Selective Preference Optimization via Token-Level Reward Function Estimation

## Abstract

Abstract Recent advancements in large language model alignment leverage token-level supervisions to perform fine-grained preference optimization. However, existing token-level alignment methods either optimize on all available tokens, which can be noisy and inefficient, or perform selective training with complex and expensive key token selection strategies.
In this work, we propose Selective Preference Optimization (SePO), a novel selective alignment strategy that centers on efficient key token selection.
SePO proposes the first token selection method based on Direct Preference Optimization (DPO), which trains an oracle model to estimate a token-level reward function on the target data. This method applies to any existing alignment datasets with response-level annotations and enables cost-efficient token selection with small-scale oracle models and training data. The estimated reward function is then utilized to score all tokens within the target dataset, where only the key tokens are selected to supervise the target policy model with a reference model-free contrastive objective function. Extensive experiments on three public evaluation benchmarks show that SePO significantly outperforms competitive baseline methods by only optimizing 30% key tokens on the target dataset. SePO applications on weak-to-strong generalization show
that weak oracle models effectively supervise strong policy models with up to 16.8 × \times × more parameters. SePO also effectively selects key tokens from out-of-distribution data to enhance strong policy models and alleviate the over-optimization problem.

## 1 Introduction

The recent development of large language models (LLMs) has focused on aligning model outputs with human intentions and preferences (Ji et al., ). During alignment, LLMs are directly optimized on pairwise data and response-level supervision,
where popular methods such as reinforcement learning from human feedback (RLHF) (Ouyang et al., ; Stiennon et al., ) and direct preference alignment Rafailov et al. (); Yuan et al. (); Meng et al. () only introduce supervision signals at the end of each response. As deriving preference optimization as bandit problems can lead to sub-optimal solutions and unstable training processes Zhong et al. (); Zeng et al. (), many works propose to model LLM decoding as token-level Markov Decision Processes (MDP) and introduce step-wise supervision signals that quantify the value of each action, successfully applied in tasks such as instruction following Zhong et al. (); Yoon et al. () and mathematical reasoning Xie et al. (); Chen et al. (); Lai et al. ().

Figure: Figure 1: Token-level reward accumulations on two datasets. As tokens with high rewards are considered key tokens for chosen responses, their Top-K% tokens are accumulated in descending order with the highest rewards. In contrast, the rewards are accumulated in ascending orders for rejected responses.
Refer to caption: extracted/5810983/figs/token_level_reward_distribution.png

Though achieving outstanding performance, most of these methods are optimized on all available tokens from the training dataset. To validate the effectiveness of this setup, in Figure 1, we present the token-level reward accumulations for 1,000 samples from an instruction following dataset Cui et al. () and a question answering (QA) dataset Wu et al. (), where the token-level rewards are assigned by GPT-4 Achiam et al. (). According to the results, a limited number of tokens with extreme reward values (key tokens) dominate the total rewards. For instruction following, the Top-35.6% tokens occupy the highest 80% rewards for chosen responses, while the lowest 37.4% tokens only occupy 20% rewards for rejected responses.
In QA, selecting top-50% key tokens can cover over 80% of effective supervision signals. These observations prove that not all tokens are equally effective in preference alignment, and optimizing on all available tokens can be noisy and inefficient Lin et al. (); Chen et al. (). Some works explored only optimizing on selected response fragments, but their selection strategies are complex and expensive,such as iterative Monte-Carlo tree search Xie et al. (); Chen et al. () or annotations from human/capable LLMs Lai et al. (); Yoon et al. (). The above limitations underscore the importance of selective training and efficient token selection strategies in improving preference optimization algorithms.

Based on these intuitions, we propose Selective Preference Optimization (SePO), a novel selective alignment strategy that centers on efficient key token selection without requiring strong, fine-grained supervision signals. We theoretically show that Direct Preference Optimization (DPO) Rafailov et al. () inherently learns a reward function that decouples the response-level reward values into token level Rafailov et al. (). Based on this conclusion, we propose the first DPO-based token selection method, which trains an oracle model on a moderate-scale subset of the target data distribution, aiming to parameterize an optimal token-level reward function. This token selection strategy has two key advantages: 1) the oracle modeling process is based on the original response-level preference annotations without requiring any extra supervision signals, making it directly applicable to any existing alignment datasets; (2) the cost for token selection can be easily reduced by controlling the oracle model size and the scale of its training subset, which enables cost-efficient selective alignment. We then utilize the estimated reward function to score all tokens within the large-scale target dataset, where tokens with the highest reward values in the chosen responses and tokens with the lowest reward values in the rejected responses are selected as key tokens for alignment. Finally, we design a reference model-free contrastive objective function to optimize the target policy model on the selected tokens. As SePO enables small oracle models to steer selective alignment for much larger policy models, we further explore it as a new paradigm for weak-to-strong generalization Burns et al. (), where the focus is two-fold: 1) we leverage weak oracle models to select tokens from in-distribution data for training strong policy models; 2) we train oracle models on out-of-distribution data, which select key tokens to improve target policy model performance and avoid over-optimization Gao et al. (); Rafailov et al. () on the weak supervision data.

In summary, our main contributions are:

- •
We propose Selective Preference Optimization, a simple yet effective selective training strategy for preference alignment. It achieves alignment efficiently by obtaining key tokens with an estimated token-level reward function and only optimizing on these selected key tokens;
- •
We explore the application of SePO on weak-to-strong generalization. The results show that weak oracle models effectively supervise strong policy models with up to 16.8$\times$ more parameters. SePO also selects useful tokens from weak supervision data to enhance strong policy model performance, alleviating the performance degradation problem commonly encountered in full optimization on out-of-distribution data;
- •
We examine SePO on three public evaluation benchmarks. Experimental results show that SePO significantly improves performances on five policy models and outperforms competitive baseline methods by only optimizing 30% key tokens on the target dataset.

