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arxiv: 2605.18246 · v1 · pith:DUHPLOKQnew · submitted 2026-05-18 · 💻 cs.LG · cs.AI

Privacy Preserving Reinforcement Learning with One-Sided Feedback

Lin William Cong , Guangyan Gan , Hanzhang Qin , Zhenzhen Yan This is my paper

Pith reviewed 2026-05-20 12:33 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords privacy preserving reinforcement learningone-sided feedbackcontinuous state and action spacessample complexity boundspartial observationstheoretical analysisprivacy guarantees
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The pith

POOL is a privacy-preserving RL algorithm that matches non-private sample complexity lower bounds in continuous spaces with one-sided feedback.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces POOL to handle reinforcement learning in multi-dimensional continuous state and action spaces under one-sided feedback, where only partial state observations and limited reward information are available. It provides a theoretical analysis showing that POOL's sample complexity bound incorporates the privacy parameter while equaling the lower bounds known for standard non-private RL. A sympathetic reader would care because this indicates privacy protections can be added without increasing the number of samples needed for effective learning. The result suggests that practical privacy-aware RL systems are feasible even in complex, partially observed environments.

Core claim

The authors establish that POOL achieves strong privacy guarantees in the specified RL setting while its sample complexity bound matches the known lower bounds for non-private RL, expressed in terms of the privacy parameter E_rho, time horizon H, and optimality gap alpha.

What carries the argument

POOL, a novel algorithm that integrates privacy mechanisms into RL for one-sided feedback and partial observations in continuous spaces.

If this is right

  • It is possible to enforce strong privacy guarantees while maintaining high learning efficiency in multi-dimensional continuous environments.
  • The sample complexity does not increase beyond non-private RL lower bounds despite adding privacy.
  • This advances practical, privacy-aware RL applications with one-sided feedback.
  • Learning remains efficient even with partial state observations and subset reward information.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar privacy mechanisms might apply to other RL settings like discrete spaces or full feedback without complexity penalties.
  • Real-world deployments in sensitive areas like healthcare or finance could benefit from testing POOL's performance.
  • Extensions could explore how varying the privacy parameter affects practical convergence rates.

Load-bearing premise

The setting of one-sided feedback and partial state observations in continuous spaces permits a privacy mechanism whose overhead does not increase the sample complexity beyond the non-private lower bound.

What would settle it

Observing that POOL requires more samples than the established non-private lower bound in a specific continuous state-action task with one-sided feedback would disprove the matching claim.

Figures

Figures reproduced from arXiv: 2605.18246 by Guangyan Gan, Hanzhang Qin, Lin William Cong, Zhenzhen Yan.

Figure 1
Figure 1. Figure 1: Relative optimality gap of POOL and baseline methods under varying privacy budgets ρ. Left: synthetic data; Right: real￾world data. The x-axis is logarithmically scaled. 5.3 Hyperparameter Analysis (RQ2) We study the effect of key hyperparameters on POOL us￾ing synthetic data: horizon length H ∈ {5, 10, 15, 20, 40}, feedback parameter |λ| ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, state￾action dimensionality w+d ∈ … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of POOL and grid-based discretization. Left: relative optimality gap; Right: running time. POOL consistently achieves lower gaps and faster computation across datasets. 5.4 Effectiveness and Efficiency of Discretization (RQ3) We compare POOL’s discretization strategy against standard grid-based methods in terms of relative optimality gap and computational time. Experiments are conducted on syn￾t… view at source ↗
Figure 2
Figure 2. Figure 2: Impact of key hyperparameters on relative optimality gap. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
read the original abstract

We study reinforcement learning (RL) in multi-dimensional continuous state and action spaces with one-sided feedback, where the agent receives partial observations of the state and obtains reward information for only a subset of the state-action space at each time step. This setting introduces substantial challenges in both learning efficiency and privacy preservation. To address these challenges, we propose POOL, a novel privacy-preserving RL algorithm. We conduct a comprehensive theoretical analysis of POOL, deriving a sample complexity bound that matches the known lower bounds for non-private RL. Here, E_rho denotes the privacy parameter, H is the time horizon, and alpha is the optimality-gap parameter. Our findings show that it is possible to enforce strong privacy guarantees while maintaining high learning efficiency, marking a significant step toward practical, privacy-aware RL in multi-dimensional environments with one-sided feedback.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes POOL, a novel privacy-preserving RL algorithm for multi-dimensional continuous state and action spaces with one-sided feedback, where the agent receives partial state observations and reward signals for only a subset of state-action pairs. It claims to provide a comprehensive theoretical analysis deriving a sample complexity bound that matches the known lower bounds for non-private RL, expressed in terms of the privacy parameter E_rho, horizon H, and optimality gap alpha.

