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REVIEW 3 major objections 5 minor 2 cited by

Under KL-regularized alignment, the optimal reward model is a prompt-dependent threshold on the user's true utility — not the reward model itself.

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2026-08-03 05:58 UTC pith:TO4I6S4C

load-bearing objection The threshold-optimality theory is clean and worth referee time; the empirical wrapper—especially the ARGS estimator—overreaches and needs major tightening before the paper's claims are credible. the 3 major comments →

arxiv 2602.02572 v2 pith:TO4I6S4C submitted 2026-01-31 cs.LG cs.AI

Reward Shaping for (Inference-Time) Alignment: A Stackelberg Game Perspective

Haichuan Wang , Tao Lin , Lingkai Kong , Ce Li , Hezi Jiang , Milind Tambe This is my paper
classification cs.LG cs.AI
keywords reward shapingStackelberg gameLLM alignmentKL regularizationthreshold rewardinference-time alignmentreward hackingbisection method
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that directly feeding a learned reward model into KL-regularized LLM alignment is suboptimal for the user, because the KL penalty keeps the policy close to a base model that may harbor biases conflicting with user preferences. To correct this, the authors cast reward design as a Stackelberg game in which the reward provider leads and the LLM follows, and they prove that the optimal reward has a threshold form: assign the maximum allowed value to outputs whose true utility exceeds a per-prompt cutoff and assign zero to the rest. The cutoff is characterized as the unique root of a monotone helper function, so it can be computed in practice by bisection on Monte Carlo samples from the base policy. A soft sigmoid version interpolates continuously between no shaping and the exact optimum, and any bounded utility admits a shaping strength that strictly improves on using the raw reward. Integrated into inference-time decoding methods (Controlled Decoding and ARGS), the shaped reward consistently raises average reward while preserving diversity and coherence, with win-tie rates against baselines above 66%.

Core claim

The core discovery is that the leader's optimal reward model for the KL-regularized alignment objective ρ_r(y|x) ∝ ρ_base(y|x) exp(r(x,y)/β) is a threshold reward r_m*, which assigns the maximal allowable value B to every response whose true utility r_U(x,y) exceeds a prompt-dependent threshold m*(x) and zero to responses below it. The threshold must satisfy the self-consistency condition m*(x) = E_{y∼ρ_{rm*}(·|x)}[r_U(x,y)], i.e., the cutoff equals the expected true utility under the induced shaped policy. The authors prove the threshold is the unique root of a continuous, strictly decreasing function F_x(m) built from base-policy expectations, enabling a bisection-based approximation using

What carries the argument

The central object is the threshold reward model r_m(x,y), which maps responses to B when r_U(x,y) > m(x), to 0 when r_U(x,y) < m(x), and to any value in [0,B] on the tie set. The argument runs through the fixed-point identity m*(x) = E_{y∼ρ_{rm*}}[r_U(x,y)], whose unique solvability is established by the helper function F_x(m) = E_{y∼ρ_base}[w_{x,y}(m)(r_U(x,y)−m)], with weight w=1 below m and exp(B/β) above. Monotonicity of F_x makes the search for m* a one-dimensional bisection problem, and replacing the expectation with base-policy samples yields a practical estimator. The same structure is then smoothed into the SRS(soft) reward B·σ(α(r_U(x,y) − m̂*(x))), which interpolates from the bas

Load-bearing premise

In the token-level ARGS variant (Eq. 8), the paper assumes that a per-token threshold computed from the top-M weighted candidates is a valid surrogate for the trajectory-level optimal threshold m*(x), an assumption for which no consistency or convergence proof is given.

