GenDICE: Generalized Offline Estimation of Stationary Values (2002.09072v1)

Abstract: An important problem that arises in reinforcement learning and Monte Carlo methods is estimating quantities defined by the stationary distribution of a Markov chain. In many real-world applications, access to the underlying transition operator is limited to a fixed set of data that has already been collected, without additional interaction with the environment being available. We show that consistent estimation remains possible in this challenging scenario, and that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions, derived from fundamental properties of the stationary distribution, and exploiting constraint reformulations based on variational divergence minimization. The resulting algorithm, GenDICE, is straightforward and effective. We prove its consistency under general conditions, provide an error analysis, and demonstrate strong empirical performance on benchmark problems, including off-line PageRank and off-policy policy evaluation.

• The paper introduces GenDICE, which employs variational divergence minimization to robustly estimate stationary values from offline data.
• It leverages neural network-based function approximations for correction ratios and dual variables to ensure convergence and computational tractability.
• Empirical and theoretical analyses demonstrate GenDICE’s superior efficiency and accuracy in offline policy evaluation compared to traditional methods.

Generalized Offline Estimation of Stationary Values: An Overview of GenDICE

The paper "GenDICE: Generalized Offline Estimation of Stationary Values" addresses a critical challenge in reinforcement learning (RL) and Monte Carlo methods: the estimation of stationary distribution quantities when only limited, pre-collected data is available. This problem is particularly relevant in offline settings where direct interaction with the environment is not feasible, necessitating robust estimation techniques that can utilize fixed datasets effectively.

Core Motivations and Problem Setting

Estimating quantities defined by the stationary distribution of a Markov chain underpins various applications such as the PageRank algorithm, approximate Bayesian inference using Markov chain Monte Carlo (MCMC) methods, and policy evaluation in RL. Traditional algorithms for these tasks often rely on the assumption of online access to transition operators or well-defined transition probabilities, a condition seldom met in practical scenarios where data is sourced offline.

Offline estimation challenges arise prominently in tasks like off-policy policy evaluation (OPE) and offline PageRank. These involve estimating the stationary values without direct environmental interaction, requiring approaches that can correct for the shifts between empirical and stationary distributions from pre-obtained data. The paper proposes GenDICE, an advanced algorithmic framework to address these offline estimation problems by calculating a stationary distribution correction ratio.

Methodology: Stationary Distribution Correction via GenDICE

GenDICE innovatively constructs a stationary distribution estimator by leveraging a dual embedding formulation within a divergence minimization framework. The algorithm is designed to ensure convergence stability through the following aspects:

1. Variational Divergence Minimization: GenDICE applies an $f$-divergence between empirical and stationary distributions, which is reformulated into a tractable dual problem. This allows for the optimization of a correction ratio—the crux of estimating stationary values from offline data.
2. Constraint Regularization: The approach incorporates a constraint to eliminate degenerate solutions, which can arise in the absence of discounting (when $\gamma = 1$). By enforcing that the estimated stationary distribution over data sums to one, GenDICE ensures a valid density ratio estimate.
3. Function Approximation Flexibility: To provide computational tractability and applicability to both discrete and continuous state spaces, the authors employ neural network-based functional approximations for both the correction ratio and dual variables.

Theoretical and Empirical Analysis

From a theoretical perspective, the consistency of GenDICE is established under general conditions, with rigorous error analysis demonstrating its superiority in controlling errors stemming from finite sample sizes and approximation mis-specifications. Empirical evaluations on benchmark tasks, such as offline PageRank and various RL environments, substantiate these theoretical claims, showcasing the algorithm's robust estimation performance across diverse scenarios.

In comparison to other existing methodologies, such as model-based approaches and IS-based methods, GenDICE shows improved efficiency and accuracy, particularly in challenging environments with complex dynamics and when using limited data. This is achieved without the need to directly estimate the transition dynamics, a common and often infeasible requirement in traditional model-based approaches.

Implications and Future Directions

The development of GenDICE has immediate applications in contexts where exploration in the environment is restricted or costly, such as web search algorithms and large-scale industrial RL systems. By enabling effective stationary value estimation from offline data, GenDICE opens avenues for optimizing decisions and actions in static datasets, potentially impacting fields ranging from search engines and recommendation systems to robotic control and autonomous vehicles.

Theoretical advancements presented in this work, such as improved understanding of dual formulations for divergence minimization, also pose intriguing questions for future research. Extensions to broader classes of divergence measures, enhancement of convergence guarantees under non-binary settings, and generalization to non-Markovian environments represent compelling paths for further exploration.

In conclusion, GenDICE represents a significant methodological advancement in offline RL domains, providing a robust framework for stationary value estimation that optimally exploits offline data. Through its innovative approach, GenDICE mitigates key challenges posed by limited data access, offering a powerful tool for academic researchers and practitioners alike.