334 research outputs found
Dynamics in atomic signaling games
We study an atomic signaling game under stochastic evolutionary dynamics.
There is a finite number of players who repeatedly update from a finite number
of available languages/signaling strategies. Players imitate the most fit
agents with high probability or mutate with low probability. We analyze the
long-run distribution of states and show that, for sufficiently small mutation
probability, its support is limited to efficient communication systems. We find
that this behavior is insensitive to the particular choice of evolutionary
dynamic, a property that is due to the game having a potential structure with a
potential function corresponding to average fitness. Consequently, the model
supports conclusions similar to those found in the literature on language
competition. That is, we show that efficient languages eventually predominate
the society while reproducing the empirical phenomenon of linguistic drift. The
emergence of efficiency in the atomic case can be contrasted with results for
non-atomic signaling games that establish the non-negligible possibility of
convergence, under replicator dynamics, to states of unbounded efficiency loss
Evolutionary Game Theory Squared: Evolving Agents in Endogenously Evolving Zero-Sum Games
The predominant paradigm in evolutionary game theory and more generally
online learning in games is based on a clear distinction between a population
of dynamic agents that interact given a fixed, static game. In this paper, we
move away from the artificial divide between dynamic agents and static games,
to introduce and analyze a large class of competitive settings where both the
agents and the games they play evolve strategically over time. We focus on
arguably the most archetypal game-theoretic setting -- zero-sum games (as well
as network generalizations) -- and the most studied evolutionary learning
dynamic -- replicator, the continuous-time analogue of multiplicative weights.
Populations of agents compete against each other in a zero-sum competition that
itself evolves adversarially to the current population mixture. Remarkably,
despite the chaotic coevolution of agents and games, we prove that the system
exhibits a number of regularities. First, the system has conservation laws of
an information-theoretic flavor that couple the behavior of all agents and
games. Secondly, the system is Poincar\'{e} recurrent, with effectively all
possible initializations of agents and games lying on recurrent orbits that
come arbitrarily close to their initial conditions infinitely often. Thirdly,
the time-average agent behavior and utility converge to the Nash equilibrium
values of the time-average game. Finally, we provide a polynomial time
algorithm to efficiently predict this time-average behavior for any such
coevolving network game.Comment: To appear in AAAI 202
Neural-network solutions to stochastic reaction networks
The stochastic reaction network is widely used to model stochastic processes
in physics, chemistry and biology. However, the size of the state space
increases exponentially with the number of species, making it challenging to
investigate the time evolution of the chemical master equation for the reaction
network. Here, we propose a machine-learning approach using the variational
autoregressive network to solve the chemical master equation. The approach is
based on the reinforcement learning framework and does not require any data
simulated in prior by another method. Different from simulating single
trajectories, the proposed approach tracks the time evolution of the joint
probability distribution in the state space of species counts, and supports
direct sampling on configurations and computing their normalized joint
probabilities. We apply the approach to various systems in physics and biology,
and demonstrate that it accurately generates the probability distribution over
time in the genetic toggle switch, the early life self-replicator, the epidemic
model and the intracellular signaling cascade. The variational autoregressive
network exhibits a plasticity in representing the multi-modal distribution by
feedback regulations, cooperates with the conservation law, enables
time-dependent reaction rates, and is efficient for high-dimensional reaction
networks with allowing a flexible upper count limit. The results suggest a
general approach to investigate stochastic reaction networks based on modern
machine learning
Discovering How Agents Learn Using Few Data
Decentralized learning algorithms are an essential tool for designing
multi-agent systems, as they enable agents to autonomously learn from their
experience and past interactions. In this work, we propose a theoretical and
algorithmic framework for real-time identification of the learning dynamics
that govern agent behavior using a short burst of a single system trajectory.
Our method identifies agent dynamics through polynomial regression, where we
compensate for limited data by incorporating side-information constraints that
capture fundamental assumptions or expectations about agent behavior. These
constraints are enforced computationally using sum-of-squares optimization,
leading to a hierarchy of increasingly better approximations of the true agent
dynamics. Extensive experiments demonstrated that our approach, using only 5
samples from a short run of a single trajectory, accurately recovers the true
dynamics across various benchmarks, including equilibrium selection and
prediction of chaotic systems up to 10 Lyapunov times. These findings suggest
that our approach has significant potential to support effective policy and
decision-making in strategic multi-agent systems
Learning
Learning and evolution are adaptive or “backward-looking” models of social and biological systems. Learning changes the probability distribution of traits within an individual through direct and vicarious reinforcement, while evolution changes the probability distribution of traits within a population through reproduction and selection. Compared to forward-looking models of rational calculation that identify equilibrium outcomes, adaptive models pose fewer cognitive requirements and reveal both equilibrium and out-of-equilibrium dynamics. However, they are also less general than analytical models and require relatively stable environments. In this chapter, we review the conceptual and practical foundations of several approaches to models of learning that offer powerful tools for modeling social processes. These include the Bush-Mosteller stochastic learning model, the Roth-Erev matching model, feed-forward and attractor neural networks, and belief learning. Evolutionary approaches include replicator dynamics and genetic algorithms. A unifying theme is showing how complex patterns can arise from relatively simple adaptive rules.</p
Selectionist and Evolutionary Approaches to Brain Function: A Critical Appraisal
We consider approaches to brain dynamics and function that have been claimed to be Darwinian. These include Edelman’s theory of neuronal group selection, Changeux’s theory of synaptic selection and selective stabilization of pre-representations, Seung’s Darwinian synapse, Loewenstein’s synaptic melioration, Adam’s selfish synapse, and Calvin’s replicating activity patterns. Except for the last two, the proposed mechanisms are selectionist but not truly Darwinian, because no replicators with information transfer to copies and hereditary variation can be identified in them. All of them fit, however, a generalized selectionist framework conforming to the picture of Price’s covariance formulation, which deliberately was not specific even to selection in biology, and therefore does not imply an algorithmic picture of biological evolution. Bayesian models and reinforcement learning are formally in agreement with selection dynamics. A classification of search algorithms is shown to include Darwinian replicators (evolutionary units with multiplication, heredity, and variability) as the most powerful mechanism for search in a sparsely occupied search space. Examples are given of cases where parallel competitive search with information transfer among the units is more efficient than search without information transfer between units. Finally, we review our recent attempts to construct and analyze simple models of true Darwinian evolutionary units in the brain in terms of connectivity and activity copying of neuronal groups. Although none of the proposed neuronal replicators include miraculous mechanisms, their identification remains a challenge but also a great promise
ON THE CONVERGENCE OF GRADIENT-LIKE FLOWS WITH NOISY GRADIENT INPUT
In view of solving convex optimization problems with noisy gradient input, we
analyze the asymptotic behavior of gradient-like flows under stochastic
disturbances. Specifically, we focus on the widely studied class of mirror
descent schemes for convex programs with compact feasible regions, and we
examine the dynamics' convergence and concentration properties in the presence
of noise. In the vanishing noise limit, we show that the dynamics converge to
the solution set of the underlying problem (a.s.). Otherwise, when the noise is
persistent, we show that the dynamics are concentrated around interior
solutions in the long run, and they converge to boundary solutions that are
sufficiently "sharp". Finally, we show that a suitably rectified variant of the
method converges irrespective of the magnitude of the noise (or the structure
of the underlying convex program), and we derive an explicit estimate for its
rate of convergence.Comment: 36 pages, 5 figures; revised proof structure, added numerical case
study in Section
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