What would settle it

For a set of prompts, sample many responses from the base policy, compute the full-trajectory threshold m*(x) by bisection on F_x, then measure the actual average true reward of the induced shaped policy. If the achieved utility is significantly below m*(x), or if a non-threshold reward can be found that beats the threshold reward on the same prompts, Theorem 1's characterization would be contradicted. For ARGS specifically, compare the top-M weighted per-token threshold against the full-trajectory threshold across prompts; consistent large mismatches would falsify the estimator that the empir

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Directly using a learned reward model in KL-regularized alignment is generically suboptimal; the optimal reward is a shaped, threshold version of it that compensates for base-policy bias.
  • The per-prompt optimal threshold is computable from base-policy samples via bisection, making the theoretically optimal shaping practically accessible without retraining the policy.
  • Bounding the shaped reward by B bounds the KL divergence between the aligned and base policies, giving a principled mechanism to control reward hacking and over-steering.
  • The shaping integrates with inference-time methods (Controlled Decoding and ARGS) with negligible added latency, consistently improving average reward and achieving win-tie rates above 66% over baselines.
  • Since the soft threshold interpolates continuously between base policy and the analytic optimum, there always exists a shaping strength that improves user utility relative to using r_U directly.

Where Pith is reading between the lines

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

  • The threshold characterization suggests a general recipe for bias compensation in any KL-regularized alignment pipeline, including train-time RLHF/DPO, where reward shaping is currently heuristic.
  • The per-token weighted estimator used in ARGS is an unproven proxy for the trajectory-level threshold; if validated, the same optimality argument would extend to any token-level decoder that can expose base-policy probabilities.
  • The framework turns reward shaping hyperparameter selection into a theoretically grounded estimation problem, replacing ad hoc amplification schedules with a bisection-derived cutoff.
  • A testable extension is to apply the same threshold shaping to offline preference-optimization objectives; if the fixed-point condition survives, it would directly mitigate base-policy bias in fine-tuning as well.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper argues that using the user reward model r_U directly in KL-regularized LLM alignment is suboptimal, and formalizes reward design as a Stackelberg game in which the reward provider (leader) chooses a bounded reward model r and the LLM (follower) responds via the exponential-tilt policy given by Eq. (2). The central theoretical contribution (Theorems 1–2) is that the optimal reward model has a threshold structure, with threshold m*(x)=E_{ρ_{r_m*}}[r_U], which is the unique root of the helper function F_x(m) and can be found by bisection. A sigmoid relaxation (SRS-soft) is introduced to improve robustness, and the method is instantiated in two inference-time aligners, CD and ARGS. Experiments on HH-RLHF and SHP with Qwen3-8B and Llama3-8B report consistent average-reward gains and GPT-4 win–tie rates above 66% against vanilla and heuristic-shaping baselines.

Significance. The Stackelberg formulation is clean and the threshold characterization is an appealing, potentially useful result for reward shaping under KL regularization. The proof of Theorem 2 correctly identifies the root condition, and the bisection procedure based on the Monte Carlo estimator in Eq. (5) is a genuine strength for the CD instantiation. The paper also provides a helpful connection to algorithmic contract design. However, the ARGS instantiation relies on an estimator (Eq. (8)) that is not a Monte Carlo estimator of F_x(m) and lacks any consistency or bias analysis; since SRS-ARGS is the only method evaluated in two of the four settings, the empirical validation of the central claim is substantially weaker than the abstract suggests. The theoretical core is defensible, but the bridge to the headline inference-time results needs repair.

