| Summary: | Irreversible perturbations in Langevin dynamics have been widely recognized for their role in accelerating convergence in simulations of multi-modal distributions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>π</mi><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></semantics></math></inline-formula>. A commonly used and easily computed standard irreversible perturbation is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>∇</mo><mo form="prefix">log</mo><mi>π</mi><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></semantics></math></inline-formula>, where <i>J</i> is a skew-symmetric matrix. However, Langevin dynamics employing a fixed-scale standard irreversible perturbation encounter a trade-off between local exploitation and global exploration, associated with small and large scales of standard irreversible perturbation, respectively. To address this trade-off, we introduce the adaptive irreversible perturbations Langevin dynamics, where the scale of the standard irreversible perturbation changes adaptively. Through numerical examples, we demonstrate that adaptive irreversible perturbations in Langevin dynamics can enhance performance compared to fixed-scale irreversible perturbations.
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