GoalRank: Group-Relative Optimization for a Large Ranking Model
Authors: Kaike Zhang
Xiaobei Wang
Shuchang Liu
HailanYang
Xiang Li
Lantao Hu
Han Li
Qi Cao
Fei Sun
Kun Gai
Venue: ICLR 2026 Poster (2026)
Keywords: Recommender System
Re-ranking
Large Ranking Model
Group-Relative Optimization
Primary area: other topics in machine learning (i.e., none of the above)

Abstract: Mainstream ranking approaches typically follow a Generator–Evaluator two-stage paradigm, where a generator produces candidate lists and an evaluator selects the best one. Recent work has attempted to enhance performance by expanding the number of candidate lists, for example, through multi-generator settings. However, ranking involves selecting a recommendation list from a combinatorially large space, simply enlarging the candidate set remains ineffective, and performance gains quickly saturate. At the same time, recent advances in large recommendation models have shown that end-to-end one-stage models can achieve promising performance with the expectation of scaling laws. Motivated by this, we revisit ranking from a generator-only one-stage perspective. We theoretically prove that, for any (finite Multi-)Generator–Evaluator model, there always exists a generator-only model that achieves strictly smaller approximation error to the optimal ranking policy, while also enjoying a scaling law as its size increases. Building on this result, we derive an evidence upper bound of the one-stage optimization objective, from which we find that one can leverage a reward model trained on real user feedback to construct a reference policy in a group-relative manner. This reference policy serves as a practical surrogate of the optimal policy, enabling effective training of a large generator-only ranker. Based on these insights, we propose GoalRank, a generator-only ranking framework. Extensive offline experiments on public benchmarks and large-scale online A/B tests demonstrate that GoalRank consistently outperforms state-of-the-art methods.

group-relative GOALRANK: GROUP-RELATIVE OPTIMIZATION FOR A
LARGE RANKING MODEL
Kaike Zhang 1.2t
Xiaobei Wang Han Lif
Shuchang Liu
Hailan Yang*
Xiang Li* Kun Gai
Lantao Hu
Qi Cao
Fei Sun
1 Kuaishou Technology, Beijing, China
2 University of Chinese Academy of Sciences, Beijing, China (kaikezhang99, caoqi 92seven ofey ofey. wangxiaobe 03, 1 liushuchang, yanghai ] (uuua shou. com [1ix 1ixiang44, hulantao, 1 1ihan08, yuyue06) kua shou. com
sunfei sunffeunfe]] (unffiieegmaill @egmail. con
ABSTRACT
Mainstream ranking approaches typically follow Generator- Seneertoo-Evallutoo two-stage paradigm, where generator produces candidate lists and an evaluator selects the best one. Recent work has attempted to enhance performance by expanding the number of candidate lists, for example, through multi multi-generator settings. How- ever, ranking involves selecting a recommendation list from combinatorially large space, simply enlarging the candidate set remains ineffective, and perfor- mance gains quickly saturate. At the same time, recent advances in large rec- ommendation models have shown that end-to-end one-stage models can achieve promising performance with the expectation of scaling laws. Motivated by this, we revisit ranking from generator-only one-stage perspective. We theoretically prove that, for any (finite Mullt-)GGeneratr-EEvlllll Evaluutto model, there always exists generator-only model that achieves strictly smaller approximation error the optimal ranking policy, while also enjoying a scaling law as its size increases. Building on this result, we derive an evidence upper bound of the one-stage op- timization objective, from which we find that one can leverage a reward model trained on real user feedback construct reference policy manner. This reference policy serves practical surrogate of the optimal pol- icy, enabling effective training of large generator-only ranker. Based on these insights, we propose GoalRank, a generator-only ranking framework. Extensive offline experiments on public benchmarks and large-scale online A/B tests demon- strate that GoalRank consistently outperforms statc-of-the-arr methods.
INTRODUCTION
Recommender systems are indispensable for coping with the exponential growth of online con- tent (Gomez- Uribe & Hunt 2015). Industrial platforms typically adopt a multi-stage pipeline, com- prising retrieval (He et al.) 2020 Zhang et al. (024) and ranking (Yu et al.) [019 Liu et al.) [2023 Zhang et al. 2025b). The ranking stage is particularly critical, as it determines the final sequence of items shown to users and has major impact both user satisfaction and platform revenue.
Formally, the ranking task can be defined as an N list-generation problem:
given candidates from the preceding stage, the model outputs ordered list of length L. The search space is the set of length-L permutations, P(N, L) = N!
(N-L)? which makes exhaustive enumeration intractable for
large N. Early approaches adopt one-stage single generator that directly produces recommen- dation lists by scoring items and arranging them greedily (Zhuang al., 2018 Ai et al., 2018 Pei et al. 2019a] Gong et al. [022] Liu et al. 2023), as illustrated in Figure Ia). However, this greedy strategy only models the item interdependencies in the candidate set (of size N) but not the output list (of size L), often resulting in suboptimal rankings.
Equual contribution. Corresponding author.

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Items
L Items
HiIl Budesis
G
Performance (%)
Plateauing
Rec. List
Candidate Generator.onll
E
G
Plateauing
Evalustor
Cundidate Rec. Lists
Nunder
(b) Snneratoo-Evaluatoo
(e) Muutf--Goerrtto--Eaaaae Exvllttto
Performance Amazon
Figure 1: Illustration of different ranking paradigms: (a) Generator-only; (b) Generator-Evaluucee
(c) multi-Generator- Generator-Evaluatoo,, and (d) Performance trend with increasing number of generators.
To address this limitation, subsequent studies propose two-stage Generator-Evaluatte paradigm (Shi et al. [023] Xi et al.] 2024 Lin et al., 2024; Ren et al.) 2024b] Zhang et al., 2025b)
(Figure [p:: generator first proposes multiple candidate lists, and an evaluator then selects the best one according to estimated list-wise value. To mitigate the risk that generators produce only locally optimal candidates, later works introduce multi-generator settings (Figure[T)) thereby increasing both the number and diversity of candidate lists. In practice, however, simply scaling the number of candidates or generators yields diminishing returns, with performance gains quickly plateauing (Figure ld).
Meanwhile, advances in end-to-end, one-stage large recommendation models suggest that a single sufficiently expressive model can subsume stult pipelines, avoid cross-stage inconsistencies, and exhibit favorable scaling behavior (Zhai et al., 2024; Deng et al. 2025).. These findings indi- cate that the two-stage Generator-Fvaluatov paradigm may not be indispensable for achieving high- quality ranking, Motivated by this, we revisit the generator-only paradigm and ask: can larger, more powerful one-stage ranker directly produce high-quality lists without relying on an external evaluator? Formally, let nT" denote the optimal ranking policy. We focus on two central questions:
For any (fiite Multi- EieeerratorEEvluaate system, does there exist single generator-only model whose policy achieves a strictly smaller approximation error with respect n"?
i If such model exists, how can it be trained effectively to realize this approximation advantage practice?
To answer these questions, we analyze (in Section 3.1 the approximation error between the pol- icy space induced by a finite set of -eeeeattrnneeeeeaiiiaaa policy π¹ This analysis proves the existence of generator-onfy model that can achieve a strictly smaller approximation error. Moreover, model increases, its approximation error with respect to π decreases accordingly. Building on these theoretical insights, we then turn to the practical challenge of how to train such one-stage ranking model. By deriving an evidence upper bound of the existing optimization objective, we find that can leverage reward model trained a group-relative manner, which serves as a surrogate for x². This enables us to train a large generator-only ranking model effectively. Based this idea, we propose GoalRank (Group-Relative OptimizAtion Atioi for Large Ranker). We validate the effectiveness of GoalRank on public benchmarks as well as through large-scale online A/B tests, showing substan- tial improvements over state-of- of-the-art baselines and clear evidence of scaling laws.
models and the optimal ranking
show that as the size of this generator-only ranking
real user feedback to construet reference policy
training framework,
The main contributions of this work can be summarized follows:
Theoretical foundation. We prove that for any (finite JGenerator-Evaluueee family, there always exists a generator-only model that achieves strictly smaller approximation error to the optimal ranking policy, and that this error decreases as model size increases (scaling law).
Optimization principle. We introduce the Group-Relativ optimization principle, which pro- vides tractable and effective criterion for training large generator-only ranking models.
Model and validation. We instantiate these ideas in GoalRank, generator-only large ranker trained under the proposed principle. Extensive offline experiments and online A/B tests demon-
2