major comments (3)
  1. [Appendix B.2 / Algorithm 4, Eq. (8)] The ARGS threshold estimator is not a Monte Carlo estimator of F_x(m). Eq. (8) sums over the deterministic top-M tokens with π_base weights, omitting the tail of π_base, so it is a truncated weighted sum with unquantified bias. It also replaces the trajectory-level reward r_U(x,y) with the per-token proxy r_U([s_t,y_t,EOS]). No consistency or finite-sample bound is supplied. Since SRS-ARGS is the only method evaluated in Eval-3 and Eval-4 and contributes most of the win–tie evidence, the empirical claims rest on this unverified estimator. Please either prove consistency/bias bounds for Eq. (8) or reframe ARGS as a heuristic with dedicated validation.
  2. [Section 4.4, Corollary 1] Corollary 1 states that for any r_U bounded by B there exists α0>0 with U(r_{m*,α0})>U(r_U). This is not true without an extra condition: if r_U is already an optimal threshold reward, or if r_U is constant, then U(r_U)=U(r*) and no strict improvement exists. The most that follows from Theorem 3 and the optimality of r* is U(r*)≥U(r_U), with strict inequality only when r_U is suboptimal. Please qualify the corollary or prove strictness under additional assumptions.
  3. [Section 6.3, Table 2 footnote; Appendix C.3] CD results are omitted for Eval-3 and Eval-4 after the fact, and Appendix C.3 concludes that vanilla CD fails to improve Llama3-8B-Instruct. Consequently, the abstract's claim of improvement 'across all evaluation settings' is supported only by ARGS in two of the four settings. The omission is disclosed, but the central claim that SRS integrates seamlessly into existing inference-time methods is weakened. Please either include the failed CD baselines in the main table or explicitly restrict the summary claim to settings where CD is applicable.
minor comments (5)
  1. [Eq. (8) / Algorithm 4] Eq. (8) is labeled a 'Monte Carlo estimator' in Algorithm 4, but it is a deterministic top-M weighted sum. Rename it to 'weighted top-M estimator' to avoid confusion.
  2. [Section 4.3, after Eq. (5)] The text says 'As bFx(m) is an unbiased estimator of Fx(m), we obtain an approximate root'. The root of an unbiased estimator is not necessarily unbiased; clarify that this is an M-estimator whose consistency requires additional regularity conditions.
  3. [Table 2] No standard errors, confidence intervals, or significance tests are reported. Given that M=10 and results appear to come from a single seed, please report variance across seeds or bootstrap intervals.
  4. [Appendix E.6] The effective prompt-level bound B_eff includes a 1.5 scaling factor for CD that is not present for ARGS. The theoretical bound B in Program (3) is therefore not the same object used in experiments; clarify how the scaling factor is chosen and whether it affects the optimality guarantees.
  5. [Footnote 1 / Section 4.3] The value k=exp(B/β) is clipped at 2 in experiments. Since the theoretical weight in F_x(m) is exp(B/β), clipping changes the objective; state whether the clipping is applied before or after computing the root and whether the optimality guarantee still applies.

Circularity Check

0 steps flagged

No circular derivation: the threshold-optimality theorem is derived from the Stackelberg program, not assumed; Eq. (8) is an unsupported estimator but not a circular reduction.

full rationale

The central derivation is self-contained. Problem (3) optimizes over all reward models r, and Lemma 2/Theorem 1 derive the threshold structure from KKT stationarity and complementary slackness rather than assuming it. Theorem 2 constructs F_x(m), proves the identity F_x(m)=Z_{r_m}(x)(E_{ρ_{r_m}}[r_U]-m), and derives continuity/strict monotonicity, so the root characterization is a genuine mathematical equivalence, not a definitional restatement. The Monte Carlo estimator in Eq. (5) is an unbiased plug-in for F_x(m), and SRS(soft) is explicitly introduced as a continuous relaxation whose limits are proven in Theorem 3. No load-bearing result is imported from the authors' prior work: the only self-citation (Kong et al. 2024, RE-Control) appears in related work and implementation adaptation, not in the proof chain. The main caveats are correctness/rigor concerns, not circularity. First, Eq. (8) is called a Monte Carlo estimator but is, as the paper admits, a 'variant' using deterministic top-M candidates weighted by base probability; it is a truncated sum with unquantified bias, not an unbiased estimator of F_x(m), so the SRS-ARGS experiments do not by themselves certify the theoretical threshold. Second, Corollary 1 is stated as an 'immediate consequence' with no proof, and the main-text theorems rely on a finite-response assumption stated only in the appendix. These weaken the empirical and rigor claims without making the derivation circular. The reported average-reward metric uses the same r_U that defines the shaping, and B/α are selected on a validation split of that metric, but this affects external validity of the evaluation, not the logical reduction of the proof chain.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 0 invented entities

The central derivation relies on standard RLHF assumptions plus several tuned hyperparameters (B, α, 1/β, scaling factor, k-clip, M) that are selected on validation data. No new physical or conceptual entities are postulated; the main unproved leap is the per-token ARGS estimator.

