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Neural Network Approximation for Pessimistic Offline Reinforcement Learning
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Derives a non-asymptotic estimation error bound for pessimistic deep adversarial offline RL with ReLU networks and C-mixing (dependent) data, with dimension-reduction results for low Minkowski dimension and low-complexity target functions.
Problem
Existing offline RL theory relies on strong assumptions (linear/tabular MDPs, finite or convex function classes) and i.i.d. data, leaving deep neural network approximation of pessimistic offline RL with dependent data without non-asymptotic guarantees.
Approach
Analyzes an adversarial (max-min, relative pessimism) offline RL framework with neural network policy and value parameterizations under geometrically C-mixing data, decomposing excess risk into approximation, generalization, and Bellman-estimation error, and uses Minkowski dimension and low-complexity compositional structure to mitigate the curse of dimensionality.
Key results
- Establishes excess-risk bound of order |D|^{-zeta*/(d+2zeta*)} log^{2+1/eta}|D| plus C2*sqrt(epsilon) under C-mixing data and Holder smoothness.
- Replaces ambient dimension d with Minkowski dimension of the support, reducing the curse of dimensionality (Theorem 2).
- Low-complexity compositional target functions give d_* = max_i d_i in the rate (Theorem 3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use low-dimensional data structure with support Minkowski dimension much smaller than the ambient dimension | Deep adversarial offline RL · Offline RL with low-dimensional data | susceptibility to the curse of dimensionality | Helped |
| Use low-complexity component functions for policy and value functions | Deep adversarial offline RL · Offline RL with low-complexity target functions | susceptibility to the curse of dimensionality | Helped |
| Use smoother target functions | Deep adversarial offline RL · General-dimensional data | estimation error rate | Helped |
Limitations
- Theory only; the max-min adversarial algorithm itself is not analyzed computationally and the paper leaves algorithm analysis to future work.
- Bound constants depend on concentrability, which can be very large under poor coverage.
- Curse of dimensionality remains for generic ambient dimension without low-dimensional structure assumptions.
Experimental setup
Metrics: excess risk upper bound (non-asymptotic)
Baselines: fitted Q-evaluation with CNNs deep ReLU offline policy evaluation/optimization analysis
Builds on: relative pessimism Holder approximation theory for ReLU networks C-mixing empirical process bounds
Closest papers by meaning
- Bellman-consistent Pessimism for Offline Reinforcement Learning (NeurIPS 2021 · similarity 0.91)
- Pessimistic Nonlinear Least-Squares Value Iteration for Offline Reinforcement Learning (ICLR 2024 · similarity 0.90)
- On the Complexity of Offline Reinforcement Learning with Q*-Approximation and Partial Coverage (NeurIPS 2026 · similarity 0.89)
- Deterministic Uncertainty Propagation for Improved Model-Based Offline Reinforcement Learning (NeurIPS 2024 · similarity 0.89)
- A Unified Principle of Pessimism for Offline Reinforcement Learning under Model Mismatch (NeurIPS 2024 · similarity 0.89)
- Enhancing Value Function Estimation through First-Order State-Action Dynamics in Offline Reinforcement Learning (ICML 2024 · similarity 0.89)
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