Deep reinforcement learning (RL) has shown remarkable success in specific offline decision-making scenarios, yet its theoretical guarantees are still under development. Existing works on offline RL theory primarily emphasize a few trivial settings, such as linear MDP or general function approximation with strong assumptions and independent data, which lack guidance for practical use. The coupling of deep learning and Bellman residuals makes this problem challenging, in addition to the difficulty of data dependence. In this paper, we establish a non-asymptotic estimation error of pessimistic offline RL using general neural network approximation with C-mixing data regarding the structure of networks, the dimension of datasets, and the concentrability of data coverage, under mild assumptions. Our result shows that the estimation error consists of two parts: the first converges to zero at a desired rate on the sample size with partially controllable concentrability, and the second becomes negligible if the residual constraint is tight. This result demonstrates the explicit efficiency of deep adversarial offline RL frameworks. We utilize the empirical process tool for C-mixing sequences and the neural network approximation theory for the Holder class to achieve this. We also develop methods to bound the Bellman estimation error caused by function approximation with empirical Bellman constraint perturbations. Additionally, we present a result that lessens the curse of dimensionality using data with low intrinsic dimensionality and function classes with low complexity. Our estimation provides valuable insights into the development of deep offline RL and guidance for algorithm model design.
Oracle Inequalities for Model Selection in Offline Reinforcement Learning
In offline reinforcement learning (RL), a learner leverages prior logged data to
learn a good policy without interacting with the environment. A major challenge
in applying such methods in practice is the lack of both theoretically principled and
practical tools for model selection and evaluation. To address this, we study the
problem of model selection in offline RL with value function approximation. The
learner is given a nested sequence of model classes to minimize squared Bellman
error and must select among these to achieve a balance between approximation and
estimation error of the classes. We propose the first model selection algorithm for
offline RL that achieves minimax rate-optimal oracle inequalities up to logarithmic
factors. The algorithm, MODBE, takes as input a collection of candidate model
classes and a generic base offline RL algorithm. By successively eliminating
model classes using a novel one-sided generalization test, MODBE returns a policy
with regret scaling with the complexity of the minimally complete model class. In
addition to its theoretical guarantees, it is conceptually simple and computationally
efficient, amounting to solving a series of square loss regression problems and then
comparing relative square loss between classes. We conclude with several numerical simulations showing it is capable of reliably selecting a good model class.
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- Award ID(s):
- 2112926
- NSF-PAR ID:
- 10382139
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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