free parameters (6)
  • Reward bound B = 5, 8, 10, 12, or 15 depending on eval setting (Table 7)
    Global upper bound on shaped rewards; selected via validation sweep over {5,8,10,12,15}. Controls how far the policy can deviate from the base policy.
  • Shaping strength α = 1.0, 1.5, or 2.0 depending on eval setting (Table 7)
    Sigmoid sharpness in SRS(soft); selected via validation sweep over {1.0,1.5,2.0}. The theoretical optimum is the α→∞ limit, but finite α is tuned for stability.
  • Reward strength 1/β = 0.5 for ARGS, 1.5 for CD
    Chosen on validation as the value with best performance before onset of reward hacking or oversteering (Appendix E.7). Shared across all methods in a setting.
  • Effective-bound scaling factor = 1.5 for SRS-CD, 1.0 for SRS-ARGS
    Hand-set in Appendix E.6 to convert the global B into a prompt-level bound B_eff = min(scale*(rmax-rmin), B). Not derived from the theory.
  • k clipping at 2 = 2
    In Eq. 5, k=exp(B/β) is clipped to 2 for numerical stability (Appendix E.6), changing the theoretical threshold equation.
  • Monte Carlo sample size M = 10
    Fixed at 10 for all main experiments (Appendix E.7); larger M gives slightly better SRS-ARGS reward (Table 5) but is not tuned in the main results.
axioms (6)
  • domain assumption User utility is represented by a scalar reward function rU, and publicly available learned reward models are valid proxies for rU.
    Section 3.1 and Section 6.1; the entire objective and evaluation assume rU is the true user utility.
  • domain assumption The follower's best response is exactly the KL-regularized exponential-tilting policy in Eq. (2).
    Section 3.1; this is the standard RLHF/DPO policy form, but the theoretical results are stated for this exact policy and not for arbitrary decoding heuristics.
  • domain assumption Bounding the reward by B mitigates reward hacking.
    Constraint C2 in Program (3), justified by prior work (Fu et al. 2025) and by the paper's own empirical study in Appendix C.1.
  • standard math The response space Y is finite and [0,B]^N is compact, so KKT conditions apply to the leader's problem.
    Lemma 2 and the proof of Theorem 1 in Appendix D.1 require finite N for the Lagrangian argument.
  • ad hoc to paper The weighted per-token estimator in Eq. (8) approximates the trajectory-level expectation over ρbase in ARGS.
    Appendix B.2 introduces Eq. (8) without a convergence or consistency proof; the empirical ARGS results depend on this assumption.
  • domain assumption GPT-4 judge scores are a valid measure of alignment quality and detect reward hacking.
    Section 6.4 uses GPT-4 head-to-head win-tie rates as the complementary quality metric, following prior work.

pith-pipeline@v1.3.0-alltime-deepseek · 29388 in / 13634 out tokens · 156116 ms · 2026-08-03T05:58:27.334625+00:00 · methodology

0 comments
read the original abstract

Existing alignment methods directly use the reward model learned from user preference data to optimize an LLM policy, subject to KL regularization with respect to the base policy. This practice is suboptimal for maximizing user's utility because the KL regularization may cause the LLM to inherit the bias in the base policy that conflicts with user preferences. While amplifying rewards for preferred outputs can mitigate this bias, it also increases the risk of reward hacking. This tradeoff motivates the problem of optimally designing reward models under KL regularization. We formalize this reward model optimization problem as a Stackelberg game, and show that a simple reward shaping scheme can effectively approximate the optimal reward model. We empirically evaluate our method in inference-time alignment settings and demonstrate that it integrates seamlessly into existing alignment methods with minimal overhead. Our method consistently improves average reward and achieves win-tie rates exceeding 66% against all baselines, averaged across evaluation settings.

Figures

Figures reproduced from arXiv: 2602.02572 by Ce Li, Haichuan Wang, Hezi Jiang, Lingkai Kong, Milind Tambe, Tao Lin.