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strate consistent improvements strong baselines and reveal clear scaling laws with respect to model capacity.
RELATED WORK AND PRELIMINARIES
The ranking task in recommender systems can be formulated as an N-L list- iist-generation problem: given N candidate items, the model outputs ordered list of length L. Let U and V denote the user and item sets. For each user the candidate set is Vu C V with [Vll = N. The generation space is
Lu = (
V v + + (i 5)},
C P(N, L) = (N-L)!
Since P(N,L L) is exponentially large, existing works build approximate ranking paradigms to ex- plore this space.
Single-Stage Generator- Onll Models. A straightforward solution is to use a single generator G
that scores items and constructs list greedily (Zhuang al. 20018 Ai al. 2018
Pei et al. 2019a
Gong et al., 2022 Liu et al. 2023 Feng et al. 2021b Xi et al. 2022 Pei et al. 2019b). Classic
models include DLCM (Ai et 2018) and PRM (Pei et 2019a). which refine item scores using
local listwise features. Formally:
G( V.). 1
Although efficient, these methods typically underexplore inter-item dependencies and may not re- main consistent with the conditioning of the original candidate set.
Two-Stage Generator-Evaluatoo Paradigm. To better address the combinatorial N-*L search space, recent work adopts a two-stage (multi-)Generator-- |Generator--vvlluatoo (G-E) framework (Chen et al. 2022 Shi et al. 2023 Xi et al. 2024 Lin et al. 2024 Ren et al. 2024b Wang al.) 2025b). A generator produces multiple candidate lists, and an evaluator scores them to select the best one:
1 arg max E(X.,,), I), LELu,F
Lu, = (G, V.) I,...,
The special case 1=1 reduces to Lungle-generato--vaaluee
model. Multi-generator extensions (k > 1) aim to enlarge the proposal space (Yang et al., (025). but empirical gains saturate rapidly as k grows. This diminishing return suggests that merely increasing the number of generators is inefficient and highlights the need for fundamentally stronger listwise modeling.
Other Directions. Other concurrent efforts incorporate large language models (Ren et al. 2024a
Gao et al. 2024 Wu et al., 2024 Gao et al.
2025 Ren al. 2025 Liu al. 2025) reinforcement
learning Feng et al.] [202cc] Wang et al.
2024
2025c Wei et al. 2020). LLM- methods
leverage textual side information, while RL based approaches decompose the listwise value function to align rankings with user utility.
METHODOLOGY
In this section, we address the research questions raised in Section [] namely: (i) can the generator- only paradigm outperform the Multii-Geeneratt--EEVluuuut paradigm, and (ii) if so, how can such generator-only ranking model be effectively learned? Building on the insights gained from these analyses, we then propose new generator-only large ranker framework, GoalRank, which lever- ages group-relative optimization to approximate the optimal ranking policy.
3.1
CAN THE EITERATOR-ONLA PARADIGM PERFORM BETTER?
To assess the feasibility of a single-stage large ranking model, we first ask whether a sufficiently large generator-only model can match even exceed the expressive power of the widely used two- stage (Multi- Seattii)Gneertttor Erenerator-Evaluator pipeline. Formally, suppose there exists an optimal ranking pol- icy x². We compare the best attainable approximation error of (i) a k-mixture of small generators combined with an evaluator, and (ii) single larger generator. To make this comparison precise, we begin by defining capacity-restrrited generator class.
3

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Definition ((a,B) By-bounded generator class). Given maximum generator width and depth B, the (a, 33-Bbundedddd generator class is defined as
9m (a, 3) = { 9m
W(gm) a, D(gm) S }
where 9m denotes generator, and (-) and D(-) measure width- and depth-type complexities, respectively.
Then, the evaluator can regarded as operating over a low-dimensional probability simplex, which determines how multiple small generators jointly influence the final ranking policy.
Definition (k-mixture (a, 3)-bounded policy space). The policy space induced by Gm (m, 8) is
8)
softmaxo Im. 9m E (m, ()
which contains all policies realizable by single generator in (a, 3) with a softmax output layer. Given k generators in 9m(a,,3) B) and an evaluator, the corresponding k-mixture (ar, B)-bounded policy space is
ch (a, = {Ei WEA Fm(a,
where A k-1 is the (k - 11 1)-dimensional probability simplex and w (wi, wk) satisfies E Wi 1 and 0.
In Definition 2 we adopt soft mixture weights w. In practice, the evaluator often implements (or approximates) hard selection (one-hot w). Thus, C* (a. 5) strictly contains the policy class real- ized by hard selection, which can both simplifies subsequent derivations and strengthens Theorem Then, to evaluate how well a policy space approximates the optimal ranking policy л² we use the following notion.
Definition 3 (Approximation distance (KL error)). Let T² be a target policy and F be policy space. The approximation distance from to x." is
Σ (1) log " 7²
E(F) = inf (I(
<I(='|<>)
REF
(7()
IEC.
where C denotes the finite space of candidate lists considered by the ranker.
With these definitions place, we can now state our main result.
Theorem Given a, 3 and any E Nso- For the k-mixture policy space C (a, 3) in Definition 2 there exists class of larger generators
(,,(,,,,) = { gM
(gg)) 2 k + n, D(gM) 2 B}, n E N
with associated policy space
Fas B, = {softmaxo gas gMr E Gar(a, }
such that
E ((Far(a,B,1))
< E(ch, (a, (a, 8)),
lim ((Far(a,B,n)) = 0.
Proofs and technical details deferred Appendix Theorem T shows that for any two-stage ranking mixing l small generators, there exists a sufficiently large one-stage generator-only ranking model whose induced policy space achieves strictly smaller approximation error to л²" Moreover, as the size of this generator increases (i.e., as n grows). the approximation error can be driven arbitrarily close zero. We remark that Theorem [ is stated in terms of width scaling: the same conclusion holds under depth scaling, with proofs provided in Appendix A
3.2 HOW CAN GENERATOR-ONE RANKING MODEL BE EFFECTIVELY LEARNED?
According to Theorem our goal is to train a larger generator- only ranking model that can achieve closer approximation the optimal ranking policy n² Suppose have access ideal reward
4

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model (1) that provides unbiased estimate of the user feedback for any candidate list E Cu of user We define the entropy-ree regula--egulrrized oracle policy as
arg max Re (r (1) + =
where H(T denotes the entropy of the policy, introduced as a regularization term to avoid greedy instability and to encourage exploration, and 7 >> controls the strength of entropy regularization.
Optimizing Equation yields the Boltzmann distribution
(esp(r(()/))
Z Σ (xp()
Moreover, the objective in Equation caan be equivalently rewritten
E [r" (1) + +((TT) Σ T(1) (1og exp(r"()/r) - (() + log Z).
Thus, T log sup Blaaa (0]++
and the supremum is attained if and only if (L(T|T]T) 0. In this case, the objective achieves its maximum. Therefore, optimizing π is equivalent to minimizing the KL divergence to π².
In practice, however, the ideal reward model r (1) is inaccessible. We therefore consider poten- tially biased reward model f(I) = (1) + b(l). where b(l) denotes the bias. Intuitively, the smaller the bias, the more reliable the reward model. When considering list group B, if the reward gaps among lists are sufficiently large, the contribution of (1) dominates the bias b(l), such that the (partial) order over B is approximately preserved. Formally, given a threshold o² 0, if
max F(4) f(4,) > o", E
(3)
we can exploit this
to construct a reference policy in a group-relative manner: exp (F(I) rB)/08)
re (1 (B) En exp (F(() rB)/OB)
(4)
where fg and og are the mean and standard deviation of f over B. We then train parametric policy no to align with no by minimizing the cross- cross-entropy (equivalently, the KL divergence up to constant): Finally, the training objective can be expressed as
((TT) = - -EB-D
Σ
π rof (1 B3) log To (1)
(5)
LiEB
This objective provides tractable surrogate for minimizing KL(TTol using only & and group- relative normalization.
3.3 GOALRANK
Based the above insights, we propose practical training framework for large ranking models in real-world recommendation scenarios.
Reward modeling. Following al. (025b),, first train reward model f using real user feedback data, which can estimate the expected feedback for a given recommendation list (details are provided in Appendix B).
Generator and policy. As illustrated in Figure given generator ga. the corresponding ranking policy is defined my = softmaxo go. Conditioned on context Xx, and the candidate item set Vu provided by the preceding stage, the generator produces recommendation list as
k arg max (1 [ X., V.))
(6)
Note that this framework is model-agnostic: the generator can be instantiated by any sequence generation model.
Here, the reward value refers the user's actual feedback list, e.g., watch time interaction hchaviors.
5

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Ref. Policy Construction
Reward Distibation
Assilirry Dulley Greup
Son
Infennttion
Generator
Rewurd Model
Pollcy xe (3)
Candidat Remtee
Ranking Policy
Recommerebeiio Group
Minimizing KI. divergence
Figure 2: Training pipeline of group-relative optimization for large ranker, GoalRank.
Group construction. As discussed in the previous section, constructing effective groups requires sufficiently large reward gaps among lists within each group, which is difficult to achieve when sam- pling multiple lists from a single generator. To address this, we introduce an auxiliary set of ranking policies M (including heuristic methods and lightweight neural models with implementation details provided in Appendix Cp. For each user we then construct a group of recommendation lists as
i arg max 7. Xu, Va), ne MM..
As an additional option, all lists in B, can be ranked by their rewards, and a uniformly sampled sub- set can then be selected, which further enforces larger reward gaps within the group and strengthens the validity of the condition in Equation
Training. Given Bu, compute the reference policy r. (B.) via Equation 4 and optimize go by minimizing the loss in Equation 5 instantiated with user-specific groups {Bu} Juzu. This realizes the group-relative principle and provides practical path align Tyy with the oracle policy structure using accessible signals.
4 EXPERIMENT
In this section, we present both offline and online experiments to evaluate the effectiveness of Goal- Rank, which are designed to address the following research questions:
How does GoalRank perform on N ranking tasks compared with state-of-the-art base- lines, and does it exhibit scaling behavior model or data size increases?
RQI:
RQ2: How do (i) the size of recommendation list group B and (ii) the reward model's prediction bias affect GoalRank performance?
RQ3 (online): How does GoalRank perform in real-worle industrial recommendation scenarios?
4.1 OFFLINE EXPERIMENTS
4.1.1
DATASETS AND OFFLINE EXPERIMENTS SETTING
We conduct offline experiments on two public datasets, ML-IM HHaper 2015) and Amazon- Book (McAuley et al. 2013), as well as two datasets of different scales collected from our industrial short-video platform, denoted as Industry and Industry-O. -.11try--.11B. I... The statistics of the four preprocessed datasets are summarized in Appendix [.I
For dataset construction, we first perform an 80/20 temporal split. For each user's interaction history (sorted chronologically), the task is framed as an N-+ list-generation ranking problem with 50 and L 6. Specifically, use pre-trained Matrix Factorization (MF) model (Koren et al.) 2009) as the retriever to select the top-50 candidate items for each user. The last six interactions in each user's 's historical sequence treated ground truth, representing the target list after ranking. For industry datasets, we define a long view (watching a video for more than 85% its duration) as a positive signal, indicating meaningful user-item engagement.