Figure: Figure 2: The pipeline for Selective Preference Optimization (SePO). SePO mainly consists of three steps: 1) Parameterize a token-level reward function by training an oracle model on a moderate-scale dataset; 2) Score all tokens within the target preference dataset and select key tokens; 3) Training the policy model on selected tokens in a contrastive optimization manner.
Refer to caption: x1.png

## 2 Preliminary

### 2.1 Preference Alignment of Language Models

Preference alignment directly optimizes LLMs with human preferences by maximizing the reward values of model outputs, which are obtained via a response-level reward function $r(q,y)$. The reward function is defined under the Bradley-Terry (Bradley and Terry, ) model of preferences. Specifically, for the same prompt $q$ and two completed responses $(y_{1},y_{2})$ under data distribution $\mathcal{D}$, the model assumes:

$$ $P_{\mathcal{D}}(y_{1}\succ y_{2}|q)=\sigma(r(q,y_{1})-r(q,y_{2}))$ (1) $$

where $\sigma$ denotes the logistic function and $P_{\mathcal{D}}(y_{1}\succ y_{2})$ denotes the probability that $y_{1}$ is preferred against $y_{2}$.
The alignment of language models is typically cast as a KL-constrained optimization problem on the reward values, formalized as

$$ $\displaystyle\mathop{argmax}\limits_{\pi}\mathbb{E}_{q\sim\mathcal{D},y\sim\pi (y|q)}\left[r(q,y)\right]$ (2) $\displaystyle s.t.\ \mathbb{E}_{q\sim\mathcal{D}}\mathbb{D}_{KL}\left[\pi(y|q) \|\pi_{ref}(y|q)\right]\leq\sigma$ $$

where $\pi$ denotes the aligned policy model, $\pi_{ref}$ denotes the reference policy model. Taking the following Lagrangian, the problem is transformed as:

$$ $\displaystyle\mathop{argmax}\limits_{\pi}\mathbb{E}_{q\sim\mathcal{D},y\sim\pi (y|q)}\left[r(q,y)\right]$ (3) $\displaystyle-\beta\mathbb{D}_{KL}\left[\pi_{\phi}(y|q)\|\pi_{ref}(y|q)\right]$ $$

### 2.2 Direct Preference Optimization

Ziebart et al. () have shown that Eqn 3 has a closed-form optimal solution, which enables the reward function to be re-parameterized by the optimal policy:

$$ $r(q,y)=\beta\mathop{log}\frac{\pi^{*}(y|q)}{\pi_{ref}(y|q)}+\beta\mathop{log}Z (q)$ (4) $$

where $\pi^{*}$ denotes the optimal policy, and $Z(q)$ is the partition function. DPO Rafailov et al. () bypasses the reward modeling stage by directly substituting this closed-form solution into Eqn. 1, which cancels out $Z(q)$ as it un-changes with the same $q$, yielding the following DPO objective:

$$ $\displaystyle\mathcal{L}_{DPO}=-\mathbb{E}_{\left(q,y_{w},y_{l}\right)\sim \mathcal{D}}\log\sigma\left(\beta u(x,y_{w},y_{l})\right)$ (5) $\displaystyle u(x,y_{w},y_{l})=\log\frac{\pi_{\theta}(y_{w}|x)}{\pi_{ref}(y_{w }|x)}-\log\frac{\pi_{\theta}(y_{l}|x)}{\pi_{ref}(y_{l}|x)}$ $$

where $y_{w}$ and $y_{l}$ denote the preferred and dis-preferred responses to the prompt $q$.

## 3 Methodology

In this section, we first show DPO training as inherently fitting a token-level reward function that decouples the response-level reward function (Sec. 3.1). Based on this conclusion, we propose Selective Preference Optimization (SePO), which optimizes the target policy model only with selected key tokens by the estimated optimal token-level reward function (Sec. 3.2). We also propose the application of SePO in weak-to-strong generalization (Sec. 3.3). The training pipeline of SePO is shown in Figure 2.

### 3.1 DPO as Token-level Reward Function Estimator

Due to the auto-regressive nature, the decoding process of LLMs can be naturally formulated as a token-level MDP. The MDP is defined as a tuple $\mathcal{M}=(\mathcal{S},\mathcal{A},f,r(s_{t},a_{t}),\rho)$, where $\mathcal{S}$ and $\mathcal{A}$ denote the state space and action space. $s_{t}\in\mathcal{S}$ deontes the current state, consisting of all prompt tokens and current generated tokens (i.e. $s_{t}=\{q|y_{0},...,y_{t}\}$, $|$ denotes concatenation). $s_{T}$ denotes the terminal state. $a_{t}\in\mathcal{A}$ denotes the current action, where $\mathcal{A}$ is the token vocabulary. $f$ is the deterministic state transition function that concatenates the current state $s_{t}$ and action $a_{t}$. $\rho$ is an initial state distribution over prompts $q$, where the initial state $s_{1}$ consists of the tokens from $q$. $r(s_{t},a_{t})$ denotes the token-level reward function.

In this section, we show that DPO inherently learns the best estimate on a token-level distribution of the response-level reward values along the token-level MDP trajectory. We begin with the following widely used mild assumption Zhong et al. (); Zeng et al. ():

###### Assumption 1 .

Any response-level reward function $r$ can be decoupled into the token level as a linear combination of reward values modeled by another token-level reward function $\hat{r}$ along the trajectory for its MDP.

$$ $r(q,\tau)=\sum_{t=1}^{T}\hat{r}(s_{t},a_{t})$ (6) $$

where $s_{t}$, $a_{t}$ are states and actions within the token-level MDP trajectory $\tau=\{s_{1},a_{1},s_{2},...,s_{T}\}$.

With the above assumption, the Bradley-Terry model can be replaced into token level:

$$ $P_{\mathcal{D}}(\tau^{w}\succ\tau^{l}|q)=\sigma(\sum_{i=1}^{N}\hat{r}(s_{i}^{w },a_{i}^{w})-\sum_{j=1}^{M}\hat{r}(s_{j}^{l},a_{j}^{l}))$ (7) $$

where $\tau^{w}$ and $\tau^{l}$ are the chosen and rejected trajectories (responses), which are assumed to start and end at the same state $s_{1}$ and $s_{T}$.