Figure 1
Figure 1. Figure 1: We illustrate the Stackelberg game formulation of LLM alignment. In this framework, [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Reward and GPT-4 win-tie rate as a function of the inference-time reward strength [PITH_FULL_IMAGE:figures/full_fig_p025_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Solid lines correspond to the left axis (Reward) and dashed line corresponds to the right [PITH_FULL_IMAGE:figures/full_fig_p026_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Solid lines correspond to the left axis (Reward) and dashed line corresponds to the right [PITH_FULL_IMAGE:figures/full_fig_p026_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Controlled Decoding (CD) performance as a function of reward strength. Performance [PITH_FULL_IMAGE:figures/full_fig_p028_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Controlled Decoding (CD) performance as a function of reward strength. Figure [PITH_FULL_IMAGE:figures/full_fig_p029_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Prompt Template for the GPT-4 Evaluation. [PITH_FULL_IMAGE:figures/full_fig_p039_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Qualitative examples showing the alignment performance of SRS. [PITH_FULL_IMAGE:figures/full_fig_p040_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Qualitative examples showing the alignment performance of SRS. [PITH_FULL_IMAGE:figures/full_fig_p041_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Qualitative examples showing the alignment performance of SRS. [PITH_FULL_IMAGE:figures/full_fig_p041_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Qualitative examples showing the alignment performance of SRS. [PITH_FULL_IMAGE:figures/full_fig_p042_11.png] view at source ↗

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Forward citations

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Reference graph

Works this paper leans on

39 extracted references · 22 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Persistent anti-muslim bias in large language models

    Abubakar Abid, Maheen Farooqi, and James Zou. Persistent anti-muslim bias in large language models. InProceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society, pages 298–306,

    2021

  2. [3]

    In contrast, when B is large, expected user utility initially increases with α but eventually degrades

    Even in the limit α→ ∞which we implement SRS (hard), performance remains stable due to the tight reward bound. In contrast, when B is large, expected user utility initially increases with α but eventually degrades. When both B and α are large, SRS (hard) assigns large rewards to a subset of tokens while leaving others unaugmented, resulting in a highly im...

    2024

  3. [5]

    Self-play fine-tuning converts weak language models to strong language models.arXiv preprint arXiv:2401.01335,

    Zixiang Chen, Yihe Deng, Huizhuo Yuan, Kaixuan Ji, and Quanquan Gu. Self-play fine-tuning converts weak language models to strong language models.arXiv preprint arXiv:2401.01335,

    Pith/arXiv arXiv

  4. [6]

    Stackelberg game preference optimization for data-efficient alignment of language models.arXiv preprint arXiv:2502.18099,

    Xu Chu, Zhixin Zhang, Tianyu Jia, and Yujie Jin. Stackelberg game preference optimization for data-efficient alignment of language models.arXiv preprint arXiv:2502.18099,

    arXiv

  5. [7]

    Ultrafeedback: Boosting language models with scaled ai feedback

    Ganqu Cui, Lifan Yuan, Ning Ding, Guanming Yao, Bingxiang He, Wei Zhu, Yuan Ni, Guotong Xie, Ruobing Xie, Yankai Lin, et al. Ultrafeedback: Boosting language models with scaled ai feedback. arXiv preprint arXiv:2310.01377,

    Pith/arXiv arXiv

  6. [10]

    The llama 3 herd of models.arXiv preprint arXiv:2407.21783,

    Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The llama 3 herd of models.arXiv preprint arXiv:2407.21783,

    Pith/arXiv arXiv

  7. [12]

    Principal-agent reinforcement learning: Orchestrating ai agents with contracts.arXiv preprint arXiv:2407.18074,

    Dima Ivanov, Paul D¨ utting, Inbal Talgam-Cohen, Tonghan Wang, and David C Parkes. Principal-agent reinforcement learning: Orchestrating ai agents with contracts.arXiv preprint arXiv:2407.18074,

    Pith/arXiv arXiv

  8. [13]

    Self-play with adversarial critic: Provable and scalable offline alignment for language models.arXiv preprint arXiv:2406.04274,

    15 Xiang Ji, Sanjeev Kulkarni, Mengdi Wang, and Tengyang Xie. Self-play with adversarial critic: Provable and scalable offline alignment for language models.arXiv preprint arXiv:2406.04274,

    Pith/arXiv arXiv

  9. [14]

    Regularized best-of-n sampling to mitigate reward hacking for language model alignment