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Table I: Overall performance of different ranking methods. The highest scores are in bold, and the runner-ups are with underlines. All improvements are statistically significant with student t-test p < 0.05. "Improv." denotes the improvements over the best baselines.
ML-IM
Indusity
Book
Methods
H@6
N66
M@6
F1@6
AUC
H66
N@6
M@6
F166
AUC
H66
N@6
M@6
F166
AUC
DNN
56.85
70.30
59.28
62.16
86.87
37.32
54.56
42.38
43.72
74.73
60.28
69.61
58.58
62.45
83.02
DLCM
62.31
73.87
63.82
89.35
75.80
Gaanly
PRS
59.35
73.10
62.51
64.72
88.84
44.75
64.39
51,88
52.59
89.93
66.15
75.70
64.84
68.64
92.01
PRM
60.09
72.85
62.21
65.51
88.20
39.92
55.93
42.97
46 18
85.15
67.86
76.88
66.44
70.42
92.00
MIR
62.22
74.33
64.17
67.97
87.76
37.01
55.79
13.16
11.50
79.95
66.08
71.48
56.62
68.62
91.82
RankMixer
60.88
64.18
91.02
68.03
EGRank
62.76
74.75
64.97
68.46
68.72
40.09
59.01
47.52
47.06
77.44
70.73
80.75
72,40
73.33
89.10
PIER
62.74
75.99
65.98
68.74
90.43
45.35
65.11
52.55
53.35
90.93
71.14
80.22
71.62
73.74
92.26
G-E
NAR4Rec
62.81
75.01
65.42
68.31
88.30
44.31
63.83
51.45
52.08
89.94
70.08
79.46
70.69
72.66
92.44
G-3
55.51
55,52
55.51
60.73
$3.44
68.76
MG-E
G-20
58.66
69.86
58.60
64.18
81.76
52.66
70.70
59.02
61.81
76.46
72.99
78.68
68.66
75.72
77.07
6-100
60.64
70.97
59.93
66, 29
76.48
55.72
72.35
60:95
64.27
75.30
77.21
82.15
73.78
80.00
77.36
GoalRank
73.561
83.43
76.161
80.151
97.641
69.93'
86.931
79.011
82.291
98.077
80.351
84.88
77.91
83.441
94.461
Improw.
+17. 12%
+9.79%
+15
+16.605
45.595
+25.
420.155
63%
0455
+7.73%
(77%)
3.33
6055
Following common practices, we report Hit Ratio@L. (H@L), NDCG@L (N@L). MAP@L
(M@L), F1 @I, and AUC with == 6. Reported results are averaged over five independent runs.
4.1.2 BASELINES
We compare GoalRank against representative satt-oof-the-rr methods from:
These approaches rely on a single generator to produce item scores and directly generate the ranking list. Simple item-wise scoring models such as DNN (Covington et al.,
Generator-only methods:
2016) estimate user feedback independently for each user-item pair, More advanced methods, including DLCM (Ai et al. 2018). PRS (Feng al. 2021a), PRM (Pei et al. (019a)), and MIR (Xi et al. 2022), explicitly capture mutual dependencies among candidate items. We additionally compare with RankMixer (Zhu et al., 2025).
methods: These methods (e.g.. EGRerank (Huzhang et al., 2021 PIER (Shi et al., 2023), and NAR4Rec (Ren et al. 2024b)) first generate multiple reranked can- didate lists and then leverage evaluator to select the most effective one for the user. Follow- ing Yang et al. (2025), for PIER, we first apply a pointwise ranking model to select the top-6 items, enumerate all possible permutations, and then use the evaluator to identify the optimal ranking.
Generator-Evaluatee
methods: These approaches ensemble multiple generators to ex- pand the candidate-list space and enhance ranking performance (Yang et al. (025). We evaluate this strategy under different ensemble sizes, with the number of generators set to 3, 20, and 100.
Multi-Gennrator-EEallaae
To ensure fairness, all baselines are tuned within their respective parameter spaces. Unless other- wise specified (e.g.. in scaling law experiments), the hidden embedding dimension of all models is fixed at 128, and model depths are kept evaluator (reward model) as GoalRank. Additional details on baseline configurations and the architecture of GoalRank are provided in Appendix D.2
all baselines share exactly the same
4.1.3 MAIN RESULTT (RQ1)
Ranking Performance. Table reports the overall results across three datasets. We highlight:
GoalRank consistently achieves the best performance. GoalRank outperforms all baselines. On ML-1M, it improves H@6 and M@6 by +17.12% and +15.43%; on the Industry dataset, the gains are even more pronounced, reaching +25.39% in H@6 and +29.63% in M@6 These results confirm that single large generator can better capture ranking signals than multi-stage model.
Two-stage G-E methods outperform early G-only approaches. Models such as PIER and NAR4Rec surpass DNN, DLCM, and PRM by explicitly modeling list-wise utility, validating the effectiveness of evaluators over greedy generation.
MG-E further improves but quickly saturates. As generator count increases from 3 to 100, H @6 rises from 49.42 to 55.77 on Industry. However, the gains diminish rapidly, and even the
7

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DNN
RankMive
PIER
MI-E
GeolRonk
01.
0.5
0.30
1888
N24
0.-
0.5
134
-34
2IM
0.10
154
6M
2001
15
455
2081
0.111
154
450
20M
9.11
Model Sizee
Model Sizee
Medel Staee
Medel Size
Figure 3: Scaling performance of GoalRank and baselines on the Industry- 0.1 dataset across model sizes from 1M to O.I parameters.
Table 2: Performance with varying group sizes [B].
Table Performance with varying bias
level A.
[8]
5
8
10
20
50
80
100
H@6
62.88
64.52
69.95
69.94
69.93
67.34
63.29
63.50
H@6
N@6
M@6
F1@6
AUC
N@6
81.76
83.42
86.82
87.17
86.93
85.33
82,76
82.94
0.0
86.93
79.01
82.29
98.07
M06
72.50
74.44
78.86
79.34
79.01
76.96
73.69
73.92
F106
74.00
75.94
82.25
82.28
82.29
79.26
74.47
74.76
0.2
65.32
83.21
74.33
76.89
97.90
AUC
97.50
97.79
98.05
98.15
98.07
98.06
97.75
97.77
0.5
63.77
82.75
73.79
75.05
97.73
strongest MG-E models remain far below GoalRank, underscoring the inefficiency of enlarging the candidate set alone.
Scaling Performance. In Section 3.1 we showed theoretically that GoalRank admits scaling laws. Here, we empirically validate this by varying hidden dimensions, layer depth, and attention heads, adjusting model size from 1M to 0. IB. We compare GoalRank with four representative baselines: DNN, RanMixer, PIER, and MG-E. For faimesss baselines are scaled in the same manner as Goal- Rank, while the size of MG-E is increased by enlarging the number of generators.
Figure presents the scaling performance on the Industry-O.. -0.r 1B dataset. We exclude AUC since GoalRank already achieves values above 0.98 even at small model sizes, though we observe further improvements as the model size increases, approaching 1.0. The model size ranges from IM to O. parameters We summarize the key findings as follows:
GoalRank demonstrates strong scaling. Metries improve steadily from 1M O.IB, with the sharpest gains between 10M and O.IB, confirming clear scaling laws.
Baselines show weak scaling. Larger sizes yield only modest improvements, reflecting the inher- ent limitation of pointwise scoring approximating the optimal policy.
MG-E saturates. Adding generators helps initially but plateaus quickly, indicating diminishing returns compared with GoalRank's single-model scaling.
4.1.4 ABLATION STUDY (RQ2)
In this section, we present ablation studics to examine two key factors: (i) the impact of the group size [B] constructing the reference policy, and (ii) the robustness of GoalRank under varying levels of bias in the reward model. We report results on the Industry dataset, which is representative of the overall trends observed across all datasets.
Influence of the Size of Table 2 reports the performance of GoalRank under different group sizes [B). We observe that very small groups (3-5) fail provide enough samples for constructing a reliable reference policy, while overly large groups (50-100) weaken the reward gaps mentioned in Equation 3 and thus amplify the bias of the reward model. The best performance is achieved with moderate group sizes (8-20), which strike balance between sample sufficiency and bias mitigation. Importantly, GoalRank consistently outperforms the best baseline even when [ is suboptimally.
Influence of Prediction Bias of Reward Models. As discussed in Section 3.2 the reward model i used to construct the reference policy inevitably biased. To examine the effect of this bias, we introduce controlled noise by defining
P x (1) = (1 - A)T(1) + Ae,
E~ N~0000 1),
For very small models, training the full dataset leads unstable convergence. To ensure fair compari- son, we proportionally sample the dataset for all models (including GoalRank) the same parameter scale.
8

