# Offline Reinforcement Learning: Fundamental Barriers for Value Function Approximation

@inproceedings{Foster2022OfflineRL, title={Offline Reinforcement Learning: Fundamental Barriers for Value Function Approximation}, author={Dylan J. Foster and Akshay Krishnamurthy and David Simchi-Levi and Yunzong Xu}, booktitle={Annual Conference Computational Learning Theory}, year={2022} }

We consider the offline reinforcement learning problem, where the aim is to learn a decision making policy from logged data. Offline RL—particularly when coupled with (value) function approximation to allow for generalization in large or continuous state spaces—is becoming increasingly relevant in practice, because it avoids costly and time-consuming online data collection and is well suited to safety-critical domains. Existing sample complexity guarantees for offline value function…

## 22 Citations

### Offline Reinforcement Learning Under Value and Density-Ratio Realizability: the Power of Gaps

- Computer ScienceUAI
- 2022

This work is the first to identify the utility and the novel mechanism of gap assumptions in ofﬂine RL with weak function approximation and provide guarantees to a simple pes-simistic algorithm based on a version space formed by marginalized importance sampling.

### Offline Reinforcement Learning with Differentiable Function Approximation is Provably Efficient

- Computer ScienceArXiv
- 2022

This work shows offline RL with differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning algorithm, and its results provide the theoretical basis for understanding a variety of practical heuristics that rely on Fitted Q-Iteration style design.

### Near-optimal Offline Reinforcement Learning with Linear Representation: Leveraging Variance Information with Pessimism

- Computer ScienceICLR
- 2022

The variance-aware pessimistic value iteration (VAPVI), which adopts the conditional variance information of the value function for time-inhomogeneous episodic linear Markov decision processes (MDPs), and provides improved offline learning bounds over the best-known existing results.

### Offline Reinforcement Learning with Realizability and Single-policy Concentrability

- Mathematics, Computer ScienceCOLT
- 2022

A simple algorithm based on the primal-dual formulation of MDPs, where the dual variables are mod-eled using a density-ratio function against ofﬂine data and enjoys polynomial sample complexity, under only realizability and single-policy concentrability.

### Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian

- Computer Science
- 2022

This paper leverages the marginalized importance sampling (MIS) formulation of RL and presents the first set of oﬄine RL algorithms that are statistically optimal and practical under general function approximation and single-policy concentrability, bypassing the need for uncertainty quantiﬁcation.

### A Sharp Characterization of Linear Estimators for Offline Policy Evaluation

- MathematicsArXiv
- 2022

Offline policy evaluation is a fundamental statistical problem in reinforcement learning that involves estimating the value function of some decision-making policy given data collected by a…

### Learning Bellman Complete Representations for Offline Policy Evaluation

- Computer ScienceICML
- 2022

This work proposes BCRL, which directly learns from data an approximately linear Bellman complete representation with good coverage, and shows that this representation enables better OPE compared to previous representation learning methods developed for off-policy RL (e.g., CURL, SPR).

### When is Realizability Sufficient for Off-Policy Reinforcement Learning?

- Computer Science
- 2022

These error bounds establish that oﬀ-policy reinforcement learning remains statistically viable even in absence of Bellman completeness, and characterize the intermediate situation between the favorable Bellman complete setting and the worst-case scenario where exponential lower bounds are in force.

### Oracle Inequalities for Model Selection in Offline Reinforcement Learning

- Computer Science
- 2022

This work proposes the first model selection algorithm for ofﬂine RL that achieves minimax rate-optimal oracle inequalities up to logarithmic factors and concludes with several numerical simulations showing it is capable of reliably selecting a good model class.

### Behavior Prior Representation learning for Offline Reinforcement Learning

- Computer ScienceArXiv
- 2022

Theoretically, it is proved that BPR carries out performance guarantees when integrated into algorithms that have either policy improvement guarantees (con-servative algorithms) or produce lower bounds of the policy values (pessimistic algorithms).

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