论文标题
非反应性边界，用于随机优化，偏见
Non-asymptotic bounds for stochastic optimization with biased noisy gradient oracles
论文作者
论文摘要
我们介绍了有偏见的梯度甲骨文，以捕获函数测量值具有估计误差的设置，该设置可以通过批处理大小参数来控制。我们提出的甲壳在几种实际情况下吸引人，例如，从一批独立和相同分布的（I.I.D.）样本或模拟优化的风险度量估计中，由于计算限制而“偏置”函数测量。无论哪种情况，增加批处理大小都会减少估计误差。我们强调了偏见的梯度甲壳在风险敏感的增强学习设置中的适用性。在随机非凸优化环境中，我们分析了具有偏置梯度甲骨文的随机随机梯度（RSG）算法的变体。我们通过在其性能上得出非反应界限来量化该算法的收敛速率。接下来，在随机凸优化设置中，我们为带有偏置梯度甲骨文的随机梯度下降（SGD）算法的最后一个迭代得出了非反应界限。
We introduce biased gradient oracles to capture a setting where the function measurements have an estimation error that can be controlled through a batch size parameter. Our proposed oracles are appealing in several practical contexts, for instance, risk measure estimation from a batch of independent and identically distributed (i.i.d.) samples, or simulation optimization, where the function measurements are `biased' due to computational constraints. In either case, increasing the batch size reduces the estimation error. We highlight the applicability of our biased gradient oracles in a risk-sensitive reinforcement learning setting. In the stochastic non-convex optimization context, we analyze a variant of the randomized stochastic gradient (RSG) algorithm with a biased gradient oracle. We quantify the convergence rate of this algorithm by deriving non-asymptotic bounds on its performance. Next, in the stochastic convex optimization setting, we derive non-asymptotic bounds for the last iterate of a stochastic gradient descent (SGD) algorithm with a biased gradient oracle.
