Analysis of an Adaptive Biasing Force method based on self-interacting dynamics

Benaı̈m, Michel; Bréhier, Charles-Édouard; Monmarché, Pierre

doi:10.1214/20-ejp490

Cited by 4 publications

(5 citation statements)

References 23 publications

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“…Moreover, a result similar to Theorem 2 has been established in [6] for a closely related self-interacting process, the adaptive biasing potential algorithm. In addition, in the recent work [8], a similar result is established for the ABF algorithm but when the occupation measure is not unbiased (see the discussion in Section 5.3).…”

supporting

confidence: 55%

“…This is clear in the mean-field limit of the algorithm, where no regularization is needed so that Ã * = A (see [35]). It is more difficult to establish for the self-interacting ABF process, but in parallel of the present paper it has been done in [8]. We tried numerically both cases, and the results were similar.…”

Section: Real Implementationmentioning

confidence: 82%

“…In general cases of self-interacting processes, as those studied in [9], the asymptotic deterministic flow may be more complicated (see in particular [8] for the ABF algorithm with the non-reweighted occupation measure). Here, as mentioned above, we are in a very simple case since for all t 0, µ is the invariant measure of the time-homogenous Markov process with generator L t , so that the flow is simply a relaxation toward this equilibrium.…”

Section: Time Change and The Ode Methodsmentioning

confidence: 99%

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Adaptive force biasing algorithms: New convergence results and tensor approximations of the bias

Ehrlacher

Lelièvre

Monmarché³

2022

Ann. Appl. Probab.

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We analyze and propose variants of the Adaptive Biasing Force method. First, we prove the convergence of a version of the algorithm where the biasing force is estimated using a weighted occupation measure, with an explicit asymptotic variance. Second, we propose a new flavour of the algorithm adapted to high dimensional reaction coordinates, for which the standard approaches suffer from the curse of dimensionality. More precisely, the free energy is approximated by a sum of tensor products of one-dimensional functions. The consistency of the tensor approximation is established. Numerical experiments on 5dimensional reaction coordinates demonstrate that the method is indeed able to capture correlations between them.

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supporting

confidence: 55%

Section: Real Implementationmentioning

confidence: 82%

Section: Time Change and The Ode Methodsmentioning

confidence: 99%

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Adaptive force biasing algorithms: New convergence results and tensor approximations of the bias

Ehrlacher

Lelièvre

Monmarché³

2022

Ann. Appl. Probab.

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“…We call the resulting non-Markovian diffusion IAKSA. Although the setting is slightly different, this idea is in reminiscence of the adaptive biasing method Benaïm and Bréhier (2019); Benaïm et al (2020); Lelièvre and Minoukadeh (2011); Lelièvre et al (2008) or the self-interacting annealing method Raimond (2009), thus avoiding the need to manually tune the parameter c for better performance. We also mention the related work of memory gradient diffusions Gadat and Panloup (2014); Gadat et al (2013).…”

Section: Introductionmentioning

confidence: 99%

On the convergence of an improved and adaptive kinetic simulated annealing

Choi¹

2020

Preprint

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Inspired by the work of Fang et al. (1997), who propose an improved simulated annealing algorithm based on a variant of overdamped Langevin diffusion with state-dependent diffusion coefficient, we cast this idea in the kinetic setting and develop an improved kinetic simulated annealing (IKSA) method for minimizing a target function U . To analyze its convergence, we utilize the framework recently introduced by Monmarché (2018) for the case of kinetic simulated annealing (KSA). The core idea of IKSA rests on introducing a parameter c > inf U , which de facto modifies the optimization landscape and clips the critical height in IKSA at a maximum of c − inf U . Consequently IKSA enjoys improved convergence with faster logarithmic cooling than KSA. To tune the parameter c, we propose an adaptive method that we call IAKSA which utilizes the running minimum generated by the algorithm on the fly, thus avoiding the need to manually adjust c for better performance. We present positive numerical results on some standard global optimization benchmark functions that verify the improved convergence of IAKSA over other Langevin-based annealing methods.

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“…Variants may involve multiple interacting replicas of the simulation, fictitious proxy coordinates, approximate gradient estimators, and additional biasing forces or potentials. ABF methods can be shown to converge quickly to equilibrium for well chosen reaction coordinates, see for example the following mathematical analysis for rigorous formulations [184,185].…”

Section: Adaptive Biasing Forcementioning

confidence: 99%