    Yuu Jinnai, Tetsuro Morimura, Kaito Ariu, and Kenshi Abe. Regularized best-of-n sampling to mitigate reward hacking for language model alignment. InICML 2024 Workshop on Models of Human Feedback for AI Alignment,

    2024

  10. [15]

    Args: Alignment as reward-guided search

    Maxim Khanov, Jirayu Burapacheep, and Yixuan Li. Args: Alignment as reward-guided search. arXiv preprint arXiv:2402.01694,

    Pith/arXiv arXiv

  11. [16]

    Hadas Kotek, Rikker Dockum, and David Sun

    URLhttps://arxiv.org/abs/2406.05954. Hadas Kotek, Rikker Dockum, and David Sun. Gender bias and stereotypes in large language models. InProceedings of the ACM Collective Intelligence Conference, pages 12–24,

    Pith/arXiv arXiv

  12. [17]

    Culture-gen: Revealing global cultural perception in language models through natural language prompting.arXiv preprint arXiv:2404.10199,

    Huihan Li, Liwei Jiang, Jena D Hwang, Hyunwoo Kim, Sebastin Santy, Taylor Sorensen, Bill Yuchen Lin, Nouha Dziri, Xiang Ren, and Yejin Choi. Culture-gen: Revealing global cultural perception in language models through natural language prompting.arXiv preprint arXiv:2404.10199,

    Pith/arXiv arXiv

  13. [18]

    Red: Unleashing token-level rewards from holistic feedback via reward redistribution

    Jiahui Li, Lin Li, Tai-Wei Chang, Kun Kuang, Long Chen, Jun Zhou, and Cheng Yang. Red: Unleashing token-level rewards from holistic feedback via reward redistribution. InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 4993–5022,

    2025

  14. [19]

    Skywork-reward-v2: Scaling preference data curation via human-ai synergy.arXiv preprint arXiv:2507.01352,

    Chris Yuhao Liu, Liang Zeng, Yuzhen Xiao, Jujie He, Jiacai Liu, Chaojie Wang, Rui Yan, Wei Shen, Fuxiang Zhang, Jiacheng Xu, et al. Skywork-reward-v2: Scaling preference data curation via human-ai synergy.arXiv preprint arXiv:2507.01352,

    Pith/arXiv arXiv

  15. [20]

    Controlled decoding from language models.arXiv preprint arXiv:2310.17022,

    Sidharth Mudgal, Jong Lee, Harish Ganapathy, YaGuang Li, Tao Wang, Yanping Huang, Zhifeng Chen, Heng-Tze Cheng, Michael Collins, Trevor Strohman, et al. Controlled decoding from language models.arXiv preprint arXiv:2310.17022,

    Pith/arXiv arXiv

  16. [21]

    Of models and tin men: a behavioural economics study of principal-agent problems in ai alignment using large-language models.arXiv preprint arXiv:2307.11137,

    Steve Phelps and Rebecca Ranson. Of models and tin men: a behavioural economics study of principal-agent problems in ai alignment using large-language models.arXiv preprint arXiv:2307.11137,

    Pith/arXiv arXiv

  17. [22]

    Direct nash optimization: Teaching language models to self-improve with general preferences.arXiv preprint arXiv:2404.03715,

    Corby Rosset, Ching-An Cheng, Arindam Mitra, Michael Santacroce, Ahmed Awadallah, and Tengyang Xie. Direct nash optimization: Teaching language models to self-improve with general preferences.arXiv preprint arXiv:2404.03715,

    Pith/arXiv arXiv

  18. [23]

    Verbosity bias in preference labeling by large language models.arXiv preprint arXiv:2310.10076,

    Keita Saito, Akifumi Wachi, Koki Wataoka, and Youhei Akimoto. Verbosity bias in preference labeling by large language models.arXiv preprint arXiv:2310.10076,

    Pith/arXiv arXiv

  19. [24]

    Improv- ing reinforcement learning from human feedback using contrastive rewards.arXiv preprint arXiv:2403.07708,

    Wei Shen, Xiaoying Zhang, Yuanshun Yao, Rui Zheng, Hongyi Guo, and Yang Liu. Improv- ing reinforcement learning from human feedback using contrastive rewards.arXiv preprint arXiv:2403.07708,

