Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism (2103.12021v2)

Published 22 Mar 2021 in cs.LG, cs.AI, math.OC, math.ST, stat.ML, and stat.TH

Abstract: Offline (or batch) reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main categories of methods are used: imitation learning which is suitable for expert datasets and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown a priori. To bridge this gap, we present a new offline RL framework that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. The new framework is centered around a weak version of the concentrability coefficient that measures the deviation from the behavior policy to the expert policy alone. Under this new framework, we further investigate the question on algorithm design: can one develop an algorithm that achieves a minimax optimal rate and also adapts to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in all three settings, LCB achieves a faster rate of $1/N$ for nearly-expert datasets compared to the usual rate of $1/\sqrt{N}$ in offline RL, where $N$ is the number of samples in the batch dataset. In the case of contextual bandits with at least two contexts, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

Authors (5)

Paria Rashidinejad (6 papers)
Banghua Zhu (38 papers)
Cong Ma (74 papers)
Jiantao Jiao (83 papers)
Stuart Russell (98 papers)

Citations (252)

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Summary

Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism

This paper proposes a novel framework for offline reinforcement learning (RL) that seeks to unify the two traditional approaches: imitation learning and vanilla offline RL. Offline RL, wherein an optimal policy is learned from a static dataset without further exploration, has typically required distinct methodologies depending on the nature of the data composition. For instance, imitation learning is well-suited for expert datasets, while vanilla offline RL demands uniformly-covered datasets. The paper contributes a unified solution by introducing a weak version of the concentrability coefficient, which measures deviation from an expert policy.

Unified Framework

The newly proposed framework interpolates smoothly between imitation learning and offline RL. This interpolation is achieved by characterizing data compositions with a concentrability coefficient, $C^\star$ , defined by the deviation from the behavior to the optimal policy. Such a formulation is minimalistic compared to existing approaches, which usually require coverage for all possible policies and are thus more stringent. Particularly, this formulation allows the model to handle data compositions throughout the spectrum, from strictly expert-driven to more diverse exploratory datasets.

Algorithmic Design and Analysis

The paper investigates algorithmic strategies that can adapt optimally to unknown data compositions, hypothesizing that a single algorithm can fit across different $C^\star$ regimes. They focus on a lower confidence bound (LCB) algorithm, positing that incorporating pessimism in uncertainty, specifically penalizing less-covered state-action spaces, can achieve satisfactory outcomes.

Multi-Armed Bandits and Contextual Bandits

In multi-armed bandits (MAB), the LCB approach achieves near-optimal sub-optimality rates, although it shows limitations due to its lack of adaptivity in the highly expert-driven regime ( $C^\star \in [1, 2)$ ). However, in contextual bandits (CB) with multiple states, LCB performs optimally. Not only does it smoothly transition between $1/N$ and $1/\sqrt{N}$ rates as $C^\star$ ranges from near-expert to more uniformly exploratory distributions, but it also mitigates errors commonly experienced in solely imitation-focused methods.

Markov Decision Processes and Theoretical Implications

The paper extends the analysis to Markov decision processes (MDP), suggesting that VI-LCB (value iteration with LCB) could potentially be optimal for a varied range of $C^\star$ . They propose upper bounds for sub-optimality that highlight the algorithm's capacity for nearly optimally transitioning between different data compositions—this aligns well with the contextual bandits findings. Interestingly, the authors suggest possible further refinements by incorporating variance reduction techniques, which might reduce the dependency on the effective horizon.

Implications and Future Directions

This proposed framework and its algorithmic insights have profound implications for practical applications where the composition of historical data varies. By proposing a pathway to unify imitation learning and offline RL, this paper pushes forward the boundaries of RL where adaptability to varied data is crucial, such as robotics, healthcare, and autonomous systems. Future research directions highlighted by the authors include confirming conjectures about the MDP regimes, improving the horizon dependency, and exploring the integration of function approximation into the framework.

Overall, the contributions of the paper present a compelling paradigm for offline RL that balances the benefits of conservatism with the versatility required for real-world applications. As AI systems continue to evolve, ensuring they can learn effectively from existing datasets will enhance their capacity for deployment in a global, dynamic environment.

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