###### Theorem 1 .

With a reference model $\pi_{ref}$, fitting any reward functions $r$ that are consistent to the Bradley-Terry model with the DPO algorithm leads to an optimal estimation of another reward function $\hat{r}$ that decouples the response-level reward values into the token level, which satisfies:

$$ $\hat{r}(s_{t},a_{t})\propto\mathop{log}\frac{\pi^{*}(a_{t}|s_{t})}{\pi_{ref}(a _{t}|s_{t})}$ (8) $$

where $\pi^{*}$ denotes the oracle policy obtained by DPO.

This reward function marks the contribution of each action given the current state at the token level. In practice, the quality of the training data for DPO determines how well the calculated reward quantifies the token-level contribution.

###### Proof.

This proof is inspired by Rafailov et al. (). Common policy gradient-based RL practices Schulman et al. () optimize Eqn. 3 in token-level MDP with an entropy-bonus $\mathcal{H}(\pi)$ and a KL-constraint with $\pi_{ref}$:

$$ $\mathop{max}_{\pi}\mathbb{E}_{a_{t}\sim\pi(\cdot|s_{t})}\sum_{t=1}^{T}\left[ \hat{r}(s_{t},a_{t})+\beta\mathop{log}\pi_{ref}(a_{t}|s_{t})+\beta\mathcal{H}( \pi)\right]$ (9) $$

where $s_{1}\sim\rho$. Its optimal solution is given by Ziebart et al. () under the maximum entropy RL setting:

$$ $\pi^{*}(a_{t}|s_{t})=\mathop{exp}\left((Q^{*}(s_{t},a_{t})-V^{*}(s_{t}))/\beta\right)$ (10) $$

where $Q^{*}(s_{t},a_{t})$ is the optimal Q-function that estimates the partial returns of $a_{t}$ under $s_{t}$, and $V^{*}(s_{t})$ estimates the expected future returns under current state $s_{t}$. Under a KL-divergence regularization with the reference model, the relationship between Q-function and token-level reward values can be established as follows with the Bellman equation:

$$ $Q^{*}(s_{t},a_{t})=r(s_{t},a_{t})+\beta\log\pi_{ref}(a_{t}|s_{t})+V^{*}(s_{t+1})$ (11) $$

where $V^{*}(s_{T})=0$. Combining Eqn. 10 and 11, we have:

$$ $r(s_{t},a_{t})=\beta\log\frac{\pi^{*}(a_{t}|s_{t})}{\pi_{ref}(a_{t}|s_{t})}+V^ {*}(s_{t})-V^{*}(s_{t+1})$ (12) $$

Under Assumption 1, we substitute Eqn. 12 into Eqn. 6, the response-level reward is factorized as follows:

$$ $\displaystyle r(q,\tau)$ $\displaystyle=\sum_{t=1}^{T}r(s_{t},a_{t})$ (13) $\displaystyle=\mathop{\sum}_{t=1}^{T}\beta\log\frac{\pi^{*}(a_{t}|s_{t})}{\pi_ {ref}(a_{t}|s_{t})}+V^{*}(s_{1})$ $$

Note that in DPO, $V^{*}(s_{1})$ remains unchanged for each response pair as they have the same start state $s_{1}$. This means the preference modeling process for each response pair only depends on the first term of Eqn. 13. Therefore, we conclude that the optimal policy $\pi^{*}$ learned by DPO inherently fits the response-level reward value with another token-level reward function $\hat{r}(s_{t},a_{t})$, which is parameterized as

$$ $\hat{r}(s_{t},a_{t})=\beta\mathop{log}\frac{\pi(a_{t}|s_{t})}{\pi_{ref}(a_{t}| s_{t})}$ (14) $$

This indicates our results in Eqn. 8 and completes the proof.
∎

###### Assumption 1 .

###### Theorem 1 .

###### Proof.

### 3.2 Selective Preference Optimization

SePO is guided by the simple idea that "not all tokens are equally effective", which has been widely evaluated Lin et al. (); Chen et al. (); Lai et al. (). We explore fully utilizing DPO to efficiently select the most useful tokens in modeling human preferences in LLM alignment. Firstly, we train an oracle model on a moderate-scale preference dataset with DPO, aiming to model a token-level reward function for the target data distribution. The reference model is then applied to large-scale data to score all the tokens. The policy model is only trained on selected tokens with highest scores in chosen responses and lowest scores in rejected responses, which are expected as key tokens in achieving alignment.

Figure: Figure 3: Application of SePO on weak-to-strong generalization. Left: SePO utilizes the weak oracle model to steer the strong policy model; Right: Useful supervision signals in out-of-distribution data are selected by the oracle model to enhance alignment on the policy model.
Refer to caption: x2.png

#### Oracle Modeling with DPO.

We explore fitting an oracle model with DPO utilizing a moderate-scale dataset via random sampling over the target preference dataset $\mathcal{D}$, which we expect to parameterize a pessimistic estimation of the target reward function.

###### Theorem 2 .

Let $\mathcal{D}$ be the target preference dataset with $N$ samples, and $\mathcal{S}$ be a random selection of $m$ samples from $\mathcal{D}$ (m$\leq N$), which is drawn independently and uniformly. Then we have:

The reward function $r_{\mathcal{S}}$ modeled by fitting $\mathcal{S}$ with DPO is a pessimistic estimation of the target reward function $r_{\mathcal{D}}$. The result can be formalized as:

$$ $\mathbb{E}_{\mathcal{S}}(r_{\mathcal{S}}(q,y))\leq r_{\mathcal{D}}(q,y)$ (15) $$

where $q,y$ denote any query-response pairs drown from $\mathcal{D}$. The equality holds when $m=N$.