    Pith/arXiv arXiv

  20. [25]

    Robust multi-objective controlled decoding of large language models.arXiv preprint arXiv:2503.08796,

    Seongho Son, William Bankes, Sangwoong Yoon, Shyam Sundhar Ramesh, Xiaohang Tang, and Ilija Bogunovic. Robust multi-objective controlled decoding of large language models.arXiv preprint arXiv:2503.08796,

    arXiv

  21. [26]

    A minimaxi- malist approach to reinforcement learning from human feedback.arXiv preprint arXiv:2401.04056,

    Gokul Swamy, Christoph Dann, Rahul Kidambi, Zhiwei Steven Wu, and Alekh Agarwal. A minimaxi- malist approach to reinforcement learning from human feedback.arXiv preprint arXiv:2401.04056,

    Pith/arXiv arXiv

  22. [27]

    Transforming and combining rewards for aligning large language models.arXiv preprint arXiv:2402.00742,

    Zihao Wang, Chirag Nagpal, Jonathan Berant, Jacob Eisenstein, Alex D’Amour, Sanmi Koyejo, and Victor Veitch. Transforming and combining rewards for aligning large language models.arXiv preprint arXiv:2402.00742,

    Pith/arXiv arXiv

  23. [28]

    Genarm: Reward guided generation with autoregressive reward model for test-time alignment.arXiv preprint arXiv:2410.08193,

    Yuancheng Xu, Udari Madhushani Sehwag, Alec Koppel, Sicheng Zhu, Bang An, Furong Huang, and Sumitra Ganesh. Genarm: Reward guided generation with autoregressive reward model for test-time alignment.arXiv preprint arXiv:2410.08193,

    Pith/arXiv arXiv

  24. [29]

    Qwen3 technical report.arXiv preprint arXiv:2505.09388,

    17 An Yang, Anfeng Li, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Gao, Chengen Huang, Chenxu Lv, et al. Qwen3 technical report.arXiv preprint arXiv:2505.09388,

    Pith/arXiv arXiv

  25. [30]

    Iterative nash policy optimization: Aligning llms with general preferences via no-regret learning.arXiv preprint arXiv:2407.00617,

    Yuheng Zhang, Dian Yu, Baolin Peng, Linfeng Song, Ye Tian, Mingyue Huo, Nan Jiang, Haitao Mi, and Dong Yu. Iterative nash policy optimization: Aligning llms with general preferences via no-regret learning.arXiv preprint arXiv:2407.00617,

    Pith/arXiv arXiv

  26. [31]

    Fair-pp: A synthetic dataset for aligning llm with personalized preferences of social equity

    Qi Zhou, Jie Zhang, Dongxia Wang, Qiang Liu, Tianlin Li, Jin Song Dong, Wenhai Wang, and Qing Guo. Fair-pp: A synthetic dataset for aligning llm with personalized preferences of social equity. arXiv preprint arXiv:2505.11861,

    Pith/arXiv arXiv

  27. [32]

    18 A Additional Related Work: Algorithmic Contract Design Algorithmic Contract DesignContract design studies how a principal can design incentive mechanisms (contracts) to align an agent’s actions with her objectives. This framework has been extensively studied in economics Holmstr¨ om [1979], Grossman and Hart [1992], leading to conceptual breakthroughs ...

    1979

  28. [33]

    [2024], Ivanov et al

    and inspiring several approaches that apply contract-based ideas to align agents in multi-agent settings Haupt et al. [2024], Ivanov et al. [2024]. Three lines of work are most closely related to ours. The first is Hadfield-Menell and Hadfield [2019], which interprets the reward model in alignment as a contract and explains reward hacking through the lens...

    2024

  29. [34]

    also studies principal–agent problem arising in LLM service providing, though their agent is the service provider, whereas in our setting the LLM itself is the agent. A.1 The Classical Contract Model In contract design, a principal commits to an incentive contract to induce an agent 5 to act in alignment with the principal’s objective [Holmstr¨ om, 1979]....

