Doubly Robust Policy Evaluation and Optimization (1503.02834v1)

Abstract: We study sequential decision making in environments where rewards are only partially observed, but can be modeled as a function of observed contexts and the chosen action by the decision maker. This setting, known as contextual bandits, encompasses a wide variety of applications such as health care, content recommendation and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strengths and overcome the weaknesses of the two approaches by applying the doubly robust estimation technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust estimation uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice in policy evaluation and optimization.

• The paper introduces a doubly robust estimator that remains unbiased if either the reward or action probability model is accurate.
• It combines model-based predictions with inverse propensity scoring to effectively reduce variance in contextual bandit settings.
• Empirical and theoretical analyses confirm the method’s efficacy, paving the way for improved policy evaluation in online applications.

An Analysis of Doubly Robust Policy Evaluation and Optimization

Introduction

The paper "Doubly Robust Policy Evaluation and Optimization" by Miroslav Dudík, Dumitru Erhan, John Langford, and Lihong Li explores advanced statistical methods for sequential decision-making in environments known as contextual bandits. The contextual bandit framework applies to various real-world applications, such as healthcare, personalized content recommendation, and online advertising. Within these settings, the primary task is to evaluate a new policy based on historical data that includes contexts, actions, and rewards. A significant challenge in this domain is that the historical data does not typically reflect the action distributions that a new policy may prescribe.

Contextual Bandits and Policy Evaluation

In contextual bandits, decision-makers select actions based on observed contextual information to maximize total rewards. However, only rewards for chosen actions are observed, introducing challenges in evaluating new policies since not all possible action outcomes are known. Traditional methods for evaluating such policies generally fall into two categories: model-based methods, which estimate reward functions, and model-free methods, which use inverse propensity scoring (IPS) for weighting historical data. Model-based approaches can suffer from bias, while model-free approaches can result in high variance.

The Doubly Robust Approach

The doubly robust (DR) method proposed leverages both model-based and model-free approaches to mitigate their respective weaknesses. A DR estimator remains unbiased if either the reward model or the action probability model is accurate—hence the "doubly robust" characterization. The DR approach applies effective risk estimation techniques that integrate predictions from a reward model with IPS-weighted observations, reducing variance without significantly introducing bias.

Theoretical and Empirical Results

The authors present rigorous theoretical analyses demonstrating that DR estimation yields lower estimation variance and more precise policy evaluation when compared to traditional methods. The paper explores statistical properties, providing bounds on the bias and variance of policy value estimates under this model. In empirical evaluations, DR shows robust improvements across various tasks, including simulated online advertising scenarios and real-world data from web search user interactions.

Practical and Theoretical Implications

From a practical standpoint, the DR framework is positioned to become a standard in policy evaluation for contextual bandit problems, offering a more reliable assessment of policies when historical data is limited or non-representative. Theoretically, this work advances the understanding of statistical efficiency in policy evaluation, particularly under partial observability, and offers insights into extending doubly robust techniques to more complex reinforcement learning scenarios.

Future Directions

The paper opens avenues for future research in improving efficiency and applicability of DR estimators. Areas of interest include exploring adaptive DR estimators that further minimize variance and developing new algorithms that can leverage DR estimation in large-scale online settings. There is also potential to expand these techniques into broader classes of decision-making problems, including those involving non-stationary environments and adaptive policies.

In summary, this paper sets a comprehensive foundation for doubly robust approaches in policy evaluation, providing both deep theoretical insights and substantial empirical validations. The convergence of model-based and model-free strategies under the DR framework marks an important progression towards more robust and generalizable methods in the field of machine learning with contextual bandits.