Sparse Offline Reinforcement Learning with Corruption Robustness
Pith reviewed 2026-05-16 18:52 UTC · model grok-4.3
The pith
Actor-critic methods with sparse robust estimator oracles deliver non-vacuous guarantees for near-optimal policies in high-dimensional sparse offline RL even under strong data corruption.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The paper shows that actor-critic methods equipped with sparse robust estimator oracles can learn near-optimal policies in sparse offline RL without pointwise pessimistic bonuses. Under assumptions of uniform coverage and sparse single-concentrability, the approach yields the first non-vacuous guarantees, and it remains effective when a fraction of the collected trajectories are arbitrarily perturbed by an adversary.
What carries the argument
Sparse robust estimator oracles, which provide robust estimates for sparse parameters in the presence of contamination and enable the actor-critic updates to proceed without overly pessimistic adjustments.
If this is right
- Learning near-optimal policies becomes possible with non-vacuous sample bounds in high-dimensional sparse MDPs under single-policy concentrability.
- The algorithm tolerates strong contamination where adversaries arbitrarily change a fraction of trajectories.
- Integration of sparsity into robust offline RL succeeds where direct application to LSVI fails due to pessimistic bonuses.
- Policy learning remains feasible in settings where traditional robust offline RL methods produce vacuous results.
Where Pith is reading between the lines
- If efficient implementations of the sparse robust oracles exist, the methods could apply to practical high-dimensional control tasks with corrupted datasets.
- The framework might extend to other RL paradigms like online learning or multi-agent settings with similar sparsity and robustness needs.
- Connections to high-dimensional robust statistics could improve the oracle constructions and tighten the bounds further.
Load-bearing premise
The analysis requires that sparse robust estimator oracles can be implemented without adding fitting parameters that would invalidate the non-vacuous bounds, and that sparse single-concentrability coverage holds.
What would settle it
A counterexample in a high-dimensional sparse MDP with single-policy concentrability where the proposed actor-critic method fails to output a near-optimal policy when a constant fraction of trajectories are corrupted, or where the derived sample complexity bound becomes vacuous despite sparsity.
read the original abstract
We investigate robustness to strong data corruption in offline sparse reinforcement learning (RL). In our setting, an adversary may arbitrarily perturb a fraction of the collected trajectories from a high-dimensional but sparse Markov decision process, and our goal is to estimate a near optimal policy. The main challenge is that, in the high-dimensional regime where the number of samples $N$ is smaller than the feature dimension $d$, exploiting sparsity is essential for obtaining non-vacuous guarantees but has not been systematically studied in offline RL. We analyse the problem under uniform coverage and sparse single-concentrability assumptions. While Least Square Value Iteration (LSVI), a standard approach for robust offline RL, performs well under uniform coverage, we show that integrating sparsity into LSVI is unnatural, and its analysis may break down due to overly pessimistic bonuses. To overcome this, we propose actor-critic methods with sparse robust estimator oracles, which avoid the use of pointwise pessimistic bonuses and provide the first non-vacuous guarantees for sparse offline RL under single-policy concentrability coverage. Moreover, we extend our results to the contaminated setting and show that our algorithm remains robust under strong contamination. Our results provide the first non-vacuous guarantees in high-dimensional sparse MDPs with single-policy concentrability coverage and corruption, showing that learning a near-optimal policy remains possible in regimes where traditional robust offline RL techniques may fail.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper investigates robustness to strong data corruption in offline sparse RL for high-dimensional MDPs where N < d. It shows that standard LSVI with sparsity integration leads to overly pessimistic bonuses and breaks down under sparse single-policy concentrability, and instead proposes actor-critic methods relying on sparse robust estimator oracles that avoid pointwise bonuses. The central claims are the first non-vacuous guarantees for near-optimal policy learning under sparse single-policy concentrability (both clean and contaminated settings) and robustness to arbitrary corruption of a fraction of trajectories.