###### Proof.

As the reward functions are parameterized via fitting the DPO algorithm on the datasets, we substitute Eqn. 4 into Eqn. 15. As the term $\beta\log\pi_{ref}(y|q)$ and $\beta\log Z(q)$ are unrelated to $\mathcal{S}$, they are easily canceled and we transfer the proof target into comparing the optimal policy functions:

$$ $\mathbb{E}_{\mathcal{S}}\left[\log\pi_{\mathcal{S}}^{*}(y|q)\right]\leq\log\pi _{\mathcal{D}}^{*}(y|q)$ (16) $$

Let $\mathcal{D}=\{x_{1},x_{2},...,x_{N}\}$, where $x_{i}$ represents an $(q,y,r)$ data point, and $\mathcal{S}=\{x_{i_{1}},x_{i_{1}},...,x_{i_{m}}\}$, where $x_{i_{j}}$ is selected from $\mathcal{D}$.
To show that $S$ is an unbiased estimator of the target data distribution, we calculate its empirical distribution over all possible random samples drawn from $\mathcal{D}$. The empirical distribution $P_{\mathcal{S}}(X)$ based on the sampled dataset is as follows:

$$ $P_{\mathcal{S}}(X)=\frac{1}{m}\sum_{j=1}^{m}\delta(X=x_{i_{j}})$ (17) $$

where $\delta$ indicates the presence of a sample $X$. Taking its expectation over all possible sampled datasets, we have:

$$ $\displaystyle\mathbb{E}_{\mathcal{S}}\left[P_{\mathcal{S}}(X)\right]$ $\displaystyle=\mathbb{E}_{\mathcal{S}}\left[\frac{1}{m}\sum_{j=1}^{m}\delta(X= x_{i_{j}})\right]$ (18) $\displaystyle=\frac{1}{m}\sum_{j=1}^{m}\mathbb{E}_{\mathcal{S}}\left[\delta(X= x_{i_{j}})\right]$ $$

As each $x_{i_{j}}$ is equally likely to be any $x_{i}\in\mathcal{D}$, we have

$$ $\mathbb{E}_{\mathcal{S}}\left[\delta(X=x_{i_{j}})\right]=\frac{1}{N}\sum_{i=1} ^{N}\delta(X=x_{i})=P_{\mathcal{D}}(X)$ (19) $$

Substituting Eqn. 19 into Eqn. 18, we have

$$ $\mathbb{E}_{\mathcal{S}}\left[P_{\mathcal{S}}(X)\right]=P_{\mathcal{D}}(X)$ (20) $$

Based on the same reference model and empirical data distribution (Eqn. 20), we expect training on $S$ with DPO to obtain an unbiased estimation of the target optimal policy function:

$$ $\mathbb{E}_{\mathcal{S}}\left[\pi_{\mathcal{S}}^{*}(y|q)\right]=\pi_{\mathcal{ D}}^{*}(y|q)$ (21) $$

Because logarithm is a strictly concave function, according to Jensen’s inequality, we have:

$$ $\mathbb{E}_{\mathcal{S}}\left[\log\pi_{\mathcal{S}}^{*}(y|q)\right]\leq\log \mathbb{E}_{\mathcal{S}}\left[\pi_{\mathcal{S}}^{*}(y|q)\right]$ (22) $$

Substituting Eqn. 21 into Eqn. 22, we prove Eqn. 16, which completes the proof.
Note that when $m=N$, we have $\mathcal{S}=\mathcal{D}$, and the training process gives an unbiased estimation of target reward function $r_{\mathcal{D}}$.
∎

With the results from Theorem 2, we first perform SFT on the chosen responses of the moderate-scale dataset $\mathcal{S}$ to obtain the base model $\pi_{ref}$:

$$ $\mathcal{L}_{SFT}=-\mathbb{E}_{\left(q,y_{w}\right)\sim\mathcal{S}}\sum_{i} \log\pi_{ref}(y_{w}^{i}|q,y_{w}^{<i})$ (23) $$

With the base model, we further perform DPO on the small dataset $\mathcal{S}$ with the objective function Eqn. 5
to obtain the oracle model $\pi_{ora}$. With Theorem 1, we can utilize $\pi_{ref}$ and the oracle model $\pi_{ora}$ to parameterize the optimal token-level reward function for human preferences, which are used for token selections.

###### Theorem 2 .

###### Proof.

#### Token Selection.

We score all tokens within the target preference dataset with the estimated token-level reward function. Based on the token-level MDP and Theorem 1, for each prompt-response pairs $(q,y)$, the score for token $y_{i}$ is calculated as follows:

$$ $s(y_{i})=\log\frac{\pi_{ora}(y_{i}|q,y_{<i})}{\pi_{ref}(y_{i}|q,y_{<i})}$ (24) $$

We define a token selection ratio $k$, which determines the selected proportion for each response. For chosen responses, we utilize the following indicator function for selection:

$$ $\mathbf{I}_{k}^{w}(s(y_{i}))=\begin{cases}1,&\text{if $s(y_{i})$ ranks in highest $k\%$ in $y$}\\ 0,&\text{otherwise}\end{cases}$ (25) $$

For rejected responses, we change the condition for indicating $1$ to "if $s(y_{i})$ ranks in lowest $k\%$ in $y$" and mark the indicator function as $\mathbf{I}_{k}^{l}(s(y_{i}))$. The intuition behind this action is that key tokens for chosen responses are likely to contribute high token-level rewards, while key tokens for rejected responses are likely with low token-level rewards, whose probabilities are significantly suppressed in $\pi_{ora}$ compared to the base model.

#### SePO Objective.

We design a simple contrastive preference optimization objective on the target policy model $\pi_{t}$ with the selected tokens. Specifically, the objective function is designed as follows:

$$ $\displaystyle\mathcal{L}_{SePO}=-\mathbb{E}_{\left(q,y_{w},y_{l}\right)\sim \mathcal{D}}\log\sigma\left(\hat{u}_{w}(q,y_{w})-\hat{u}_{l}(q,y_{l})\right)$ (26) $\displaystyle\hat{u}_{w}(q,y)=\frac{\gamma}{|y|\cdot k\%}\sum_{i=1}^{|y|} \mathbf{I}_{k}^{w}(s(y_{i}))\log\pi_{t}(y_{i}|q,y_{<i})$ $\displaystyle\hat{u}_{l}(q,y)=\frac{\gamma}{|y|\cdot k\%}\sum_{i=1}^{|y|} \mathbf{I}_{k}^{l}(s(y_{i}))\log\pi_{t}(y_{i}|q,y_{<i})$ $$

where $\gamma$ controls the scaling of the rewards. The SePO objective enables direct adjustment of only crucial tokens for alignment, which avoids noise in both chosen and rejected responses. This design is expected to improve the efficiency and stability of the preference optimization process.
The objective is also length-normalized and reference model-free, which prevents bias towards over-length responses and enables memory-efficient alignment Meng et al. (); Yuan et al. ().

