Doubly-Robust Off-Policy Evaluation with Estimated Logging Policy

We introduce a novel doubly-robust (DR) off-policy evaluation (OPE) estimator for Markov decision processes, DRUnknown, designed for situations where both the logging policy and the value function are unknown. The proposed estimator initially estimates the logging policy and then estimates the value function model by minimizing the asymptotic variance of the estimator while considering the estimating effect of the logging policy. When the logging policy model is correctly specified, DRUnknown achieves the smallest asymptotic variance within the class containing existing OPE estimators. When the value function model is also correctly specified, DRUnknown is optimal as its asymptotic variance reaches the semiparametric lower bound. We present experimental results conducted in contextual bandits and reinforcement learning to compare the performance of DRUnknown with that of existing methods.

Wasserstein Geodesic Generator for Conditional Distributions

Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional distributions. Based on this result, we propose a novel conditional generation algorithm where conditional distributions are fully characterized by a metric space defined by a statistical distance. We employ optimal transport theory to propose the Wasserstein geodesic generator, a new conditional generator that learns the Wasserstein geodesic. The proposed method learns both conditional distributions for observed domains and optimal transport maps between them. The conditional distributions given unobserved intermediate domains are on the Wasserstein geodesic between conditional distributions given two observed domain labels. Experiments on face images with light conditions as domain labels demonstrate the efficacy of the proposed method.

Double Doubly Robust Thompson Sampling for Generalized Linear Contextual Bandits

We propose a novel contextual bandit algorithm for generalized linear rewards with an $\tilde{O}(\sqrt{\kappa^{-1} \phi T})$ regret over $T$ rounds where $\phi$ is the minimum eigenvalue of the covariance of contexts and $\kappa$ is a lower bound of the variance of rewards. In several practical cases where $\phi=O(d)$, our result is the first regret bound for generalized linear model (GLM) bandits with the order $\sqrt{d}$ without relying on the approach of Auer [2002]. We achieve this bound using a novel estimator called double doubly-robust (DDR) estimator, a subclass of doubly-robust (DR) estimator but with a tighter error bound. The approach of Auer [2002] achieves independence by discarding the observed rewards, whereas our algorithm achieves independence considering all contexts using our DDR estimator. We also provide an $O(\kappa^{-1} \phi \log (NT) \log T)$ regret bound for $N$ arms under a probabilistic margin condition. Regret bounds under the margin condition are given by Bastani and Bayati [2020] and Bastani et al. [2021] under the setting that contexts are common to all arms but coefficients are arm-specific. When contexts are different for all arms but coefficients are common, ours is the first regret bound under the margin condition for linear models or GLMs. We conduct empirical studies using synthetic data and real examples, demonstrating the effectiveness of our algorithm.