arXiv 2009.061882020-09math.OC

离散随机最优化的模拟退火样本有效化

Making Simulated Annealing Sample Efficient for Discrete Stochastic Optimization

Suhail M. Shah

摘要：

研究了基于模拟退火算法求解离散随机最优化问题的不足。主要的理论结论是，遗憾的模拟退火算法，无论是噪音或无噪音的意见，主要取决于相关的吉布斯措施的收敛速度的最佳状态。与以前的作品相比，我们表明，SA不需要增加估计工作（数量\textit{pulls/samples}的选择\textit{arm/solution}每轮有限的地平线$n$）与噪声观测收敛的概率。通过简单的修改，我们可以使每次迭代收敛所需样本个数（按概率）按$\mathcal{O}\big(n)$缩放。此外，我们表明，模拟退火启发式可以解决随机多武装匪徒（MAB）的问题，这意味着它遭受了$\mathcal{O}(\log \,n)$遗憾。因此，我们的论点是，SA应该被认为是一个可行的候选人，列入家庭的有效探索算法的强盗和离散随机最优化问题。

英文摘要：

We study the regret of simulated annealing (SA) based approaches to solving discrete stochastic optimization problems. The main theoretical conclusion is that the regret of the simulated annealing algorithm, with either noisy or noiseless observations, depends primarily upon the rate of the convergence of the associated Gibbs measure to the optimal states. In contrast to previous works, we show that SA does not need an increased estimation effort (number of \textit{pulls/samples} of the selected \textit{arm/solution} per round for a finite horizon $n$) with noisy observations to converge in probability. By simple modifications, we can make the total number of samples per iteration required for convergence (in probability) to scale as $\mathcal{O}\big(n)$. Additionally, we show that a simulated annealing inspired heuristic can solve the problem of stochastic multi-armed bandits (MAB), by which we mean that it suffers a $\mathcal{O}(\log \,n)$ regret. Thus, our contention is that SA should be considered as a viable candidate for inclusion into the family of efficient exploration heuristics for bandit and discrete stochastic optimization problems.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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