Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution
Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution
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DOI：
10.1609/aaai.v34i06.6572
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发表时间：
2019-11
期刊：
影响因子：
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通讯作者：
Artyom Gadetsky;Kirill Struminsky;Christopher Robinson;Novi Quadrianto;D. Vetrov
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文献类型：
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作者：
Artyom Gadetsky;Kirill Struminsky;Christopher Robinson;Novi Quadrianto;D. Vetrov
由于梯度估计的高方差，使用随机梯度下降来学习具有离散潜变量的模型仍然是一个挑战。现代方差缩减技术主要考虑分类分布，当可能结果的数量变得很大时，其适用性有限。在这项工作中，我们考虑模型与潜在的排列，并提出控制变量的Plackett-Luce分布。特别是，控制变量允许我们使用随机梯度下降优化排列上的黑盒函数。为了说明这种方法，我们考虑了连续和离散数据的各种因果结构学习任务。我们表明，我们的方法优于竞争松弛为基础的优化方法，也适用于不可微的得分函数。
Learning models with discrete latent variables using stochastic gradient descent remains a challenge due to the high variance of gradient estimates. Modern variance reduction techniques mostly consider categorical distributions and have limited applicability when the number of possible outcomes becomes large. In this work, we consider models with latent permutations and propose control variates for the Plackett-Luce distribution. In particular, the control variates allow us to optimize black-box functions over permutations using stochastic gradient descent. To illustrate the approach, we consider a variety of causal structure learning tasks for continuous and discrete data. We show that our method outperforms competitive relaxation-based optimization methods and is also applicable to non-differentiable score functions.