---

Table Online performances improvement of GoalRank. All results are statistically significant.
Method
APP Stay Time
Watch Time
Effective View
Like
Comment
GoalRank MG-E n.S. MG-E
0.092%
0.111% 0.197%
0.836 1.212%
0.228% 0.227%
0.506%
GoalRank v.s. MG-E
0.149%
0.802%
and evaluate GoalRank under different bias levels X {0.0, 0.2, Results in Table show that performance degrades only slightly À increases, indicating that GoalRank is robust to reward model bias. Remarkably, even with À 0.5, GoalRank still outperforms state-of-the-art baselines.
4.2
LIVE EXPERIMENTS
4.2.1
EXPERIMENTAL SETUP
We evaluate GoalRank through a large-scale online A/B test on a real-world short-video recommen- dation platform. The platform serves half billion daily active users, with item pool of tens of millions of videos. The system follows a two-stage workflow: (i) retrieval, which selects can- didate items from millions, and (ii) ranking, which generates a final recommendation list of length L. Gaal is deployed in the ranking stage, where N = 120 candidates are provided and L 6 items are exposed each user. The workflow and latency illustrated in Figure (Appendix).
4.2.2 EVALUATION PROTOCOL
We randomly partition online traffic into eight buckets, each covering about one-eighth of total users (tens of millions per bucket). We compare three settings: the production MG-E faseline(which con- sists of tens of generator models and hundreds of candidate lists), hybrid setting where GoalRank serves 30% of the traffic alongside MG-E, and pure GoalRank deployment. Each A/B test runs for at least days to ensure statistical reliability. We track standard business metrics, including App Stay Time (a key overall engagement indicator), Watch Time (average continuous viewing length), Effective Views (total view count), and other behavior-specific rates on recommended items.
4.2.3 RESULTS ANALYSIS
We report the results of the two-week online A/B tests in Table GoalRank consistently outper- forms the production MG-E framework across all business-critical metrics. Even in the hybrid set- ting (GoalRank + MG-E), we observe significant gains, while a full deployment of GoalRank yields the largest improvements. These results demonstrate that GoalRank can not only complement but also fully replace the existing MG-E framework, providing superior ranking quality without incur- ring trade-offs. GoalRank MG-E has been deployed to serve the full user traffic in production.
5 CONCLUSION
In this work. we revisit the design of ranking models recommender systems and challenged the prevailing Muultii/Gennertto--Evllaaa BattiiiGGennertto--valaaaa model, there always exists a generator-only ranker that achieves strictly smaller approximation error the optimal ranking policy, and that this error decreases further as model size grows. Building on this result, we derived an evidence upper bound of the one-stage objective and introduced the group-relative optimization principle, which leverages a reward model trained on real user feedback to construct a reference policy and provides a practical training objec- tive for generator-onle rankers. We instantiated these insights in GoalRank, large generator-one ranker optimized under the proposed principle. Extensive offline and online experiments demon- strated that GoalRank consistently outperforms SOTA methods and exhibits clear scaling behavior.
paradigm. We theoretically proved that, for any (finite
Limitation and Future Work. In real-world applications, ranking often needs to accommodate diverse and frequently changing business objectives. Compared with Bellii-Geenerato-EEvaabeee models, generator-only framework like GoalRank is less flexible in adapting to such shifts. A promising direction is to incorporate business-specife contextual signals into GoalRank, thereby enhancing its adaptability and generalization across objectives. Moreover, recent progress in large recommendation models has demonstrated remarkable success in the retrieval stage. However, most of these efforts overlook list-wise modeling, limiting their ability capture the benefits unique to

---

ranking. Future work may therefore explore how large retrieval and large ranking models can be jointly optimized to build more powerful end-to-end recommender systems.
Reproducibility Statement. For the theoretical results, detailed derivations provided in Ap- pendix [ For the empirical studies, we will release the implementation and training code at https:
//g /tgttttttbbbb cow//aike---eeeeeeoeee www.aaaaeeeaagggaaaaaa
Rank to ensure reproducibility.
Ethics Statement, This work aims to improve the ranking stage of recommedeer systems to enhance user satisfaction. It does not raise any specific ethical concerns.
REFERENCES
Qingyao Ai, Keping Bi, Jiafeng Guo, and W. Bruce Croft. Learning deep listwise context model for ranking refinement. In The 41st International ACM SIGIR Conference on Research & Devel- opment in Information Retrieval, SIGIR 18, pp. 135-144, New York, NY, USA. 2018, Associ- ation for Computing Machinery. ISBN 9781450356572. doi: 10.1145/32099988.22999888 URL
www.ooggo1..... 1e..:..114222000 https: http://ddo..ogo...///oo
3209985
Midhun T Augustine. A survey universal approximation theorems.
arXiv preprint
arXiv:2407.12895 2024.
Chi Chen, Hui Chen, Kangzhi Zhao, Junsheng Zhou, Li He, Hongbo Deng, Jian Xu, Bo Zheng, Yong Zhang, and Chunxiao Xing. Extr: click-through rate prediction with externalities in e-commerce sponsored search. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 2732-2740, 2022.
Paul Covington, Jay Adams, and Emre Sargin. Deep neural networks for youtube recommendations. In Proceedings of the 10th ACM Conference on Recommender Systems, RecSys '16, pp. 191-198, New York, NY, USA. 2016. Association for Computing Machinery. ISBN 9781450340359, doi: 00.11455/959100229999999 URL
George Cybenko. Approximation by superpositions of sigmoidal function. Mathematics control, signals and systems, 2(4):303-314, 1989.
Jiaxin Deng, Shiyao Wang, Kuo Cai, Lejian Ren, Qigen Hu, Weifeng Ding, Qiang Luo, and Guorui Zhou. Onerec: Unifying retrieve and rank with generative recommender and iterative preference alignment. arXiv preprint arXiv:2502.18965 2025.
Pavlos Efraimidis and Paul G Spirakis. Weighted random sampling with a reservoir. Information processing letters, 97(5): 181-8888 2006.
Yufei Feng, Yu Gong, Fei Sun, Junfeng Ge, and Wenwu Ou. Revisit recommender system in the permutation prospective. arXiv preprint arXiv:2102. 12057, 202
Yufei Feng, Yu Gong, Fei Sun, Junfeng Ge, and Wenwu Ou. Revisit recommender system in the permutation prospective. arXiv preprint arXiv:2102.1200 /2057, 2021b.
Yufei Feng, Binbin Hu, Yu Gong, Fei Sun, Qingwen Liu, and Wenwu Ou. Grn: Generative rerank network for context-wise recommendation. arXiv preprint arXiv:2104.00860 2021c.
Jingtong Gao, Bo Chen, Xiangyu Zhao, Weiwen Liu, Xiangyang Li, Yichao Wang, Zijian Zhang, Wanyu Wang, Yuyang Ye, Shanru Lin, et al. Lim-enhanced reranking in recommender systems. arXiv preprint arXiv:2406. 12433, 2024.
Jingtong Gao, Bo Chen, Xiangyu Zhao, Weiwen Liu, Xiangyang Li, Yichao Wang, Wanyu Wang, Huifeng Guo, and Ruiming Tang. LIm4rerank: Llm-based auto-reranking framework for recom- mendations. In Proceedings of the ACM on Web Conference 2025, pp. 228-233 2025.
Carlos A Gomez-Uribe and Neil Hunt. The netflix recommender system: Algorithms, business value, and innovation. ACM Trans. Manag. Inf. Syst., 6(4):1-19, 2015.
10

---

Xudong Gong, Qinlin Feng, Yuan Zhang, Jiangling Qin, Weijie Ding, Biao Li, Peng Jiang, and Kun Gai. Real-time short video recommendation on mobile devices. Proceedings of the 3CM International Conference
Information & Knowledge Management, CIKM '2,, pp. 3103-3112, New York, NY, USA, 2022. Association for Computing Machinery. ISBN 9781450392365. doi: / wtg.dio.org//00 11t.//10.1111444 1145/351 3 3557065
(..14553511808.3555 855.7556 htRlhtts:://// //doi:::/dddi..
F Maxwell Harper. The movielens datasets: History and context. aem transactions interactive in- telligent systems (tiis) 5 4 (2015) 1-19. f maxwell harper and joseph a konstan. 2015. the movie- lens datasets: History and context. aem transactions interactive intelligent systems (tiis) 5
(2015) 1-19, 2015.
Xiangnan He, Kuan Deng, Xiang Wang, Yan Li, YongDong Zhang, and Meng Wang. Lighgen Simplifying and Powering Graph Convolution Network for Recommendation. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval, pp. 639,648, 2020.
Ari Holtzman, Jan Buys, Li Du, Maxwell Forbes, and Yejin Choi. The curious case of neural text degeneration. arXiv preprint arXiv: 1904:099409 2019.
Kurt Hornik. Approximation capabilities of multilayer feedforward networks. Neural networks, (2):251-257, 1991.
Kurt Hornik, Maxwell Stinchcombe, and Halbert White. Multilayer feedforward networks are uni- versal approximators. Neurul networks, 2(5):359-366, 1989.
Guangda Huzhang. Zhen-Jia Pang, Yongqing Gao, Yawen Liu, Weijie Shen, Wen-Ji Zhou, Qianying Lin, Qing Da, An-Xiang Zeng, Han Yu, et al. Aliexpress baaming-to-rank Maximizing online model performance without going online. IEEE Transactions on Knowledge and Data Engineer- ing, (5())5))))1111222) 2021.
Vivek Jayaram and John Thickstun. Parallel and flexible sampling from autoregressive models via langevin dynamics. In International Conference on Machine Learning, pp. 4807-4818 PMLR, 2021.
Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for recommender systems. Computer, 42(8):30-37, 2009.
Moshe Leshno, Vladimir Ya Lin, Allan Pinkus, and Shimon Schocken. Multilayer feedforward net- works with nonpolynomial activation function can approximate any function. Neural networks, 6(6):811-867, 1993.
Xiao Lin, Xiaokai Chen, Chenyang Wang, Hantao Shu, Linfeng Song, Biao Li, and Peng Jiang. Discrete conditional diffusion for reranking in recommendation. In Companion Proceedings of the ACM Web Conference 2024, WWW '24, pp. 161-169, New York, NY. USA, 2024. Associ- ation for Computing Machinery. ISBN 9798400701126.
doi: 0011455/388933536688133 URL
httt:::/ddo..rgg/// http://...111////11 1145/ 005555/5883355333 3648313
Qi Liu, Bo Wang, Nan Wang, and Jiaxin Mao. Leveraging passage embeddings for efficient listwise reranking with large language models. In Proceedings of the ACM on Web Conference 2025, pp- 4274-4283, 2025.
Shuchang Liu, Qingpeng Cai, Zhankui He, Bowen Sun, Julian McAuley, Dong Zheng, Peng Jiang, and Kun Gai. Generative flow network for listwise recommendation. Proceedings of the 29th ACM SIGKDD Conference Knowledge Discovery and Data Mining, KDD '23, pp. 1524-1534, New York, NY, USA, 2023. Association for Computing Machinery, ISBN 9798400701030. doi: 10.1145//580005535999664 URLptttps://dol org/10. 1145/118000000 3591533003033393344
Julian McAuley, Christopher Targett, Qinfeng Shi, and Anton Van Den Hengel. Image-based rec- ommendations on styles and substitutes. In Proceedings of the 38th international ACM SIGIR conference on research and development in information retrieval, pp. 43-52, 2015.
Nicholas Metropolis, Arianna W Rosenbluth, Marshall N Rosenbluth, Augusta H Teller, and Edward Teller. Equation of state calculations by fast computing machines. The journal of chemical physics, 2166):08771102. 1953.
11