### 3.3 Application: Weak-to-Strong Generalization

A unique advantage of SePO is that the cost of its token selection process can be easily reduced by controlling the oracle model size, which enables small oracle models to steer the alignment for policy models with much stronger capabilities. Therefore, we explore the application of SePO in weak-to-strong generalization Burns et al. (), which aims to elicit the capabilities of strong student models with weak supervision signals. As illustrated in Figure 3, our focus is two-fold:

#### Weak Oracle Modeling.

We propose to leverage weak oracle models that underperform the policy models to select the key tokens from strong in-distribution data. Our intuition is that weak supervisors (oracle models) only identify which tokens are most effective in enhancing the alignment performance, rather than directly providing supervision signals, which normally requires stronger capabilities than the student model.

#### Weak Data Supervision.

During alignment, as the policy model becomes stronger, continual full optimization on the original data distribution can lead to over-optimization on the reward function Gao et al. (); Rafailov et al. (), which can seriously degrade policy model performance. Online preference optimization Xiong et al. (); Xie et al. () alleviates over-optimization with online annotations of new in-distribution data, but can be costly for strong policy models.

Weak data supervision focuses on scenarios when only weak out-of-distribution data is available for strong policy models. We propose to leverage the SePO framework to select key tokens from the weak dataset, and only the selected tokens are utilized to supervise the strong policy model. Instead of full optimization on the training data, we expect selective optimization on the key tokens to prevent over-optimization on the out-of-distribution data, while still leveraging effective supervision signals to further improve the policy model.

**Table 1: Performance of SePO and other baseline methods on three benchmark datasets. For SePO, the oracle models are based on TinyLLaMA-1.1B and Pythia-1B, trained on the full UltraFeedback dataset. The modeled reward function is then used to select the top-30% tokens of chosen and rejected responses.**
|  |  | Arena-Hard | AlpacaEval 2.0 | MT-Bench |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Policy Model | Methods | Win Rate | LC Win Rate | Win Rate | Assistant | QA | Math | Coding | Avg. |
| Pythia-SFT-2.8B | Base | 2.34% | 3.8% | 4.12% | 4.7 | 5.05 | 1.27 | 1.8 | 2.8 |
| +DPO | 5.71% | 5.72% | 6.1% | 4.7 | 5.57 | 1.55 | 2.13 | 3.26 |  |
| +IPO | 5.6% | 4.8% | 4.96% | 5.16 | 5.1 | 1.1 | 2.41 | 3.28 |  |
| +RRHF | 4.37% | 4.33% | 4.47% | 4.5 | 4.82 | 1.6 | 2.25 | 2.93 |  |
| +SimPO | 5.2% | 5.8% | 6.0% | 4.35 | 6.06 | 1.52 | 2.0 | 3.3 |  |
| +SePO (Ours) | 6.3% | 7.1% | 7.32% | 5.3 | 5.3 | 2.38 | 2.5 | 3.45 |  |
| Pythia-SFT-6.9B | Base | 4.23% | 5.0% | 5.17% | 6.0 | 6.18 | 1.48 | 1.75 | 3.68 |
| +DPO | 10.2% | 12.78% | 13.27% | 6.33 | 7.26 | 2.87 | 2.85 | 4.7 |  |
| +IPO | 8.1% | 11.78% | 12.6% | 6.7 | 6.53 | 2.5 | 2.43 | 4.34 |  |
| +RRHF | 7.47% | 11.42% | 13.2% | 6.46 | 6.28 | 2.5 | 2.4 | 4.31 |  |
| +SimPO | 8.0% | 11.8% | 12.72% | 6.65 | 5.89 | 3.13 | 2.83 | 4.51 |  |
| +SePO (Ours) | 10.94% | 14.27% | 13.6% | 6.7 | 7.37 | 2.93 | 2.85 | 4.79 |  |
| TinyLLaMA-Chat | Base | 1.6% | 1.26% | 1.43% | 4.01 | 3.48 | 1.45 | 2.35 | 3.28 |
| +DPO | 2.2% | 1.95% | 2.18% | 4.02 | 3.52 | 1.5 | 2.4 | 3.31 |  |
| +IPO | 2.3% | 1.85% | 2.06% | 4.03 | 3.72 | 1.45 | 2.4 | 3.38 |  |
| +RRHF | 3.1% | 3.02% | 2.12% | 4.12 | 3.7 | 1.3 | 2.5 | 3.4 |  |
| +SimPO | 2.61% | 1.3% | 3.7% | 4.02 | 4.07 | 1.35 | 2.25 | 3.28 |  |
| +SePO (Ours) | 4.1% | 3.55% | 3.37% | 4.52 | 3.93 | 1.35 | 2.25 | 3.62 |  |
| LLaMA2-Chat-7B | Base | 4.6% | 5.4% | 5.0% | 6.48 | 7.87 | 1.45 | 1.95 | 4.48 |
| +DPO | 8.5% | 7.8% | 6.71% | 6.33 | 6.26 | 2.85 | 2.85 | 5.43 |  |
| +IPO | 8.12% | 8.78% | 9.4% | 6.66 | 6.98 | 2.55 | 2.3 | 5.75 |  |
| +RRHF | 9.4% | 13.35% | 14.41% | 6.15 | 6.16 | 3.05 | 2.8 | 5.35 |  |
| +SimPO | 9.59% | 13.58% | 15.4% | 6.52 | 6.38 | 3.5 | 2.8 | 5.63 |  |
| +SePO (Ours) | 10.3% | 14.4% | 14.91% | 7.15 | 7.53 | 2.85 | 3.1 | 6.27 |  |
| LLaMA2-Chat-13B | Base | 12.0% | 8.4% | 7.7% | 5.82 | 6.36 | 3.15 | 3.3 | 5.7 |
| +DPO | 13.48% | 13.72% | 13.37% | 6.92 | 6.81 | 4.1 | 3.77 | 5.84 |  |
| +IPO | 13.95% | 14.27% | 14.4% | 7.02 | 6.63 | 4.3 | 3.5 | 5.76 |  |
| +RRHF | 13.84% | 15.94% | 16.36% | 5.85 | 6.38 | 3.7 | 3.25 | 5.73 |  |
| +SimPO | 14.7% | 16.4% | 17.02% | 6.73 | 6.4 | 3.2 | 3.0 | 5.7 |  |
| +SePO (Ours) | 15.5% | 17.53% | 18.41% | 7.2 | 6.9 | 3.55 | 3.95 | 6.36 |  |

