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Register a new userDoubly Robust Bias Reduction in Infinite Horizon Off-Policy Estimation
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Yihao Feng
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Infinite horizon off-policy policy evaluation is a highly challenging task due to the excessively large variance of typical importance sampling (IS) estimators. Recently, Liu et al. (2018a) proposed an approach that significantly reduces the variance of infinite-horizon off-policy evaluation by estimating the stationary density ratio, but at the cost of introducing potentially high biases due to the error in density ratio estimation. In this paper, we develop a bias-reduced augmentation of their method, which can take advantage of a learned value function to obtain higher accuracy. Our method is doubly robust in that the bias vanishes when either the density ratio or the value function estimation is perfect. In general, when either of them is accurate, the bias can also be reduced. Both theoretical and empirical results show that our method yields significant advantages over previous methods.
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We consider the off-policy estimation problem of estimating the expected reward of a target policy using samples collected by a different behavior policy. Importance sampling (IS) has been a key technique to derive (nearly) unbiased estimators, but is known to suffer from an excessively high variance in long-horizon problems. In the extreme case of in infinite-horizon problems, the variance of an IS-based estimator may even be unbounded. In this paper, we propose a new off-policy estimation method that applies IS directly on the stationary state-visitation distributions to avoid the exploding variance issue faced by existing estimators.Our key contribution is a novel approach to estimating the density ratio of two stationary distributions, with trajectories sampled from only the behavior distribution. We develop a mini-max loss function for the estimation problem, and derive a closed-form solution for the case of RKHS. We support our method with both theoretical and empirical analyses.
We study the problem of off-policy evaluation (OPE) in reinforcement learning (RL), where the goal is to estimate the performance of a policy from the data generated by another policy(ies). In particular, we focus on the doubly robust (DR) estimators that consist of an importance sampling (IS) component and a performance model, and utilize the low (or zero) bias of IS and low variance of the model at the same time. Although the accuracy of the model has a huge impact on the overall performance of DR, most of the work on using the DR estimators in OPE has been focused on improving the IS part, and not much on how to learn the model. In this paper, we propose alternative DR estimators, called more robust doubly robust (MRDR), that learn the model parameter by minimizing the variance of the DR estimator. We first present a formulation for learning the DR model in RL. We then derive formulas for the variance of the DR estimator in both contextual bandits and RL, such that their gradients w.r.t.~the model parameters can be estimated from the samples, and propose methods to efficiently minimize the variance. We prove that the MRDR estimators are strongly consistent and asymptotically optimal. Finally, we evaluate MRDR in bandits and RL benchmark problems, and compare its performance with the existing methods.
This paper investigates the problem of online prediction learning, where learning proceeds continuously as the agent interacts with an environment. The predictions made by the agent are contingent on a particular way of behaving, represented as a value function. However, the behavior used to select actions and generate the behavior data might be different from the one used to define the predictions, and thus the samples are generated off-policy. The ability to learn behavior-contingent predictions online and off-policy has long been advocated as a key capability of predictive-knowledge learning systems but remained an open algorithmic challenge for decades. The issue lies with the temporal difference (TD) learning update at the heart of most prediction algorithms: combining bootstrapping, off-policy sampling and function approximation may cause the value estimate to diverge. A breakthrough came with the development of a new objective function that admitted stochastic gradient descent variants of TD. Since then, many sound online off-policy prediction algorithms have been developed, but there has been limited empirical work investigating the relative merits of all the variants. This paper aims to fill these empirical gaps and provide clarity on the key ideas behind each method. We summarize the large body of literature on off-policy learning, focusing on 1- methods that use computation linear in the number of features and are convergent under off-policy sampling, and 2- other methods which have proven useful with non-fixed, nonlinear function approximation. We provide an empirical study of off-policy prediction methods in two challenging microworlds. We report each methods parameter sensitivity, empirical convergence rate, and final performance, providing new insights that should enable practitioners to successfully extend these new methods to large-scale applications.[Abridged abstract]
We study the problem of off-policy policy evaluation (OPPE) in RL. In contrast to prior work, we consider how to estimate both the individual policy value and average policy value accurately. We draw inspiration from recent work in causal reasoning, and propose a new finite sample generalization error bound for value estimates from MDP models. Using this upper bound as an objective, we develop a learning algorithm of an MDP model with a balanced representation, and show that our approach can yield substantially lower MSE in common synthetic benchmarks and a HIV treatment simulation domain.
Off-policy learning is a framework for evaluating and optimizing policies without deploying them, from data collected by another policy. Real-world environments are typically non-stationary and the offline learned policies should adapt to these changes. To address this challenge, we study the novel problem of off-policy optimization in piecewise-stationary contextual bandits. Our proposed solution has two phases. In the offline learning phase, we partition logged data into categorical latent states and learn a near-optimal sub-policy for each state. In the online deployment phase, we adaptively switch between the learned sub-policies based on their performance. This approach is practical and analyzable, and we provide guarantees on both the quality of off-policy optimization and the regret during online deployment. To show the effectiveness of our approach, we compare it to state-of-the-art baselines on both synthetic and real-world datasets. Our approach outperforms methods that act only on observed context.
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