---

Changhua Pei, Yi Zhang. Yongfeng Zhang, Fei Sun, Xiao Lin, Hanxiao Sun, Jian Wu, Peng Jiang, Junfeng Ge. Wenwu Ou, and Dan Pei. Personalized re-ranking for recommendation. In Pro- ceedings of the 13th ACM Conference on Recommender Systems, RecSys 19, pp. 3-11, New York, NY, USA, 2019a. Association for Computing Machinery. ISBN 9781450362436. 01115/3328668,33447000
doi:
URL http:ttt:: wrg. 1tt 11..0...11112218818
Changhua Pei, Yi Zhang, Yongieng Zhang, Fei Sun, Xiao Lin, Hanxiao Sun. Jian Wu, Peng Jiang, Junfeng Ge, Wenwu Ou, et al. Personalized re-ranking for recommendation. In Proceedings of the 13th ACM conference on recommender systems, pp. 3-11, 2019b.
Ruiyang Ren, Yuhao Wang, Kun Zhou, Wayne Xin Zhao, Wenjie Wang, Jing Liu, Ji-Rong Wen, and Tat-Seng Chua. Self-calibrated listwise reranking with large language models. In Proceedings of the ACM on Web Conference 2025, pp. 3692-3701, 2025.
Xubin Ren, Wei Wei, Lianghao Xia, Lixin Su, Suqi Cheng, Junfeng Wang, Dawei Yin, and Chao Huang. Representation learning with large language models for recommendation. In Proceedings New York, NY, USA, 2024a.
of the ACM Web Conference 2024, WWW 224, pp.
Association for Computing Machinery. ISBN 9798400701119 doi: 10.1 00.144555588333334455888 0ee.e1145588988
URL http:htps:/// httttp::/ddoii.rgge
3645458
Yuxin Ren, Qiya Yang, Yichun Wu, Wei Xu, Yalong Wang, and Zhiqiang Zhang. Non-autoregreessive generative models for reranking recommendation. In Proceedings of the 30th ACM SIGKDD
Conference on Knowledge Discovery and Data Mining, KDD '24, pp. 5625-5634 NY, USA, 2024b. Association for Computing Machinery. ISBN 9798400704901. 3637528.3671666 645.. URL hnttps:///ol http://oooo.oogl./o
New York, wtt. 10 /41114333335 3375288 367164
doi: 10.1145/
Xiaowen Shi, Fan Yang. Ze Wang, Xiaoxu Wu, Muzhi Guan, Guogang Liao, Wang Yongkang, Xingxing Wang, and Dong Wang. Pier: Permutation-level interest-based end-to-end re-ranking framework in e-commerce. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD '23, pp. 4823 4831, New York, NY, USA, 2023. Associa- tion for Computing Machinery. ISBN 9798400701030. doi: 0111455/380305.35999888 URL httpp:://dii.org// http//11.111....1
1145 0004455553030555 3599886
Sho Sonoda and Noboru Murata. Neural network with unbounded activation functions is universal approximator. Applied and Computational Harmonic Analysis, 43(2):233-268, 2017.
Shuli Wang, Yinqiu Huang, Changhao Li, Yuan Zhou, Yonggang Liu, Yongqiang Zhang, Yinhua Zhu, Haitao Wang, and Xingxing Wang. You only evaluate once: tree-based rerank method at meituan. arXiv preprint ar5iv:2508. 14420, 2025a.
Shuli Wang, Xue Wei, Senjie Kou, Chi Wang, Wenshuai Chen, Qi Tang, Yinhua Zhu, Xiong Xiao, and Xingxing Wang. Nlgr: Utilizing neighbor lists for generative rerank in personalized rec- ommendation systems. In Companion Proceedings of the ACM on Web Conference 2025, pp. 530-537, 2025b.
Xiaobei Wang, Shuchang Liu, Xueliang Wang, Qingpeng Cai, Lantao Hu, Han Li, Peng Jiang, Kun Gai, and Guangming Xie. Future impact decomposition in request-level recommendations. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 5905-5916, 2024.
Xiaobei Wang, Shuchang Liu, Qingpeng Cai, Xiang Li, Lantao Hu, Han Li, and Guangming Xie. Value function decomposition in markov recommendation process. In Proceedings of the ACM on Web Conference 2025, pp. 379-390 390, 2025c.
Jianxiong Wei, Anxiang Zeng, Yueqiu Wu, Peng Guo, Qingsong Hua, and Qingpeng Cai. Generator and critie: A deep reinforcement learning approach for slate re-ranking in e-commerce. arXiv preprint XiXx:2005.112000 2020.
Likang Wu, Zhi Zheng, Zhaopeng Qiu, Hao Wang, Hongchao Gu, Tingjia Shen, Chuan Qin, Chen Zhu, Hengshu Zhu, Qi Liu, et al. A survey on large language models for recommendation. World Wide Web, 67, 2024.
12

---

Yunjia Xi, Weiwen Liu, Jieming Zhu, Xilong Zhao, Xinyi Dai, Ruiming Tang, Weinan Zhang, Rui Zhang, and Yong Yu. Multi-level interaction reranking with user behavior history. In Proceedings of the 45th International ACM SIGIR Conference Research and Development in Information Retrieval, pp. 1336-1346, 2022.
Yunjia Xi, Weiwen Liu, Xinyi Dai, Ruiming Tang, Qing Liu, Weinan Zhang, and Yong Yu. Utility- oriented reranking with counterfactual context. ACM Trans. Knowl. Discov. Data. 18(8). July
2024. ISSN 1556-4681. doi: 10.1145/3671044 URL
3671004
Hailan Yang, Zhenyu Qi, Shuchang Liu, Xiaoyu Yang, Xiaobei Wang, Xiang Li, Lantao Hu, Han Li, and Kun Gai. Comprehensive list generation for mulli-generaa reranking. In Proceedings of the 48th International ACM SIGIR Conference on Research and Development in Information 2025.
Retrieval, pp.
Lu Yu, Chuxu Zhang, Shangsong Liang, and Xiangliang Zhang. Multi-order attentive ranking model for sequential recommendation. In Proceedings of the AAAI conference on artificial intelligence, volume 33, pp. 5709-5716, 2019.
Chulhee Yun, Srinadh Bhojanapalli,, Ankit Singh Rawat, Sashank J Reddi, and Sanjiv Kumar. Are transformers universal approximators of sequence-to-sequeece functions? arXiv preprint arXiv:1912.10077, 2019.
Jiaqi Zhai, Lucy Liao, Xing Liu, Yueming Wang, Rui Li, Xuan Cao, Leon Gao, Zhaojie Gong, Fangda Gu, Michael He, al. Actions speak louder than words: 12.4422..15.... 17152, 2024.
sequential
transducers for generative recommendations. arXiv preprint arXiv:2402.
Kaike Zhang, Qi Cao, Yunfan Wu, Fei Sun, Huawei Shen, and Xueqi Cheng. Understanding and improving adversarial collaborative filtering for robust recommendation. Advances in Neural Information Processing Systems, 37: 1202111020110.. 2024.
Kaike Zhang, Qi Cao, Fei Sun, Yunfan Wu, Shuchang Tao, Huawei Shen, and Xueqi Cheng. Robust recommender system: a survey and future directions. ACM Computing Surveys, 58(1):1-38, 2025a.
Kaike Zhang, Xiaobei Wang, Xiaoyu Liu, Shuchang Liu, Hailan Yang, Xiang Li, Fei Sun, and Qi Cao. From generation to consumption: Personalized list value estimation for re-ranking. arXiv preprint arXiv:2508.0022: 2025b.
Jie Zhu, Zhifang Fan, Xiaoxie Zhu, Yuchen Jiang, Hangyu Wang, Xintian Han, Haoran Ding, Xin- min Wang, Wenlin Zhao, Zhen Gong, al. Rankmixer: Scaling up ranking models in industrial recommenders. In Proceedings of the 34th ACM International Conference on Information and Knowledge Management, pp. 6309-6316, 2025.
Tao Zhuang, Wenwu Ou, and Zhirong Wang. Globally optimized mutual influence aware ranking in e-commerce search. In Proceedings of the 27th International Joint Conference on Artificial Intelligence, ICAAI18, pp. 3725-3731. AAAI Press, 2018. ISBN 9780999241127.
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A PROOF OF THEOREM
Notation. Recall the space of the ranking list in Section 2 For simplicity and clarity, in this section, we omit the u E ll in the expressions of the following symbols. The space of ranking list L is:
N!
C 6== (......, vL) VL vs # vy {)) [4] = L)N (N - L)!
Then the state set during the generation process can be expressed as:
S = (i, [L], Lee Vi=1, + ub (a # 6)}.
and corresponding actions at state l=)):
A(i, (ii, : V fu....., e--1 [((i,==) -
Given a score vector E RV and feasible set A C V, the masked softmax is
Eied
e
jEA,
(softmax
0,
j j
For a finite index set and x E R-, write ||0]|ooaT = maxiez [zs). We use KL(-II-) for Kull- back-Leibler divergence.
Lemma 1. Let l E N and 9m,s E 9m (i i...., k) be k generators. Assume each gm.s is locally
Lipschitz in its parameter 0; E [A, Bjdm, and the masking set A(t, Lex) depends only on (t, Le)
(not on parameters). For mixing weights (illi A k
define
T O₂ -1-11
O₂ ([A, Bjnm)
A
where
(0 W)
Wi n ggm..
where Tgm, = (T ()) is the masked-softmax autoregressive policy induced by Jm Then Ck. imb satisfies:
1. Ch, is compact;
2. dimHHus (Ch) S min {kdm + (k - 1), [C] - 1}.
Proof: Compactness. Each parameter domain [A, Bjdm is compact, and finite Cartesian products preserve compactness; the simplex list 1 E L and position i, given the smoothness of softmax and zm, is C², the masked-softmax distribution
A k-1 is also compact. Hence O₃ compact. For a fixed
exp (Ell,(e)))
T Bm,
II [=1 EjEALLLED exp (2)))
(tm.(t,
is C in 0;, as masking only discards coordinates independent of parameters.
Since & is convex combination of such policies, it is C+ in (0I.,, w), hence continuous. By continuity of d on the compact domain θ₁. its image Ch. is compact.
Dimension bound. On O₂ (compact), each map (f,,w) + W;Tgm. is Lipschitz: 8; + 20) is Lip- schitz; composition with masked-softmax is Lipschitz (bounded Jacobian the relevant compact image); the product over / and convex mixing in w preserve Lipschitzness since all factors are uni- formly bounded. Thus Lipschitz on θç. Lipschitz maps do not increase Hausdorff dimension, yielding
dimHaus (im ()) < dimnaus (4x) kd,, + (I: - 1),
and trivially dim (im($)) < [C] 1, giving the stated minimum.
14

