrium concept is a Mean Field Equilibrium (MFE). Algorithms for learning MFE in dynamic MFGs are unknown in general. Our focus is on an important subclass that possess a monotonicity property called Strategic Complementarities (MFG-SC). We introduce a natural refinement to the equilibrium concept that we call Trembling-Hand-Perfect MFE (T-MFE), which allows agents to employ a measure of randomization while accounting for the impact of such randomization on their payoffs. We propose a simple algorithm for computing T-MFE under a known model. We also introduce a model-free and a model-based approach to learning T-MFE and provide sample complexities of both algorithms. We also develop a fully online learning scheme that obviates the need for a simulator. Finally, we empirically evaluate the performance of the proposed algorithms via examples motivated by real-world applications. 

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4. Hierarchical game theoretical distributed adaptive control for large scale multi‐group multi‐agent system

   https://doi.org/10.1049/cth2.12506  

   Dey, Shawon ; Xu, Hao ( August 2023 , IET Control Theory & Applications)

   This paper introduces a distributed adaptive formation control for large‐scale multi‐agent systems (LS‐MAS) that addresses the heavy computational complexity and communication traffic challenges while directly extending conventional distributed control from small scale to large scale. Specifically, a novel hierarchical game theoretic algorithm is developed to provide a feasible theory foundation for solving LS‐MAS distributed optimal formation problem by effectively integrating the mean‐field game (MFG), the Stackelberg game, and the cooperative game. In particular, LS‐MAS is divided into multiple groups geographically with each having one group leader and a significant amount of followers. Then, a cooperative game is used among multi‐group leaders to formulate distributed inter‐group formation control for leaders. Meanwhile, an MFG is adopted for a large number of intra‐group followers to achieve the collective intra‐group formation while a Stackelberg game is connecting the followers with their corresponding leader within the same group to achieve the overall LS‐MAS multi‐group formation behavior. Moreover, a hybrid actor–critic‐based reinforcement learning algorithm is constructed to learn the solution of the hierarchical game‐based optimal distributed formation control. Finally, to show the effectiveness of the presented schemes, numerical simulations and Lyapunov analysis is performed.

    

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5. Improving structured population models with more realistic representations of non‐normal growth

   https://doi.org/10.1111/2041-210X.13240  

   DeMarche, Megan L. ; Morris, William ; Linares, Cristina ; Doak, Daniel ; Altwegg, ed., Res ( July 2019 , Methods in Ecology and Evolution)

   Structured population models are among the most widely used tools in ecology and evolution. Integral projection models (IPMs) use continuous representations of how survival, reproduction and growth change as functions of state variables such as size, requiring fewer parameters to be estimated than projection matrix models (PPMs). Yet, almost all published IPMs make an important assumption that size‐dependent growth transitions are or can be transformed to be normally distributed. In fact, many organisms exhibit highly skewed size transitions. Small individuals can grow more than they can shrink, and large individuals may often shrink more dramatically than they can grow. Yet, the implications of such skew for inference from IPMs has not been explored, nor have general methods been developed to incorporate skewed size transitions into IPMs, or deal with other aspects of real growth rates, including bounds on possible growth or shrinkage.

   Here, we develop a flexible approach to modelling skewed growth data using a modified beta regression model. We propose that sizes first be converted to a (0,1) interval by estimating size‐dependent minimum and maximum sizes through quantile regression. Transformed data can then be modelled using beta regression with widely available statistical tools. We demonstrate the utility of this approach using demographic data for a long‐lived plant, gorgonians and an epiphytic lichen. Specifically, we compare inferences of population parameters from discrete PPMs to those from IPMs that either assume normality or incorporate skew using beta regression or, alternatively, a skewed normal model.

   The beta and skewed normal distributions accurately capture the mean, variance and skew of real growth distributions. Incorporating skewed growth into IPMs decreases population growth and estimated life span relative to IPMs that assume normally distributed growth, and more closely approximate the parameters of PPMs that do not assume a particular growth distribution. A bounded distribution, such as the beta, also avoids the eviction problem caused by predicting some growth outside the modelled size range.

   Incorporating biologically relevant skew in growth data has important consequences for inference from IPMs. The approaches we outline here are flexible and easy to implement with existing statistical tools.

    

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