Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model

Paga, Pierre; Kühn, Reimer

doi:10.1103/physreve.96.022126

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…In this sense it is natural to consider Model 1 to support a phase transition. Model 1 is unlike the Ising model in that the speed of its large-deviation principle does not change at the transition point, remaining K (in this respect it is more similar to the mean-field version of the Ising model [43]).…”

Section: Discussionmentioning

confidence: 99%

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Large deviations in the presence of cooperativity and slow dynamics

Whitelam

2018

Phys. Rev. E

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We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative or when its basic time scale diverges. In the first case the unbiased trajectory distribution undergoes a symmetry breaking, leading to a change in shape of the large-deviation rate function for a particular dynamical observable. In the second case the symmetry of the unbiased trajectory distribution remains unbroken. Comparison of these models suggests that singularities of the dynamical large-deviation formalism can signal the dynamical equivalent of an equilibrium phase transition but do not necessarily do so.

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Section: Discussionmentioning

confidence: 99%

“…In such cases it is helpful, in order to establish a consistent physical picture, to use a method of ratefunction reconstruction able to cope with non-convex functions [9,15,43,44,46]. In Fig.…”

Section: Discussionmentioning

confidence: 99%

Large deviations in the presence of cooperativity and slow dynamics

Whitelam

2018

Phys. Rev. E

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“…1(b) of Ref. [45]. These trajectory types are controlled by stable fixed points in phase space; for the reversible model we have up to three coexisting stable fixed points.…”

Section: A Reversible Model Of Growthmentioning

confidence: 92%

Rare behavior of growth processes via umbrella sampling of trajectories

et al. 2018

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We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the "s-ensemble" large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium.

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Understanding the stochastic dynamics of sequential decision-making processes: A path-integral analysis of multi-armed bandits

Yeung

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The multi-armed bandit (MAB) model is one of the most classical models to study decision-making in an uncertain environment. In this model, a player chooses one of K possible arms of a bandit machine to play at each time step, where the corresponding arm returns a random reward to the player, potentially from a specific unknown distribution. The target of the player is to collect as many rewards as possible during the process. Despite its simplicity, the MAB model offers an excellent playground for studying the trade-off between exploration vs exploitation and designing effective algorithms for sequential decision-making under uncertainty. Although many asymptotically optimal algorithms have been established, the finite-time behaviors of the stochastic dynamics of the MAB model appear much more challenging to analyze due to the intertwine between the decision-making and the rewards being collected. In this paper, we employ techniques in statistical physics to analyze the MAB model, which facilitates the characterization of the distribution of cumulative regrets at a finite short time, the central quantity of interest in an MAB algorithm, as well as the intricate dynamical behaviors of the model. Our analytical results, in good agreement with simulations, point to the emergence of an interesting multimodal regret distribution, with large regrets resulting from excess exploitation of sub-optimal arms due to an initial unlucky output from the optimal one.

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Large deviations of the finite-time magnetization of the Curie-Weiss random-field Ising model

Cited by 3 publications

References 30 publications

Large deviations in the presence of cooperativity and slow dynamics

Large deviations in the presence of cooperativity and slow dynamics

Rare behavior of growth processes via umbrella sampling of trajectories

Understanding the stochastic dynamics of sequential decision-making processes: A path-integral analysis of multi-armed bandits

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