---

Theorem 2.
Let V be the candidate with N : | and let & be the set of length-L lists without
repetition, so := [C] - P(N. L) - 1. Let CK (a, B] C A be the k-mixture (a,, B) B--bounded
policy space. Assume Lemma Coammaaaoooo holds with
dim (a. B)) r kd + (k 1)
and
r r<d. d.
Then for lebesgue-almenn every fully supported targel policy x² E int)
inf KL (T) > 0.
(8)
TEC (0.8)
Proof. By Lemma 1 C, Hence the d-dimensional relative Lebesgue measure (equivalently, the d-dimensional Hausdorff measure) of C. (a, inside (A)( is zero. Therefore, for Lebesgue-a.e. x² E int((Ad) we have n & C. (), 8).
(a, B) is compact and dim (C,, (a, 3)) S
(am(af((A)))
Fix such n² with n² > Every Ch (a, (3) assigns strictly positive probability each I C, so the map
(1) log TT (I)
V (x)
KI( n (|x)
Σ
(1)
IEC.
is finite and continuous on the compact set C (a, 3); thus the minimum
== min
KL( π [|xT)
TEC (a.
attained. Since (T((T"][x)) = 0 iff π x and n" & C% (a, (3), Equation 8
we must have 6 0, proving
Classical universal approximation results Cybenko 1989 Hornik et al. 1989 Hornik 1991
Leshno et al. 1993 Sonoda Murata 2017) yield the following lemma. For clarity and gen- erality, we adopt MLP-based generators the foundational model class. The goal is to show that even the most basic architecture- MLP- alr-ady has sufficient expressive power to approximate the target policy. Universal approximation for Transformers (and related architectures) in sequence modeling is also known; see Yun et al. (2019); Augustine (2024).
Lemma 2. Let K C. R" be compact and let F K + R be continuous. Let Φ R + R be any continuous activation function that is not polynomial on any interval Then for every > O there exists a fixed-depth (e.g., one hidden layer), arbitrarily wide MLP he K IRm with activation such that
lhee - FlloosK < 1/-
Consequently, for any finite Borel measure μ K and any S < co, also have I|he Fl) < T. Remark (Finite domains). On a funite domain K (E1,....,27) continuity is automatic and
Ihe Fllx. max
|1 (x,) F(xe)looo
:E[T]
which coincides with the maximum pointwise error.
To adapt Lemma to the ranking setting, encode the autoregressive state action tuples into compact Euclidean set.
Corollary 1. Let
P:D-R,
D: ((i,ken))) : A(i,ce))
be defined by
pli, (i,lehh) =
where x² is a fully supported target autoregressive policy on the feasible sets Ali, Fix any injective encoding 1b D + K C Rd with K compact. Then for any a > there exists an MLP he K - R such that
ha 1b p ploxeD S
Thiis common activations such as sigmoid, tanh, ReI.U, leaky-ReLUU, ELU, and softplus.
15

---

Proof. The index set D is finite (since N, L oc), hence any function defined (D) K is continuous w.r.t. the subspace topology. Apply Lemma with m to obtain he with the desired uniform bound.
Lemma 3. Let p()) el finite set and q(ī) x elitess with | S for all j. Then for all j.
q(j)
e-2 2a 2 p(j)
S 20
and in particular
KT,(plgg) I 20, I|p- 4111 S -1 -
Moreover, for an autoregressive policy over length-L lists,
1.
(I(
Σ
Eler KL (es))la kcill] I 2La.
Fact 1. Fix a feasible set A. Letp softmax and = softmax,(6) with a. E R If ||a bl: S a, then
KI.(pllg) S 2a.
Proof. Write Ej = bj 0g for j E A. so 18y1 aa. Then
Li e E
e
- E" [E-20 2
Pj eai //EEEAEE Eat
ErEAPrEF
e-o
Hence log Pi < 2o for all j E A, and
KL(pl11) = Σ
Pj
log
Pj
<
Σ
Pj
2a
2a.
4j
JEA
JEA
Fact 2. Let n² and be autoregressive list policies on y of length I, with conditionals supported
on A(i, 12)) Then
KL(TT [|)) = Σ
Bie KL(T
(1 Me)))
T[
1=1
Proof. By the chain rule,
Ch,,.., 121
L
π (I Lei) T(4 lex)
log x(11...,, (2)
Σ
log
1=1
Taking expectation w.r.t. x² yields
<" (2s) T(I, Lzs)
KL( ([T)
Ble Bi (Rea) log
which is the stated form because the inner expectation equals KL
(T' KL(TT
[Z))[ |22)).
Theorem 3. Let GMuP be the class of (fixed-depth, arbitrary-width) MLP generators that, given (i, Lee), produce logits g(i, lei E IRV. Define the induced policy class
FMLP == { Te Tel. tex) = ssoftmax A(i,te))) (geli, les. }.
Then for every
0 there exists width W(s, N, T.) and parameters O such that
KL(T")] T[e) S s,
hence
lim E(FMLP) = 0, W4200
where E(F) infrer KT(x*1Im))
16

---

Proof. Define target logits the effective domain D by ((i,l.i.)) = log "4 Lei) for j E A(i, Fix an injective encoding & D K C R" into a compact K.
By Corollary I for any 0 there exists MLP he K R such that ||ke v. plox; a. Use ge (i,))))) == he (v (2).)) for E V. Define the policy
Te j (ea) softmaxA(idee)) (ei (1,(i,
For each prefix Lei, Fact
with p(i, b yields
KL(TT les) TT(- lei)) s 20.
Applying Fact 2 gives
L Σ
KL( (T)
B Bi [L (-11)))) [<)) s 2Lo.
Choose 0 = =2L) to obtain (L(TT [m)) I E. Finally, by Lemma (or the finiteness of D), the achievable tends O width W oc, proving lim {FFMPP) = O.
Proposition 1. Let Gm (cx 3), Fm (o, (3,, and C² (a, () be as in Definitions 12 For E Noo, let the large-generator class be
(a, 3, n) = 9M W(MM) 2 ka + D(gu) 2 BB}
with induced policy class Far 3, n) (softmaxo 9M 9M E G (a, (a,(a,,,1)) B,n)3. Assume the list- generation domain has a finite effective index set D ((i,kee,,)) :j A(i and the activation enjoys universal- universalapprroximaan approxmmatoonnno property on compact sets (e.g., standard MLP activations). Then
C₂ (a, 3) S Farla,B,r
where the closure is taken w.r.t. uniform convergence of masked conditionals D.
Proof. Fix any mixture element mmix E Ch (), By Definition 2 there exist generators gm.r E Gm (a, B), I,...,k, with logits (,, on A(i,les) and mixture weights (i, (2)) 2
with Σ (r le)) = such that
k
mmix 6 ((())) Σ r=1
Note that here we extend the mixture weights to be prefix-dependent, i.e., (i, Lz)). This exten- sion makes the proposition both stricter and more flexible, thereby broadening its generalization capability, If one wishes to exactly follow Definition the weights can simply be degenerated to wr (1).
Step (block-diagonal embedding of the & small generators). Without loss of generality, pad each Im.r to width exactly a per hidden layer by adding zero weights/units. Construct a depth- B, width-M network gM with M ka whose hidden layers partitioned into & disjoint generator blocks of width a and one evaluator block width n:
M a at..+t
blocks
evaluntor
For layers 1,..., 1, set the lurge-layer weights to be block-diagond
that the r-th generator block exactly replicates the corresponding layer of gm.r. and the evaluator block either copies its previous state computes auxiliary features (details in Step 2). Thus, after 3 hidden layers, the first ka coordinates of the big network's ' hidden state equal the concatenation of the B - 1-th hidden activations of {gm,r )
Step 2 (parameterizing the evaluator weights w with k- degrees of freedom). Use the evaluator block (of width > 1) produce mixture logits u(i, R with the constraint that one coordinate is fixed as reference (e.g., 0), and define
qur(teee
(i,le))) = Σ (Mu(tdle))
I...,,.,,k)
17

