Stochastic regret bounds for online algorithms are usually derived from an ''online to batch'' conversion. Inverting the reasoning, we start our analyze by a ''batch to online'' conversion that applies in any Stochastic Online Convex Optimization problem under stochastic exp-concavity condition. We obtain fast rate stochastic regret bounds with high probability for non-convex loss functions. Based on this approach, we provide prediction and probabilistic forecasting methods for non-stationary unbounded time series.
翻译:在线算法的“ 在线到批量” 误差通常源于“ 在线到 在线” 转换。 反之, 我们用“ 批次到 在线 ” 转换法开始分析, 在任何 Stochactic Online Convex 优化化问题中, 都适用这种转换法 。 我们获得快速速率的误差误差, 且非 convex 损失功能的概率很高 。 基于这个方法, 我们提供非静止无约束时间序列的预测和概率预测方法 。