Off-policy evaluation (OPE) is the problem of estimating the value of a target policy using historical data collected under a different logging policy. OPE methods typically assume overlap between the target and logging policy, enabling solutions based on importance weighting and/or imputation. In this work, we approach OPE without assuming either overlap or a well-specified model by considering a strategy based on partial identification under non-parametric assumptions on the conditional mean function, focusing especially on Lipschitz smoothness. Under such smoothness assumptions, we formulate a pair of linear programs whose optimal values upper and lower bound the contributions of the no-overlap region to the off-policy value. We show that these linear programs have a concise closed form solution that can be computed efficiently and that their solutions converge, under the Lipschitz assumption, to the sharp partial identification bounds on the off-policy value. Furthermore, we show that the rate of convergence is minimax optimal, up to log factors. We deploy our methods on two semi-synthetic examples, and obtain informative and valid bounds that are tighter than those possible without smoothness assumptions.

翻译：离策略评估（OPE）是利用在另一记录策略下收集的历史数据估计目标策略价值的问题。OPE方法通常假设目标策略与记录策略间存在重叠，从而支持基于重要性加权和/或插补的解决方案。本研究在不假设重叠或良好指定模型的前提下，通过考虑基于条件均值函数非参数假设（特别关注Lipschitz平滑性）的部分识别策略来探讨OPE问题。基于此类平滑性假设，我们构造了一对线性规划，其最优值分别构成离策略价值中未重叠区域贡献的上下界。我们证明这类线性规划具有可高效计算的简洁闭式解，且在Lipschitz假设下其解收敛于离策略价值的锐化部分识别界。进一步地，我们证明该收敛速度（忽略对数因子）达到极小极大最优性。通过在两个半合成示例中部署方法，我们获得了比无平滑性假设时更紧致的信息性有效边界。