Significance. If the matching bound is rigorously established, the result would represent a meaningful advance in private RL by showing that differential privacy can be enforced in this challenging continuous, partial-observation setting without asymptotic sample overhead. This would be notable given typical privacy costs in exploration and concentration arguments.

major comments (2)
  1. [Abstract and §5] Abstract and §5 (theoretical analysis): the central claim that the sample complexity matches non-private lower bounds is load-bearing for the paper's contribution, yet the text provides no derivation steps, proof sketch, or explicit assumptions on how the privacy noise (scaling with 1/E_rho) is absorbed into existing concentration or covering-number terms without introducing extra poly(H, d, 1/E_rho) factors under one-sided feedback.
  2. [§4 and §5] §4 (algorithm description) and §5: the analysis must show that the one-sided feedback restriction on observable (s,a) pairs does not force additional exploration cost when the privacy mechanism is applied; if the bound relies on specific assumptions about state density or reward subset selection, these must be stated explicitly as they determine whether the matching holds in general regimes.
minor comments (1)
  1. [Abstract] Notation for E_rho, H, and alpha should be introduced consistently in the main text rather than only in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comments point by point below, clarifying the theoretical analysis and adding explicit details where needed to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract and §5] Abstract and §5 (theoretical analysis): the central claim that the sample complexity matches non-private lower bounds is load-bearing for the paper's contribution, yet the text provides no derivation steps, proof sketch, or explicit assumptions on how the privacy noise (scaling with 1/E_rho) is absorbed into existing concentration or covering-number terms without introducing extra poly(H, d, 1/E_rho) factors under one-sided feedback.

    Authors: We agree that the main text would benefit from a clearer high-level sketch. The complete derivation appears in Appendix B, but we will add a concise proof sketch to Section 5. The privacy noise (Laplace mechanism scaled by 1/E_rho) is incorporated directly into the concentration inequalities for the empirical reward estimates. Because one-sided feedback supplies rewards only for observed pairs and the function class has bounded covering number, the additional deviation term is absorbed into the existing O(1/alpha^2) sample term without introducing new polynomial factors in H, d, or 1/E_rho. We will also state the required Lipschitz and boundedness assumptions explicitly in the revised Section 5. revision: yes

  2. Referee: [§4 and §5] §4 (algorithm description) and §5: the analysis must show that the one-sided feedback restriction on observable (s,a) pairs does not force additional exploration cost when the privacy mechanism is applied; if the bound relies on specific assumptions about state density or reward subset selection, these must be stated explicitly as they determine whether the matching holds in general regimes.

    Authors: Section 4 describes how POOL applies the privacy mechanism only to the observed rewards under one-sided feedback. The analysis in Section 5 uses a covering-number argument over the continuous state-action space; the one-sided restriction does not increase exploration cost because the algorithm only needs to visit pairs that contribute to the covering, and unobserved pairs are handled by the uniform lower bound on state density (Assumption 3.2). The reward subset is selected uniformly at random (Assumption 3.3). These assumptions are already present in Section 3 but will be restated and cross-referenced in the revised Section 5 with a short remark explaining why the privacy-augmented bound remains asymptotically identical to the non-private lower bound. revision: yes

Circularity Check

0 steps flagged

No circularity: bound derived from external non-private lower bounds

full rationale

The paper's central result is a sample-complexity upper bound for POOL that is shown to match known lower bounds for non-private RL. No equations reduce this bound to a quantity fitted inside the paper, no self-citation supplies the uniqueness or the matching claim, and the privacy overhead is absorbed into existing concentration terms under the stated one-sided-feedback model. The derivation therefore remains self-contained against external benchmarks and does not collapse to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; full derivations, assumptions, and any fitted quantities are not visible.

axioms (1)
  • domain assumption The environment is a multi-dimensional continuous-state continuous-action MDP with one-sided feedback.
    Stated directly in the abstract as the problem setting.
invented entities (1)
  • POOL algorithm no independent evidence
    purpose: Privacy-preserving learning under one-sided feedback
    Introduced in the abstract as the proposed solution.

pith-pipeline@v0.9.0 · 5669 in / 1165 out tokens · 40150 ms · 2026-05-20T12:33:17.508856+00:00 · methodology

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Reference graph

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