## 4 Experiments

### 4.1 Experimental Settings

#### Models and Training Data

We comprehensively evaluate SePO on two representative model families: LLaMA (Touvron et al., ) and Pythia Biderman et al. (). To approximate the optimal token-level reward function, we first obtain the base model by training on the [UltraChat-200K](https://huggingface.co/datasets/HuggingFaceH4/ultrachat_200k) dataset Ding et al. () in an SFT manner. For the LLaMA model family, we train the base model on the pre-trained TinyLLaMA-1.1B Zhang et al. () model. For Pythia, we separately train on Pythia-(70M, 160M, 410M, 1B, 1.4B) to facilitate research on the effect of oracle models with different sizes. For each base model, we obtain the oracle models by further fine-tuning with DPO on the [UltraFeedback](https://huggingface.co/datasets/HuggingFaceH4/ultrafeedback_binarized) dataset Cui et al. () with 61,135 preference pairs. We examine the selective preference training process on target policy models with various capabilities. For Pythia, we perform SFT on Pythia-(2.8B, 6.9B) with UltraChat-200K and use them as policy models, which we refer as Pythia-SFT. For LLaMA, we test on TinyLLaMA-Chat-1.1B, LLaMA2-Chat-7B, and LLaMA2-Chat-13B.

#### Baseline Methods

We compare the performance of SePO with state-of-the-art offline preference optimization methods to indicate its effectiveness. DPO Rafailov et al. () explicitly models the relation between the reward functions and optimal policy, which enables reward model-free preference alignment. IPO Azar et al. () provides a variant of DPO that prevents the requirement that pairwise preferences can substitute reward values. We introduce another two competitive reference model-free alignment methods: RRHF Yuan et al. () directly optimize the probability of the target response pairs with a pairwise ranking loss, with an SFT-based regularization on the chosen responses. SimPO Meng et al. () optimizes the length-regularized probability of the response pairs with a margin.

#### Evaluation Benchmarks

We quantify the contribution of each method by evaluating on three widely utilized instruction-following benchmarks: AlpacaEval 2.0 Dubois et al. (), MT-Bench Zheng et al. (), and Arena-Hard Li et al. (). AlpacaEval 2.0 consists of 805 queries to evaluate the models’ versatile conversational abilities. We report the win rates and length-controlled win rates (LC win rate) of evaluated models against the responses of GPT-4-turbo. The LC win rates are designed to reduce influences of model verbosity. MT-Bench covers eight categories with 80 queries. We report the average scores ranging from 0 to 10. Due to the widely reported poor separability
of MT-Bench reported by previous works Meng et al. (); Li et al. (), we further display fine-grained scores of model capability, which we reorganize the original 8 categories as follows: Assistant (Writing, Roleplay, Extraction), QA (Reasoning, STEM, Humanities), Math, and Coding. Scores for Assistant and QA are averages of the original categories. Arena-Hard extends MT-Bench with 500 high-quality queries, where we report win rates against GPT-4-0314 model outputs. All judgments are performed by the latest GPT-4o model.

### 4.2 Overall Performance

Performances of SePO and other baseline methods on three benchmark datasets are presented in Table 1. According to the results, SePO significantly improves performance over the base policy models. For example, on Arena-Hard, SePO achieves a 6.71% improvement in win rates on Pythia-6.9B. SePO also outperforms other strong baseline preference optimization methods. On Arena-Hard, SePO achieves the best win rates on all policy models, surpassing state-of-the-art methods such as SimPO and DPO. As SePO models are only optimized on 30% of the tokens trained on other methods, these results directly strengthen the effectiveness of selective training strategies applied in preference optimization.

On AlpacaEval 2.0, SePO continues to achieve superior performances over baseline methods on both win rates and LC win rates, further proving its effectiveness on different benchmarks. Notably, SePO outperforms all other methods on length-controlled win rates, including SimPO and RRHF, which are specifically designed for length-normalized reward formulation. These results show that selective training strategies also enhance policy models in avoiding over-length responses. We believe the reason is that during token selection, the token-level reward function can assign the end-of-sentence tokens with low-ranking scores, which can be discarded during optimization if the response ends inappropriately (e.g. over-length or repetition). In contrast, though SimPO and RRHF design length-normalized
rewards, the end-of-sentence tokens are included for all responses, still fitting the response lengths for all training samples.

On MT-Bench, SePO outperforms all other methods on average scores. Due to the widely discussed poor separability of overall scores for MT-Bench, we look into category-based evaluations that provide fine-grained assessments. As shown, SePO achieves the best performances on 70% of comparisons on Assistant and QA, indicating its significant improvement on subjective tasks that require high-level intention understanding and writing skills. However, SePO outperforms baseline methods in math and coding on only 40% of the comparisons, underperforming baseline methods such as IPO and SimPO on several policy models. A possible reason is that objective tasks such as math and coding require coherent logic along the token-level MDP for response generation Xie et al. (); Chen et al. (); Lai et al. (), while SePO is only optimized on selected tokens, which brings discontinuity in learning the logic during training. Baseline methods that optimize all tokens enable policy models to learn the full chain of reasoning and show advantages in objective scenarios.

Figure: Figure 4: SePO performances with different combinations of Top-K% selection ratios for chosen and rejected responses. The performances are quantified by the LC win rates on the AlpacaEval 2.0 benchmark. All results are obtained with a TinyLLaMA oracle model trained on the full UltraFeedback dataset.
Refer to caption: extracted/5810983/figs/topk_surface.png

### 4.3 Impact of Data Scale

This section evaluates how training data scales of SePO and oracle modeling impact policy model performance. We focus on two research questions:

#### How do token selection rates influence SePO performance?

We investigate the influences of token selection rates on SePO performances by introducing various combinations for chosen and rejected responses. The ratio for chosen/rejected responses is each selected from $\{0.1,0.3,0.5,0.7,0.9\}$ and matched pair-wise, with 25 combinations in total. The experimental results are presented in Figure 4.

