arxiv: 2604.19024 · v1 · submitted 2026-04-21 · 💻 cs.LG

Recognition: unknown

Policy Gradient Primal-Dual Method for Safe Reinforcement Learning from Human Feedback

Qiang Liu , Adrienne Kline , Ermin Wei

Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:19 UTC · model grok-4.3

classification 💻 cs.LG

keywords safe rlhfpolicy gradientprimal-dual optimizationconstrained mdpinfinite horizonhuman feedbackconvergence guaranteesreinforcement learning

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The pith

Safe RLHF can be cast as an infinite-horizon discounted constrained MDP and solved with primal-dual policy gradient methods that converge globally without fitting reward models.

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

The paper shows that human feedback on helpfulness and harmlessness can be modeled as a continuing interaction process using an infinite-horizon constrained Markov decision process. It introduces two algorithms based on primal-dual optimization that update policies directly from preference queries, avoiding the need to fit separate reward models. These methods provide theoretical guarantees of global convergence at polynomial rates depending on the number of iterations, samples, and queries. This matters because it allows training safer language models over flexible, potentially long sequences of interactions rather than fixed short episodes. A sympathetic reader would care because it bridges empirical RLHF successes with rigorous convergence proofs for the infinite-horizon case.

Core claim

The authors formulate safe RLHF as an infinite horizon discounted Constrained Markov Decision Process (CMDP) and propose primal-dual policy gradient algorithms that achieve global, non-asymptotic convergence with rates polynomial in policy gradient iterations, trajectory lengths, and human preference queries. Unlike prior approaches, the methods do not require fitting fixed-horizon reward models and support flexible trajectory lengths.

What carries the argument

The primal-dual method applied to policy gradients in the infinite-horizon discounted CMDP, where the dual variables enforce the safety constraints from human feedback on harmlessness.

If this is right

Training can proceed over sequences of arbitrary length instead of requiring fixed finite episodes.
Human preference data can be used directly without an intermediate step of fitting reward models.
Global convergence holds with explicit polynomial dependence on iteration count, sample length, and query number.
Both helpfulness and harmlessness objectives are handled simultaneously inside one CMDP.

Where Pith is reading between the lines

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

The same primal-dual structure might apply to other preference-driven RL settings where interactions continue indefinitely rather than ending in fixed episodes.
Skipping reward model fitting could reduce error accumulation in the safety constraint when scaling to larger models.
If the polynomial rates hold in practice, query efficiency would become the dominant cost factor for safe training.

Load-bearing premise

The formulation assumes human preferences on helpfulness and harmlessness can be decoupled into a CMDP with infinite-horizon discounting and that primal-dual updates converge without additional approximations or reward-model intermediaries.

What would settle it

Training a policy with the proposed primal-dual algorithms on a continuing interaction task and observing that the policy either diverges or violates the harmlessness constraint as iterations increase would falsify the global convergence claim.

Figures

Figures reproduced from arXiv: 2604.19024 by Adrienne Kline, Ermin Wei, Qiang Liu.

read the original abstract

Safe Reinforcement Learning from Human Feedback (Safe RLHF) has recently achieved empirical success in developing helpful and harmless large language models by decoupling human preferences regarding helpfulness and harmlessness. Existing approaches typically rely on fitting fixed horizon reward models from human feedback and have only been validated empirically. In this paper, we formulate safe RLHF as an infinite horizon discounted Con- strained Markov Decision Process (CMDP), since humans may interact with the model over a continuing sequence of interactions rather than within a single finite episode. We propose two Safe RLHF algorithms that do not require reward model fitting and, in contrast to prior work assuming fixed-length trajectories, support flexible trajectory lengths for training. Both algo- rithms are based on the primal-dual method and achieve global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries. To the best of our knowledge, this is the first work to study infinite horizon discounted CMDP under human feedback and establish global, non-asymptotic convergence.

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.

Desk Editor's Note private letter to a colleague

The paper casts safe RLHF as an infinite-horizon discounted CMDP and claims two primal-dual algorithms achieve global polynomial-rate convergence without reward-model fitting.

read the letter

The main takeaway is that the authors model Safe RLHF as an infinite-horizon discounted constrained MDP and develop two primal-dual methods that converge globally at polynomial rates in the number of policy gradient iterations, trajectory samples, and human preference queries. They do this without fitting a reward model and with support for variable-length trajectories during training. This formulation is new because most prior work on RLHF with safety constraints has stayed in finite-horizon settings and relied on learned reward models. Treating the problem as ongoing makes sense for language models that users interact with repeatedly, and the flexible trajectories could reduce some practical constraints in training. The primal-dual structure is a reasonable choice for handling the constraints on harmlessness while optimizing for helpfulness. The paper does well in clearly stating the gap it aims to fill and in positioning the contribution relative to existing empirical methods. The claim that this is the first such infinite-horizon treatment with non-asymptotic bounds seems to hold based on the abstract. Where it is soft is that the abstract provides no proof details or assumption statements. I cannot assess whether the convergence results actually go through under the kinds of function approximation needed for LLMs or if they require idealized conditions on the human feedback. The assumption that preferences can be directly mapped to a CMDP without intermediaries might turn out to be the key point that needs validation in the full paper. This work is for people in the safe RL and AI alignment communities who care about theoretical guarantees for long-term interactions. A reader focused on immediate empirical improvements might not get much yet, but someone looking for foundations could find value once the proofs are examined. I would recommend sending it to peer review. The idea is coherent and addresses a real modeling choice, so referees can check the math and any supporting experiments.

