Consensus-based optimization matches or beats natural evolution strategies as a closed-box adversarial attack method in easier attack scenarios, and consensus hopping is shown to be a gradient-descent-like limit of CBO.
Mathematical Analysis of the PDE Model for the Consensus-based Optimization
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a diffusion term that is both singular and degenerate. By employing a regularization procedure in combination with a compactness argument, we establish the global existence and uniqueness of weak solutions in $L^\infty(0,T;L^1\cap L^\infty(\mathbb{R}^d))$. Furthermore, we show that the weak solutions exhibit improved $H^2$-regularity when the initial data is regular.
fields
math.OC 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Consensus-based optimization matches or beats natural evolution strategies as a closed-box adversarial attack method in easier attack scenarios, and consensus hopping is shown to be a gradient-descent-like limit of CBO.