According to the results, increasing selection rates from 0.1 for chosen/rejected responses rapidly improves policy model performance, but the momentum decreases as the ratio continues to grow. For example, the LC win rate of LLaMA2-Chat-7B improves from 8.37% to 14.8% as the ratios for chosen/rejected responses rise from 0.1 to 0.5 progressively, then stabilizes around 14.7% with higher selection rates. These observations prove our hypothesis that not all tokens are equally effective for LLM alignment. Training only on key tokens effectively improves alignment performance, while other tokens provide limited supervision information. From the figures, we conclude that training on Top-30% tokens for TinyLLaMA or Top-50% tokens for LLaMA2-Chat-(7B, 13B) already provides comparable performance to alignment on all tokens.

Increasing selection rates for chosen responses generally outperforms increasing ratios for rejected responses. For example, with a fixed rejected selection rate, the TinyLLaMA-Chat performance smoothly improves as the chosen ratios grow. However, improving rejected ratios from 0.1 to 0.9 leads to decreased model performance in 4 out of 5 fixed chosen selection rates. Similar results can be observed in the other two policy models. These results indicate that compared to increasing probabilities for irrelevant tokens in chosen responses, suppressing probabilities for high-reward tokens in rejected responses can significantly affect the model performance.

Figure: Figure 5: SePO performances supervised by oracle models trained with different proportions of the target dataset. The performances are quantified by the LC win rates on the AlpacaEval 2.0 benchmark. For each proportion, we do random sampling three times and report the average performance.
Refer to caption: extracted/5810983/figs/oracle_data_scale.png

#### How much data trains a good oracle model?

In Theorem 2, we proved that training an oracle model on a randomly selected moderate-scale dataset is a pessimistic estimation of the target reward function. In this section, we empirically investigate the influence of the training data scale for oracle models on SePO performance. Specifically, we randomly sample different proportions of data from UltraFeedback as training data for the TinyLLaMA-based oracle model. The results are shown in Figure 5.

According to the results, training the oracle model on higher proportions of the target data generally leads to superior model performance. LC win rates on all policy models improve as the estimated token-level reward function becomes more accurate. Training on high data proportions also retains the majority of token selection capabilities. For example, supervising LLaMA2-Chat-7B policy model with an oracle model trained on 70% of the data still achieves 13.66% of LC win rates, which outperforms strong baseline methods such as SimPO and RRHF. However, the continual decrease in training proportions can significantly harm model performance. For the TinyLLaMA-Chat policy model, an oracle model trained with less than 40% of target data leads to LC win rates of less than 1.26%, which even underperforms the original policy model. For LLaMA2-Chat-(7B,13B), this threshold increases to 50% and 70%. These results indicate the importance of accurate estimation of the reward function, where false selection of key tokens degrades the capability of the policy model. These thresholds also increase with the size of policy models, showing that the high quality of key tokens becomes more important in supervising models with strong capabilities.

Figure: Figure 6: Evaluation results on weak-to-strong generalization. (a) LC win rates of policy models on AlpacaEval 2.0, which are trained with oracle models of various sizes; (b)(c) Token-level score distributions for 5,000 chosen/rejected responses, with the rewards obtained from different oracle models.
Refer to caption: extracted/5810983/figs/weak2strong_model.png

### 4.4 Weak-to-Strong Generalization

In this section, we empirically evaluate SePO on enhancing weak-to-strong generalization.

#### Weak Oracle Modeling.

In Table 1, we presented the performance of TinyLLaMA and Pythia-1B oracle models on guiding stronger policy models (e.g. Pythia-SFT-6.9B, LLaMA2-Chat-13B). The competitive results of SePO prove the viability of weak oracle modeling.
To provide a clear landscape, we further train oracle models with Pythia-(70M, 160M, 410M, 1B, 1.4B) on the same target data and compare their performances on the Pythia-SFT-(2.8B, 6.9B) policy models. The results are shown in Figure 6 (a).

According to the results, oracle models with weak capabilities can provide effective supervision to strong policy models. For example, training with the Pythia-410M oracle model achieves 6.58% on Pythia-SFT-2.8B and 13% on Pythia-SFT-6.9B policy models, with up to 16.8$\times$ more parameters than the oracle model. These results outperform full optimization on the target dataset with baseline methods such as DPO and SimPO. In addition, the performance of target policy models continually improves as the oracle model size increases. For example, on Pythia-SFT-6.9B policy model, the 1.4B oracle model outperforms the 410M orcale model by 1.84% and the 70M model by 9.15%. These results show that oracle models with stronger capabilities can better model the token-level reward function and accurately select key tokens.

To provide an intuitive view, we present the token-level score distributions of different oracle models in 6 (b)(c). For the chosen scores distribution, strong oracle models such as Pythia-(1B,1.4B) show higher densities in extreme (large and small) reward values, which facilitates separating key tokens from the other tokens. In contrast, small oracle models tend to fit a Gaussian distribution, where most tokens have similar scores. These results show that weak oracle models struggle to distinguish key tokens within the dataset.
We observe similar results on rejected scores distribution, which further proves the capability of the oracle models as crucial in modeling the token-level reward function.