    1979

  30. [35]

    The model generates responses for 1,000 test prompts, of which 300 are randomly selected for GPT-4 evaluation against base-policy answers generated without alignment

    on Qwen3-8B with greedy decoding on the HH-RLHF dataset. The model generates responses for 1,000 test prompts, of which 300 are randomly selected for GPT-4 evaluation against base-policy answers generated without alignment. The evaluation follows the same protocol as our main experiments. We sweep the reward strength {0.5, 1.0, 1.5, 2.0}. At low reward st...

    2025

  31. [37]

    This behavior indicates that the learned value function ˆQ(st,y ) fails to provide a meaningful estimate of the reward for expected model completions

    As the reward strength increases, CD performance degrades rapidly, with noticeable drops even at small reward strength. This behavior indicates that the learned value function ˆQ(st,y ) fails to provide a meaningful estimate of the reward for expected model completions. We next repeat the experiment using the UltraRM reward model. UltraRM-13b [Cui et al.,...

    2023

  32. [38]

    Recall we also have ˆQr ˆm∗,α(st, yt)≤r max ≤B

    Therefore Cβ(st) ≥ P yt πbase(yt|st) = 1, which implies logC β(st) ≥ 0 ∀st. Recall we also have ˆQr ˆm∗,α(st, yt)≤r max ≤B. Hence, log ˆρr ˆm∗,α(y|x) ρbase(y|x) ≤ 1 β T B. Plug in Eq. (12) we conclude that DKL ˆρr ˆm∗,α(y|x), ρbase(y|x) ≤ 1 β T B. E Experiment Details E.1 Computing Infrastructure Our experiment is done on a cluster wth NVIDIA A100 (80GB V...

    2024

  33. [39]

    ""USER_PROMPT =

    Hyperparameters are selected using a validation sweep over B∈ {5, 8, 10, 12, 15} and α∈ {1.0, 1.5, 2.0}. Vanilla inference-time methods and MEANSTD do not involve tunable hyperparameters and are therefore omitted from the table. E.8 GPT-4 Evaluation Following Khanov et al. [2024], Chakraborty et al. [2024], we use a GPT-based judge to conduct head-to-head...

    2024

  34. [1992]

    Incomplete contracting and ai alignment

    Dylan Hadfield-Menell and Gillian K Hadfield. Incomplete contracting and ai alignment. In Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society, pages 417–422,

    2019

  35. [2021]

    Training a helpful and harmless assistant with reinforcement learning from human feedback.arXiv preprint arXiv:2204.05862,

    Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, Deep Ganguli, Tom Henighan, et al. Training a helpful and harmless assistant with reinforcement learning from human feedback.arXiv preprint arXiv:2204.05862,

    Pith/arXiv arXiv

  36. [2022]

    Reward shaping to mitigate reward hacking in rlhf.arXiv preprint arXiv:2502.18770,

    Jiayi Fu, Xuandong Zhao, Chengyuan Yao, Heng Wang, Qi Han, and Yanghua Xiao. Reward shaping to mitigate reward hacking in rlhf.arXiv preprint arXiv:2502.18770,

    arXiv

  37. [2023]

    Simple versus optimal contracts

    Paul D¨ utting, Tim Roughgarden, and Inbal Talgam-Cohen. Simple versus optimal contracts. In Proceedings of the 2019 ACM Conference on Economics and Computation, pages 369–387,

    2019

  38. [2024]

    Strategyproof reinforcement learning from human feedback.arXiv preprint arXiv:2503.09561,

    Thomas Kleine Buening, Jiarui Gan, Debmalya Mandal, and Marta Kwiatkowska. Strategyproof reinforcement learning from human feedback.arXiv preprint arXiv:2503.09561,

    arXiv

  39. [2025]

    Parl: A unified framework for policy alignment in reinforcement learning from human feedback.arXiv preprint arXiv:2308.02585,

    Souradip Chakraborty, Amrit Singh Bedi, Alec Koppel, Dinesh Manocha, Huazheng Wang, Mengdi Wang, and Furong Huang. Parl: A unified framework for policy alignment in reinforcement learning from human feedback.arXiv preprint arXiv:2308.02585,

    Pith/arXiv arXiv