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Improved Langevin Monte Carlo for stochastic optimization via landscape modification
Given a target function $H$ to minimize or a target Gibbs distribution $\pi_{\beta}^0 \propto e^{-\beta H}$ to sample from in the low temperature, in this paper we propose and analyze Langevin Monte Carlo (LMC) algorithms that run on an alternative landscape as specified by $H^f_{\beta, c, 1}$ and target a modified Gibbs distribution $\pi^f_{\beta, c, 1} \propto e^{-\beta H^f_{\beta, c, 1}}$, where the landscape of $H^f_{\beta, c, 1}$ is a transformed version of that of $H$ which depends on the parameters $f,\beta$ and $c$.
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