Significance. If the oracle-based analysis holds with the claimed sparsity level and without extra parameters inflating sample complexity, the result would be significant: it would close a gap between uniform-coverage robust offline RL and the weaker single-policy concentrability regime that is more realistic for sparse high-dimensional problems, while providing the first explicit non-vacuous bounds under corruption. The work correctly identifies the tension between sparsity exploitation and pessimistic bonus construction.
major comments (2)
- [Abstract and proposed actor-critic method] The non-vacuous guarantee under sparse single-policy concentrability is load-bearing on the assumption that sparse robust estimator oracles exist and can be realized at the same sparsity level without introducing new fitting parameters or regularization that would invalidate the N ≪ d regime (see skeptic note on oracle realizability). No explicit construction or sample-complexity analysis for these oracles is referenced in the abstract or high-level claims.
- [LSVI discussion] The claim that LSVI analysis 'may break down' due to pessimistic bonuses under sparsity is central, yet the abstract provides no quantitative comparison (e.g., how the bonus term scales with d versus the sparse estimator variance) to show the breakdown is unavoidable rather than an artifact of a particular bonus design.
minor comments (1)
- [Abstract] Notation for the sparse single-concentrability coefficient and the contamination fraction should be defined explicitly at first use rather than left implicit in the abstract.
Simulated Author's Rebuttal
We thank the referee for the careful reading and constructive feedback. We address the two major comments point by point below, agreeing that clarifications are needed and committing to revisions that strengthen the presentation without altering the core technical claims.
read point-by-point responses
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Referee: [Abstract and proposed actor-critic method] The non-vacuous guarantee under sparse single-policy concentrability is load-bearing on the assumption that sparse robust estimator oracles exist and can be realized at the same sparsity level without introducing new fitting parameters or regularization that would invalidate the N ≪ d regime (see skeptic note on oracle realizability). No explicit construction or sample-complexity analysis for these oracles is referenced in the abstract or high-level claims.
Authors: We agree that the abstract should more explicitly reference the oracle construction to avoid any ambiguity. The sparse robust estimator oracles are instantiated via standard robust sparse regression procedures (e.g., robust truncated Lasso or Huberized sparse estimators) that operate at the same sparsity level s as the underlying MDP features and incur no additional regularization parameters beyond the model sparsity itself. Their sample-complexity guarantees follow directly from existing minimax rates for sparse estimation under arbitrary contamination (O(s log(d)/N) variance scaling), which are already cited in Section 3.2 of the manuscript. We will revise the abstract to include a one-sentence pointer to this construction and its parameter-free nature with respect to the N ≪ d regime. revision: yes
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Referee: [LSVI discussion] The claim that LSVI analysis 'may break down' due to pessimistic bonuses under sparsity is central, yet the abstract provides no quantitative comparison (e.g., how the bonus term scales with d versus the sparse estimator variance) to show the breakdown is unavoidable rather than an artifact of a particular bonus design.
Authors: We accept that a scaling comparison would make the motivation sharper. In the revised manuscript we will add a brief quantitative remark (in both the abstract and the introduction) showing that any pointwise pessimistic bonus for LSVI must scale at least as Ω(√(d log(1/δ)/N)) to cover the full feature space, which becomes vacuous whenever d ≫ N, whereas the sparse oracle estimator variance scales as O(√(s log(d)/N)) and remains non-vacuous under the single-policy concentrability assumption. This scaling difference is independent of the precise bonus functional form and arises because LSVI bonuses are constructed pointwise over the entire d-dimensional space. revision: yes
Circularity Check
No significant circularity detected in derivation chain
full rationale
The paper's central contribution consists of new actor-critic algorithms that employ sparse robust estimator oracles to obtain non-vacuous bounds under sparse single-policy concentrability (rather than uniform coverage) while handling strong contamination. No equation or claim in the abstract reduces a prediction to a fitted parameter by construction, nor does any load-bearing step rely on a self-citation chain that itself lacks independent verification. The realizability of the oracles is treated as an explicit modeling assumption whose validity is left to future algorithmic work, without circular redefinition of the target quantities. The analysis therefore remains self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Uniform coverage and sparse single-concentrability assumptions hold for the MDP.
discussion (0)
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