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- W2911335089 abstract "Given a target function $U$ to minimize on a finite state space $mathcal{X}$, a proposal chain with generator $Q$ and a cooling schedule $T(t)$ that depends on time $t$, in this paper we study two types of simulated annealing (SA) algorithms with generators $M_{1,t}(Q,U,T(t))$ and $M_{2,t}(Q,U,T(t))$ respectively. While $M_{1,t}$ is the classical SA algorithm, we introduce a simple and greedy variant that we call $M_{2,t}$ which provably converges faster. Under any $T(t)$ that converges to $0$ and mild conditions on $Q$, the Markov chain generated by $M_{2,t}$ is weakly ergodic. When $T(t) > c_{M_2}/log(t+1)$ follows the logarithmic cooling schedule, our proposed algorithm is strongly ergodic both in total variation and in relative entropy, and converges to the set of global minima, where $c_{M_2}$ is a constant that we explicitly identify. If $c_{M_1}$ is the optimal hill-climbing constant that appears in logarithmic cooling of $M_{1,t}$, we show that $c_{M_1} geq c_{M_2}$ and give simple conditions under which $c_{M_1} > c_{M_2}$. Our proposed $M_{2,t}$ thus converges under a faster logarithmic cooling in this regime. The other situation that we investigate corresponds to $c_{M_1} > c_{M_2} = 0$, where we give a class of fast and non-logarithmic cooling schedule that works for $M_{2,t}$ (but not for $M_{1,t}$). To the best of our knowledge this is the first instance where strong ergodicity and convergence in relative entropy are proved for faster than logarithmic cooling. Finally, we give an algorithm to simulate $M_{2,t}$ by uniformization of Markov chains." @default.
- W2911335089 created "2019-02-21" @default.
- W2911335089 creator A5058187515 @default.
- W2911335089 date "2019-01-29" @default.
- W2911335089 modified "2023-10-16" @default.
- W2911335089 title "An accelerated variant of simulated annealing that converges under fast cooling" @default.
- W2911335089 hasPublicationYear "2019" @default.
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