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which realizes arbitrary point in Ak-1 through a k 1a8--ldinng 1-dimensional parameterization. Because D is finite, the map (i, 12)) + (i, Les) can be approximated arbitrarily well by the evaluator block via UAT.
Step (combiner at depth 3: realizing the log-sum-exp logits). Define for j E A(i, Lei) the target combined logits
wr(t, earsbiles,, (ci)
2y(i, log
E etralidee)
tEA(H))))
At the last hidden layer (the 3-th nonlinear layer), allow cross-block connections from all generator blocks and the evaluator block into a width-M hidden layer that serves as single-hidden-layer approximator for the multivariate continuous mapping
Φ (zi...., w) +
2 on the finite domain D.
By universal approximation, there exist weights in this last hidden layer (and the final linear readout) so that the resulting gM satisfies
I - 2 D S a for any prescribed o > O. Note that the depth requirement D(gM) 2 3 is met (we used exactly B nonlinear layers), and the width requirement W (gg) 2 ka + n is used to house the embedded blocks (ka units) and the evaluator block (n units).
Step 4 (from logits to conditionals). By the identity
DoltmaxxAiitesEE(ii. (e,,)) = Σ
wir (i, (u:
the conditional produced by Softmax equals the target mixture conditional. Since ll olloo S a and the masked softmax is continuous, softmax (9MM) converges uniformly on D to softmaxA(3) = Tiix as a 1 O. Therefore miix E Fa, B,n). Because Tmix was arbitrary, the claimed inclusion holds.
Li
(Why ka + and k- - neurons for w). The ka term guarantees disjoint capacity to exactly embed the & small generators via block-diagonal copying across the first 3-1 hidden layers. The additional units form evaluator head; choosing 2 k - suffices to purameterize the simplex k-1 via softmax logits u E R& with one fixed reference coordinate, while also providing enough width for the last-layer universal approximation of the log-sum-exp combiner.
Remark 2
Proof of Theorem 7 Step 1 (Coverage of k-mixtures by a single large generator). By Proposi- tion
c* (ax 3) C Fas (,,,,,,,), n), where the closure is taken w.r.t. uniform convergence of masked conditionals on the finite effective domain. Because T (I) 0 for all / E and L finite, the map क + KL [[)] is continuous under uniform convergence of the conditionals. Hence, for every n,
{FFi(a, 8))) I E(hh (),
Step 2 (Arbitrary accuracy by increasing width). By Theorem 3 (UAT-backed policy approxima- tion), for every 8 > 0 there exists a fixed depth Lo and a width threshold W N, L), together with parameters O such that the induced policy та satisfies KL((T") I[Te) < s. Choose the fixed depth in Theorem 3 so that Tag 2 8, which is allowed by the theorem. Then, taking large enough to ensure ka (E, L), we have тe FM B, and therefore
(a, n)) S 6.
(10)
Since e > 0 was arbitrary, it follows that lim (FM((,,,n) = 00.
Step 3 (Strict improvement over the k-mixture space). By Theorem
2 there exists 8 > 0 0uch
that ECk (a, 3)) 8. Apply Step with = 8/2. Then for some no.
E {FM (a, 3,ng)) < 6/2 By monotonicity in n (the class Far 8, n) enlarges with n), the strict inequality holds for all nng Combining with equation Aquationncoonccei concludes the proof of both statements.
= E(ct (a. B)).
18

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B REWARD MODEL TRAINING
Following Zhang et al. (025b), we train a reward model to approximate user feedback on exposed recommendation lists. Let U denote user with context information X, (e.g., historical inter- actions or side features). Suppose la = (Vi,..., UI() is the exposure list presented to user where V V. S V and [[] is the list length. The corresponding real user feedback, such as watch time, clicks, other engagement signals, denoted by ri, R.
The reward model is defined as a function
X V
which, given the user context X, and candidate list Lus predicts the expected feedback i(1u, X.)). To train the reward model, we minimize the mean squared error between the predicted feedback f(lu X.) and the observed feedback ri., across all users:
[(F) = EnEzr (f( Kx) -rt.) rr.)))
C METHODS FOR GROUP CONSTRUCTION
We consider multiple strategies for constructing groups of candidate lists, beyond the standard au- toregressive sampling approach. The main methods are summarized as follows:
Autoregressive list generation (Jayaram & Thickstun 2021): The conventional approach sam- ples a single list by generating the entire trajectory in an autoregressive generator. While effective in capturing dependencies, this method is relatively slow and produces only one list per sampling trajectory.
Parallel tree-structured generation (Jayaram Thickstun 2021; Wang al. 2025a): To improve efficiency and diversity, allow the autoregressive generator to branch out in the first K steps are then completed
K steps, forming a tree of partial sequences. The remaining deterministically, enabling parallel exploration of multiple candidate lists.
Softmax-based stochastic sampling (Holtzman et al. 2019: Efraimidis & Spirakis, 2006): After the first step of scoring by generator, items are sampled probabilistically according the softmax distribution of their scores, instead of deterministically selecting the top item, which encourages more diverse list generation.
The list generation process mod- eled as Markov chain, where each step only conditions on the immediately preceding item rather than the full history. We exhaustively explore and score all possible two-item pairs in the first two steps and the remaining items in the list are sampled sequentially in chain-like manner.
Markov process approximation (Metropolis al. 1953):
Random selection: As a simple baseline, we randomly sample six items to form a candidate list without using model guidance.
Heuristic substitution (Wang et al. 2025b): Starting from already sampled lists, we heuristically replace up to two items to create new candidate lists while maintaining partial consistency with existing ones.
Diversity-oriente generation (Yang et al., 2025 we generate lists that are explicitly encour- aged to differ significantly from previously sampled lists, thereby enhancing the diversity of the candidate set.
D DETAILS OF OFFLINE EXPERIMENTS SETTINGS
D. DETAILS OF DATASET
The ML- 1M dataset is a widely used public benchmark in recommender systems, containing approx- imately 1 million ratings provided by over 6,000 users more than 3,900 movies. The Amazon Books dataset is a large-scale collection of product reviews focused on books available on Amazon, consisting of about 2 million reviews from over 35, 5,,000 users spanning more than 39, (000 books. The
19

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Exposure
Li
Stage for List Generation
N - Ranker
Lz
Topl
List
items
Lvv
Stage for Item Selection
Retrieval Models
Multi G
E
Online Recšys
Millions of Henus
Directly
Exposue
List
Exposure
Request
Rank
Candidate
Users
Figure 4: Online workflows.
Industry dataset is collected from a real-world short-video platform that serves over half billion daily active users and hosts an item pool tens of millions of videos. We construct two versions of this dataset: smaller with over million interactions from 89,310 users 10,395 videos, and a larger one with over 0.1 billion interactions from I million users on 0.3 million videos.
For preprocessing, all interactions organized in chronological order, and users/items with fewer than 20 interactions are filtered out following the standard 20-core protocol Zhang et al. (2025a). We employ Matrix Factorization (MF) model as the retriever simulator generate candidate items for the ranking stage. The data is split into training and testing sets with ratio of 8:2. For the ranking stage, interactions are sorted chronologically, and the last six interactions are used the item list exposed to users after reranking. Table 5 reports the statistics of the processed datasets, including the number of users, items, interactions, and revealed lists.
Table 5: Dataset Statistics
Dataset
[
[
# Interaction
List
ML-1M
6,020
3,043
995,154
161,646
Amazon-Bonn Boook
35,732
38,121
1,960.674
311,386
Industry
89,310
10,395
3,270,132
513,010
Industry-0.1B
1,146,032
312,573
100,269,812
16,099,612
D.2 DETAILS OF BASELINES
We detail the compared baselines of our main experiments in the following, covering three major categories: Generator-only methods, Generator-Evaluace methods, and Balli-Geenerato-EEvaleeee methods:
Generator-only methods: These approaches directly predict the item- weie-wise scores for candidates and rank them accordingly, without explicit evaluation of whole lists.
DNN (Covington al. 2016) learn the user feedback for each user-item interaction.
DLCM (ii et al. 2018) refines initial rankings by leveraging local context from top-retrieved documents using recurrent neural network capture document interactions and an attention- based loss function to capture item interactions.
PRS (Feng et al., (021a) also known as SetRank, which is a neural learning-to- to-rankk model em- ploys permutation-inver invariant neural ranking with multi-head self-attention to model cross-iten de- pendencies, achieving robust performance across variable-length input sets.
PRM (Pei et al. [2019a) addresses personalized re-ranking by integrating user-specific preferences into the re-ranking process, thus enhancing both personalization and relevance.
MIR (Xi et al. 2022) captures complex hierarchical interactions between user actions and candi- date list features improve the accuracy of list-wise recommendation.
20

---

Ienerator-Evaluatee Methods: These methods adopt two-stage paradigm where the generator produces candidate lists and the evaluator selects the most promising one.
EGRerank (Huzhang et al. 2021) proposes an evaluator genirrator framework for e-commerce ranking. The evaluator estimates list utility given context, while the generator leverages reinforce- ment learning to maximize evaluator scores, with an additional discriminator ensuring evaluator generalization.
PIER (Shi et al. 2023) follows a two-stage architecture consisting of a Fine-grained Permutation Selection Module (FPSM) and an Omnidirectional Context-aware Prediction Module (OCPM). The FPSM leverages SimHash to identify the top-K candidate permutations based on user inter- ests, while the OCPM evaluates these permutations through an omnidirectional attention mecha- nism.
NAR4Rec (Ren et al. 2024bb introduces a non-autoregressive generative re-ranking model that al- leviates data sparsity and candidate variability via contrastive decoding and unlikelihood training, while also considering its integration into broader -everuuttre frameworks.
Multi Generator-Evaluatoor These methods extend the generator-evall evaluuato paradigm by ensem- bling multiple generators to enlarge the candidate list space and improve final ranking quality. For example, MG-E Yangg et al. (025) aggregates outputs from multiple generators, each specializing in different candidate distributions, before applying evaluation for list selection.
To ensure fair comparison, we adopt a relatively lightweight generator architecture for GoalRank. Specifically, the GoalRank Generator consists of two blocks: lower block that performs feature crossing over all candidate items using several Transformer layers, and an upper block implemented as Transformer decoder. During list generation, the decoder autoregressively predicts next-item scores over the full candidate set at each step, and GoalRank constructs the final list by sequentially selecting items (via Top-1 or sampling-base based strategies).
D.3 ONLINE LATENCY AND MFU
To demonstrate the efficiency and resource-utilization advantages of GoalRank's single-stage chitecture, we report both the online latency and MFU of GoalRank compared with the existing Saati--Generatoo-Faauuuee
(MGE) pipeline. Notably, during training, many components of Goal- Rank can be executed in parallel. For example, the construction of auxiliary ranking-policy groups for reference-policy generation can be fully parallelized, resulting in negligible additional overhead. Under this setting:
Latency. GoalRank achieves an online latency of 18.611 ms. which is substantially faster than the multi-stage MGE pipeline (34.235 ms). This improvement stems from GoalRank's ability to directly generate the final list in single stage, eliminating evaluator scoring and multiple candidate-liss constructions.
MFU. GoalRank attains an MFU of 12.65%. compared with 2.03% for the traditional two-stage MGE pipeline. The higher MFU reflects significantly better hardware utilization, ensuring that GoalRank does not increase overall training cost despite offering stronger performance.
These results validate that GoalRank is practical, efficient, and deployment-ready Furthermore, GoalRank has been successfully deployed in our online environment to serve full user traflic.
E USE OF LLMS
Large language models (LLMs) were employed polish the main body of this paper. Their use was limited to grammar checking and correction of typographical errors.
21


