Liyuan Xu

Yutian Chen, Liyuan Xu, Caglar Gulcehre et al.

We show that the popular reinforcement learning (RL) strategy of estimating the state-action value (Q-function) by minimizing the mean squared Bellman error leads to a regression problem with confounding, the inputs and output noise being correlated. Hence, direct minimization of the Bellman error can result in significantly biased Q-function estimates. We explain why fixing the target Q-network in Deep Q-Networks and Fitted Q Evaluation provides a way of overcoming this confounding, thus shedding new light on this popular but not well understood trick in the deep RL literature. An alternative approach to address confounding is to leverage techniques developed in the causality literature, notably instrumental variables (IV). We bring together here the literature on IV and RL by investigating whether IV approaches can lead to improved Q-function estimates. This paper analyzes and compares a wide range of recent IV methods in the context of offline policy evaluation (OPE), where the goal is to estimate the value of a policy using logged data only. By applying different IV techniques to OPE, we are not only able to recover previously proposed OPE methods such as model-based techniques but also to obtain competitive new techniques. We find empirically that state-of-the-art OPE methods are closely matched in performance by some IV methods such as AGMM, which were not developed for OPE. We open-source all our code and datasets at https://github.com/liyuan9988/IVOPEwithACME.

Liyuan Xu, Heishiro Kanagawa, Arthur Gretton

Proxy causal learning (PCL) is a method for estimating the causal effect of treatments on outcomes in the presence of unobserved confounding, using proxies (structured side information) for the confounder. This is achieved via two-stage regression: in the first stage, we model relations among the treatment and proxies; in the second stage, we use this model to learn the effect of treatment on the outcome, given the context provided by the proxies. PCL guarantees recovery of the true causal effect, subject to identifiability conditions. We propose a novel method for PCL, the deep feature proxy variable method (DFPV), to address the case where the proxies, treatments, and outcomes are high-dimensional and have nonlinear complex relationships, as represented by deep neural network features. We show that DFPV outperforms recent state-of-the-art PCL methods on challenging synthetic benchmarks, including settings involving high dimensional image data. Furthermore, we show that PCL can be applied to off-policy evaluation for the confounded bandit problem, in which DFPV also exhibits competitive performance.

Liyuan Xu, Yutian Chen, Siddarth Srinivasan et al.

Instrumental variable (IV) regression is a standard strategy for learning causal relationships between confounded treatment and outcome variables from observational data by utilizing an instrumental variable, which affects the outcome only through the treatment. In classical IV regression, learning proceeds in two stages: stage 1 performs linear regression from the instrument to the treatment; and stage 2 performs linear regression from the treatment to the outcome, conditioned on the instrument. We propose a novel method, deep feature instrumental variable regression (DFIV), to address the case where relations between instruments, treatments, and outcomes may be nonlinear. In this case, deep neural nets are trained to define informative nonlinear features on the instruments and treatments. We propose an alternating training regime for these features to ensure good end-to-end performance when composing stages 1 and 2, thus obtaining highly flexible feature maps in a computationally efficient manner. DFIV outperforms recent state-of-the-art methods on challenging IV benchmarks, including settings involving high dimensional image data. DFIV also exhibits competitive performance in off-policy policy evaluation for reinforcement learning, which can be understood as an IV regression task.

Liyuan Xu, Junya Honda, Gang Niu et al.

Uncoupled regression is the problem to learn a model from unlabeled data and the set of target values while the correspondence between them is unknown. Such a situation arises in predicting anonymized targets that involve sensitive information, e.g., one's annual income. Since existing methods for uncoupled regression often require strong assumptions on the true target function, and thus, their range of applications is limited, we introduce a novel framework that does not require such assumptions in this paper. Our key idea is to utilize pairwise comparison data, which consists of pairs of unlabeled data that we know which one has a larger target value. Such pairwise comparison data is easy to collect, as typically discussed in the learning-to-rank scenario, and does not break the anonymity of data. We propose two practical methods for uncoupled regression from pairwise comparison data and show that the learned regression model converges to the optimal model with the optimal parametric convergence rate when the target variable distributes uniformly. Moreover, we empirically show that for linear models the proposed methods are comparable to ordinary supervised regression with labeled data.

Yuko Kuroki, Liyuan Xu, Atsushi Miyauchi et al.

We study the problem of stochastic combinatorial pure exploration (CPE), where an agent sequentially pulls a set of single arms (a.k.a. a super arm) and tries to find the best super arm. Among a variety of problem settings of the CPE, we focus on the full-bandit setting, where we cannot observe the reward of each single arm, but only the sum of the rewards. Although we can regard the CPE with full-bandit feedback as a special case of pure exploration in linear bandits, an approach based on linear bandits is not computationally feasible since the number of super arms may be exponential. In this paper, we first propose a polynomial-time bandit algorithm for the CPE under general combinatorial constraints and provide an upper bound of the sample complexity. Second, we design an approximation algorithm for the 0-1 quadratic maximization problem, which arises in many bandit algorithms with confidence ellipsoids. Based on our approximation algorithm, we propose novel bandit algorithms for the top-k selection problem, and prove that our algorithms run in polynomial time. Finally, we conduct experiments on synthetic and real-world datasets, and confirm the validity of our theoretical analysis in terms of both the computation time and the sample complexity.

Masahiro Kato, Liyuan Xu, Gang Niu et al.

We consider a problem of learning a binary classifier only from positive data and unlabeled data (PU learning) and estimating the class-prior in unlabeled data under the case-control scenario. Most of the recent methods of PU learning require an estimate of the class-prior probability in unlabeled data, and it is estimated in advance with another method. However, such a two-step approach which first estimates the class prior and then trains a classifier may not be the optimal approach since the estimation error of the class-prior is not taken into account when a classifier is trained. In this paper, we propose a novel unified approach to estimating the class-prior and training a classifier alternately. Our proposed method is simple to implement and computationally efficient. Through experiments, we demonstrate the practical usefulness of the proposed method.

Liyuan Xu, Junya Honda, Masashi Sugiyama

We formulate and study a novel multi-armed bandit problem called the qualitative dueling bandit (QDB) problem, where an agent observes not numeric but qualitative feedback by pulling each arm. We employ the same regret as the dueling bandit (DB) problem where the duel is carried out by comparing the qualitative feedback. Although we can naively use classic DB algorithms for solving the QDB problem, this reduction significantly worsens the performance---actually, in the QDB problem, the probability that one arm wins the duel over another arm can be directly estimated without carrying out actual duels. In this paper, we propose such direct algorithms for the QDB problem. Our theoretical analysis shows that the proposed algorithms significantly outperform DB algorithms by incorporating the qualitative feedback, and experimental results also demonstrate vast improvement over the existing DB algorithms.

Liyuan Xu, Junya Honda, Masashi Sugiyama

We propose the first fully-adaptive algorithm for pure exploration in linear bandits---the task to find the arm with the largest expected reward, which depends on an unknown parameter linearly. While existing methods partially or entirely fix sequences of arm selections before observing rewards, our method adaptively changes the arm selection strategy based on past observations at each round. We show our sample complexity matches the achievable lower bound up to a constant factor in an extreme case. Furthermore, we evaluate the performance of the methods by simulations based on both synthetic setting and real-world data, in which our method shows vast improvement over existing methods.