Referee Report

2 major / 1 minor

Summary. The paper formulates Safe RLHF as an infinite-horizon discounted Constrained Markov Decision Process (CMDP) to model continuing interactions between humans and language models. It proposes two primal-dual policy-gradient algorithms that optimize the CMDP directly from human preference queries without fitting separate reward models, support variable-length trajectories, and claim to achieve global non-asymptotic convergence at polynomial rates in the number of iterations, samples, and queries. The work asserts it is the first to provide such theoretical guarantees for this setting.

Significance. If the stated convergence results hold, the contribution would be notable for supplying the first non-asymptotic global convergence analysis of safe RLHF under an infinite-horizon discounted CMDP formulation. This moves the field beyond purely empirical reward-model approaches and fixed-horizon assumptions, potentially enabling more reliable theoretical guidance for aligning large language models on helpfulness and harmlessness constraints.

major comments (2)

Abstract: the claim of 'global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries' is presented without any theorem statement, assumption list, proof sketch, or reference to a later section containing the analysis. This absence makes the central theoretical contribution impossible to verify from the provided text and is load-bearing for the paper's primary claim.
The formulation section (implicit in the abstract's CMDP setup): the decoupling of human preferences into a single infinite-horizon discounted CMDP with a cost constraint is asserted but not accompanied by a concrete mapping from preference queries to the cost function or constraint violation measure. Without this, it is unclear whether the primal-dual updates remain valid when trajectory lengths vary and no reward model is fitted.

minor comments (1)

Notation for the two proposed algorithms is introduced in the abstract but not distinguished (e.g., by name or equation number), which will hinder readability once the full algorithmic descriptions appear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and valuable feedback on our manuscript. The comments highlight important areas for improving clarity in the abstract and formulation. We address each point below and have revised the manuscript to incorporate the suggestions.

read point-by-point responses

Referee: Abstract: the claim of 'global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries' is presented without any theorem statement, assumption list, proof sketch, or reference to a later section containing the analysis. This absence makes the central theoretical contribution impossible to verify from the provided text and is load-bearing for the paper's primary claim.

Authors: We agree that the abstract would benefit from an explicit pointer to the theoretical results. The full statement of the global non-asymptotic convergence (including assumptions on the CMDP, bounded costs, and query noise, plus a proof sketch) appears in Theorem 4.1 of Section 4, with the complete analysis in Sections 4 and 5. In the revised manuscript we will update the abstract to read: '...Both algorithms achieve global convergence guarantees with polynomial rates in terms of policy gradient iterations, trajectory sample lengths, and human preference queries (see Theorem 4.1 for the formal statement, assumptions, and proof sketch).' This change directly addresses the verifiability concern without altering any technical claims. revision: yes
Referee: The formulation section (implicit in the abstract's CMDP setup): the decoupling of human preferences into a single infinite-horizon discounted CMDP with a cost constraint is asserted but not accompanied by a concrete mapping from preference queries to the cost function or constraint violation measure. Without this, it is unclear whether the primal-dual updates remain valid when trajectory lengths vary and no reward model is fitted.

Authors: We appreciate the request for greater concreteness. Section 2.2 already defines the CMDP with the helpfulness objective as the (estimated) reward and harmlessness as the cost constraint, where preference queries directly supply unbiased estimates of the cost violation measure via the Bradley-Terry model without fitting a separate reward function. To make the mapping explicit, the revised version will add a paragraph and a small illustrative example in Section 2.2 showing how a variable-length trajectory pair yields a query-based cost estimate that is plugged into the primal-dual Lagrangian update; the discounted infinite-horizon formulation ensures the updates remain valid for continuing interactions of arbitrary length. The convergence proof in Theorem 4.1 accounts for the resulting estimation error. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper formulates Safe RLHF as an infinite-horizon discounted CMDP and derives two primal-dual policy gradient algorithms with global non-asymptotic convergence rates. These steps rest on standard CMDP theory and primal-dual optimization results rather than reducing to quantities defined or fitted within the same paper. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or high-level claims. The novelty assertion (first study of this setting) is external and does not create internal circularity. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the modeling choice that human feedback preferences admit a CMDP representation with decoupled helpfulness/harmlessness constraints and on the applicability of primal-dual policy gradients to that model without reward fitting.

axioms (2)

domain assumption Safe RLHF preferences can be expressed as constraints in an infinite-horizon discounted CMDP
Explicitly stated as the modeling step that enables the algorithms.
ad hoc to paper Primal-dual methods yield global convergence under the stated CMDP and human-feedback setting
The paper's main theoretical contribution depends on this property holding.

pith-pipeline@v0.9.0 · 5474 in / 1265 out tokens · 39455 ms · 2026-05-10T02:19:52.442438+00:00 · methodology

discussion (0)

Reference graph

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