Reviews:
[{"review_id": "j4yUfpaYC8", "reviewer": "Reviewer_t9JT", "summary": "This paper proposes GoalRank, a single-stage large-model ranking method based on Group-Relative Optimization. The authors demonstrate that a sufficiently large generator model can more closely approximate the optimal ranking strategy compared to the traditional two-stage \"generator-evaluator\" framework. GoalRank is trained by constructing a reference policy using a reward model, significantly outperforming existing methods on multiple public datasets and industrial-grade online tests, and exhibiting good scaling law and improved real-world business performance.", "questions": "See the weaknesses.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "Theoretically Superior: It has been theoretically proven that a single large-scale generator model can approach the optimal ranking strategy more closely than the traditional multi-generator-evaluator framework, and it exhibits scalability (scaling law).\n\nSimpler Structure: Employing an end-to-end architecture with a single-stage generator eliminates the evaluator stage, avoiding inconsistencies between multiple stages and making model design and training processes more unified.", "weaknesses": "Limited Adaptability: As a single generator model, it lacks the flexibility of an independent evaluator. When business objectives or optimization metrics change frequently, model adjustment costs are high, making it less adaptable than a two-stage architecture.\n\nStrong Dependence on Reward Model: The training process relies on a reward model trained based on user feedback. If the reward model is biased or noisy, it may lead to inaccurate reference strategies, affecting overall ranking quality.\n\nHigh Training and Resource Costs: GoalRank's core advantage comes from large-scale models and group optimization, but this also means higher computational resources and training costs, making it less friendly to small- to medium-scale application scenarios.\n\nLack of Strong Baseline Comparisons: The lack of comparisons with baselines for solving large candidate ranking, such as Onerec and Tiger, makes the paper's experimental results less convincing.\n\nThe paper's writing is confusing and difficult to understand.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pDrKDQIlhr", "reviewer": "Reviewer_HWxM", "summary": "This paper proposes GoalRank, a framework advocating for a shift from multi-stage Generator-Evaluator (G-E) ranking paradigms to a single-stage, \"Generator-only\" (G-only) model. The authors present a theoretical argument that a single large generator can better approximate the optimal ranking policy than any finite G-E system. For training, they introduce \"Group-Relative Optimization,\" which uses a reward model to create a reference policy from a group of candidate lists, serving as a learning target.", "questions": "Please refer to the weakness section.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. Empirical Validation: The inclusion of a online A/B test on a major commercial platform is a significant strength, providing real-world evidence of the model's effectiveness in a production environment.   \n2. Clarity and Scope: The paper is well-written, clearly articulating its motivation and methodology. The experiments are extensive, covering multiple datasets and demonstrating a clear scaling law, which adds valuable empirical data to the field.", "weaknesses": "1. Experimental Fairness: The experimental comparison between GoalRank and the G-E baselines raises fairness concerns.\n- The GoalRank framework relies heavily on a powerful, pre-trained Reward Model to provide its training signal. This reward model is functionally equivalent to an evaluator, albeit used offline.   \n- For a fair comparison, the G-E and MG-E baselines should have been equipped with the exact same reward model to serve as their online evaluator. Without this, the observed performance lift of GoalRank may not stem from the superiority of its \"G-only\" architecture but rather from the fact that it was trained by a more powerful \"teacher\" (the reward model) than the evaluators used by the baselines.\n2. Positioning of the paper: The fundamental goal of both GoalRank and listwise learning to rank (LTR) is the same: to learn a function that can optimally order an entire list of items by considering the items collectively, rather than in isolation. What are the differences between them?\n3. Practicality and Online Feasibility: While the paper demonstrates strong online performance, it omits a critical discussion of the training cost. The \"Group Construction\" step requires generating and evaluating multiple lists for every training sample, which implies a training cost that could be orders of magnitude higher than for the baseline models. This potentially prohibitive cost could severely limit the model's practical applicability in industrial settings that require frequent retraining.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "a7sWTyeNde", "reviewer": "Reviewer_JXWv", "summary": "This paper proposes GoalRank, a novel ranking framework that replaces the complex Multi-Generator-Evaluator paradigm with a single large generator model. The contributions are threefold: theoretically, it proves that a sufficiently large generator can better approximate the optimal ranking policy than any finite M-G-E system, with error decreasing via scaling laws; methodologically, it introduces group-relative optimization, which trains the generator using robust relative comparisons within list groups rather than absolute rewards; empirically, large-scale offline and online experiments demonstrate consistent and significant improvements over state-of-the-art baselines, validating the framework's effectiveness and scalability.", "questions": "1. If you need the model to optimize for a new goal (like promoting new content instead of maximizing watch time), how would you adapt GoalRank without having to retrain the whole model from scratch?\n2. How important is the quality and variety of the helper models used to create the candidate lists? Could a poorly chosen set of helpers limit how good GoalRank can become?\n3. Since GoalRank learns from the reward model's relative rankings, is there a risk that it could also learn and even amplify any biases that exist in that reward model?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "1.  The paper provides a rigorous theoretical proof that a single large generator can surpass any finite M-G-E system, with a clear scaling law. This theory is strongly supported by empirical results, creating a cohesive narrative.\n2. The proposed group-relative optimization is an innovative solution for training large rankers. It effectively leverages relative comparisons within groups to create a robust training signal that is resilient to reward model bias.\n3. The paper offers thorough validation, from offline benchmarks to large-scale online A/B tests on a major platform. The consistent and significant improvements across both academic and business metrics convincingly demonstrate real-world impact.", "weaknesses": "1.  The training process itself is complex and resource-heavy, The proposed method shifts complexity to the training stage, requiring a costly and intricate pipeline, especially for large-scale industry recommendation systems. \n2. The architectural details and specific implementation of the generator model itself are not sufficiently elaborated, making it difficult to fully assess the proposed method's design choices and reproduce the results.\n3. The monolithic generator is inherently less adaptable to new business objectives compared to the more modular M-G-E paradigm, which allows for quicker adjustments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DRrhR5nEQ9", "reviewer": "Reviewer_LY4d", "summary": "The paper proposes GoalRank, a novel framework for training a single-stage, large-scale ranking model to replace the inefficient traditional two-stage Generator-Evaluator (G-E) paradigm. The G-E paradigm suffers from performance saturation due to the vast combinatorial ranking space. GoalRank introduces the Group-Relative Optimization Principle, using a pre-trained Reward Model and relative normalization within a group of lists to construct a Reference Policy. This allows the single-stage model to be trained effectively, achieving a superior approximation of the optimal policy. The framework is theoretically proven to surpass finite G-E systems and validated on a massive industrial platform, showing significant lifts in core business metrics.", "questions": "1. Placing the Related Work section entirely in the appendix detracts from the integrity of the main paper structure, making it difficult for the reader to immediately contextualize the work against existing literature during the initial review.\n\n2. The paper's claimed field focus is sometimes ambiguous. While positioned as a solution for ranking, many of its baselines and related works cited (e.g., DLCM, PRM) are strongly associated with the re-ranking. If the work truly aims to target the ranking field, it should include comparisons against more foundational CTR-prediction methods and other contemporary Large Ranking Model (LRM) approaches like RankMixer: Scaling Up Ranking Models in Industrial Recommenders. If this work focuses on reranking, why not use some datasets and experimental settings more commonly used in the reranking field, such as Avito and Kuaishou?\n\n3. Key engineering details, such as the specific construction of the Auxiliary Ranking Policy Group ($\\mathcal{B}$) and the exact large model architecture, are either simplified or omitted. \n\n4. The scalability experiments primarily focus on demonstrating superiority over the two-stage (G-E) paradigm, which quickly saturates. However, the comparison within the single-stage paradigm only includes simple DNN baselines. The paper fails to demonstrate that other, more sophisticated single-stage solutions (beyond simple DNNs) cannot also achieve similar or superior scaling behavior.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. This work provides a strong theoretical proof that a sufficiently large single-stage ranker can achieve a strictly lower approximation error than any finite two-stage system, confirming its strong potential for scaling laws.\n\n2. The Group-Relative Optimization is an practical solution for training against the unobservable optimal policy in large-scale production environments.\n\n3. It achieved significant and convincing lifts in key business metrics during large-scale online A/B testing on a platform with over 500 million daily active users.", "weaknesses": "1. The paper’s academic context is weakened by placing related work in the appendix, and its scope is blurred between the ranking and re-ranking domains, leading to an incomplete set of comparative baselines. See details in Questions 2\n\n2. The theoretical proof is contingent on the optimal strategy $\\pi^{*}$, which is substituted by an approximate Reward Model $\\hat{r}$ in practice. While the paper claims robustness against bias in $\\hat{r}$, the inherent difficulty in training a truly optimal reward model means this approximation gap remains a potential bottleneck, limiting the performance ceiling achievable in the real world.\n\n3. The overall reproducibility is a concern and the scalability experiments fails to demonstrate that other, more sophisticated single-stage solutions (beyond simple DNNs) cannot also achieve similar or superior scaling behavior.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)