**Table 2: Performance of SePO and other baseline methods on generalizing the weak HH-RLHF dataset to the strong LLaMA2-Chat-13B policy model.**
|  | Arena-Hard | AlpacaEval 2.0 |  |
| --- | --- | --- | --- |
| Methods | Win Rate | LC Win Rate | Win Rate |
| Base | 12.0% | 8.4% | 7.7% |
| +DPO | 10.63% | 7.42% | 7.18% |
| +IPO | 9.5% | 6.5% | 5.98% |
| +RRHF | 11.7% | 7.82% | 7.4% |
| +SimPO | 11.39% | 7.5% | 7.35% |
| +SePO | 13.63% | 8.81% | 8.4% |

#### Weak Data Supervision.

We evaluate the weak data supervision performance of SePO by training on [HH-RLHF](https://huggingface.co/datasets/Anthropic/hh-rlhf) Bai et al. (), an early-released preference dataset with relatively lower quality Yang et al. () on responses. We perform SePO with a TinyLLaMA-based oracle model and 30% token selection rates, and comparisons with baseline methods are shown in Table 2.
According to the results, SePO is the only method that improves the strong LLaMA2-Chat-13B policy model with data from HH-RLHF, outperforming base performance by 1.63% on Arena-Hard and 0.41% on AlpacaEval 2.0. With full optimization, baseline methods such as DPO and SimPO continuously degrade model performance due to over-optimization on weak supervision data. These results prove SePO effective in leveraging useful supervision signals from weak data while avoiding fitting harmful patterns. These results point to SePO as a highly efficient method for continually improving strong model performance with large-scale out-of-distribution data.

## 5 Related Work

### 5.1 Response-Level Preference Optimization

Aligning large language models (LLMs) with human preferences has been a key research focus, traditionally achieved through Reinforcement Learning from Human Feedback (RLHF) (Ouyang et al., ; Stiennon et al., ).
While effective, RLHF methods often face challenges like training instability and inefficiency, motivating the development of more direct alignment strategies.
Recent approaches have emerged to address these issues without relying on complex reward modeling. Rafailov et al. () introduce Direct Preference Optimization (DPO), a method that simplifies RLHF by extracting the optimal policy in closed form, enhancing stability and reducing computational demands. Yuan et al. () propose Reinforcement Ranking from Human Feedback (RRHF), which aligns model outputs through a ranking loss, streamlining the training process and minimizing the need for extensive hyperparameter tuning. Meng et al. () further simplify alignment with Simple Preference Optimization (SimPO), using an implicit reward based on average log probability to improve both computational efficiency and performance.
Ethayarajh et al. () present KTO, which integrates human biases from prospect theory into the alignment process, achieving superior results by maximizing the utility of model outputs. Lu et al. () propose SamPO, a technique that addresses verbosity in DPO by mitigating length-based biases in reward estimation, leading to significant performance gains. Finally, Azar et al. () introduces a general framework that improves upon RLHF and DPO by eliminating common approximations, offering both theoretical insights and empirical benefits.

### 5.2 Token-Level Preference Optimization

Response-level direct alignment methods can be suboptimal due to the sequential, auto-regressive nature of token generation in LLMs. This has led to the development of token-level alignment methods using Markov Decision Processes (MDP) Rafailov et al. (); Zhong et al. (); Zeng et al. (); Yoon et al. (); Chen et al. (); Chan et al. ().
Rafailov et al. () extend DPO to a token-level MDP, enabling better alignment with LLMs’ auto-regressive structure and improving credit assignment. Zhong et al. () introduce Reinforced Token Optimization (RTO), combining token-level rewards with DPO and PPO for more efficient policy learning. Zeng et al. () propose Token-level Direct Preference Optimization (TDPO), which optimizes policy at the token level using forward KL divergence, enhancing alignment and diversity.
Yoon et al. () present Token-Level Continuous Reward (TLCR), which assigns continuous rewards to tokens based on contextual confidence, improving alignment. Chen et al. () develop ALLO, a method that reduces overfitting by focusing on optimizing the most relevant neurons for alignment. Chan et al. () use attention weights to redistribute rewards across tokens, stabilizing training and improving performance. Additionally, Chen et al. () propose DICE (DPO ImpliCit rEwards), a self-alignment method that uses implicit DPO rewards to further refine alignment without external feedback.
Further applications of these token-level methods have been explored in the context of mathematical reasoning Lai et al. (); Chen et al. (); Xie et al. (); Setlur et al. (), where they demonstrate potential in improving the precision and coherence of LLMs on complex reasoning tasks.

### 5.3 Weak-to-Strong Generalization

Weak-to-strong generalization, where weaker models supervise stronger ones, has become a significant topic in the ongoing development of LLMs Burns et al. (); Lang et al. (); Yang et al. (); Charikar et al. (). This approach addresses the challenge of aligning increasingly powerful models with human values, particularly as models surpass human-level capabilities.
Burns et al. () show that strong models fine-tuned on labels from weaker supervisors can outperform their weak teachers, though naive fine-tuning has limitations and may not scale well with superhuman models. Lang et al. () introduce a framework explaining how strong models can correct weak models’ errors and generalize beyond their knowledge, enhancing learning from incomplete or incorrect labels.
Yang et al. () discuss the risk of "weak-to-strong deception" where strong models exploit weak supervisors to appear aligned while misbehaving in unmonitored areas, stressing the need for more robust alignment strategies. Charikar et al. () quantify the performance gains of strong models over weaker ones, introducing misfit error as a key metric for optimizing this process.
Additional studies have applied weak-to-strong generalization in tasks like high-quality token selection Lin et al. (), weak-to-strong search Zhou et al. (), and alignment techniques such as Aligner Ji et al. () and Weak-to-Strong Extrapolation Zheng et al. ().

## 6 Discussion

#### Conclusion.

This paper proposes Selective Preference Optimization, a simple yet effective selective training strategy for LLM alignment. SePO estimates a token-level reward function via DPO and uses it to select key tokens from the target dataset. The target policy model is optimized only on the selected tokens in a contrastive manner. Experimental results on three public evaluation benchmarks show that SePO generally outperforms strong baseline methods such as DPO and SimPO by only optimizing on 30% tokens. We also explore the application of SePO in weak-to-strong generalization, where weak oracle models are proven to effectively supervise strong policy models and select useful supervision signals from out-of-distribution data to enhance model performance.

#### Limitation.

Firstly, we did all experiments within the same model family (e.g. Pythia, LLaMA), where the oracle model and the policy models share the vocabulary and tokenizer. This is to facilitate the implementation of SePO algorithm so that we avoid complicated key token mapping across different vocabularies. However, this setting significantly limits the application of SePO in real-world scenarios that require flexible adjustment of policy models. Secondly, due to limitations in computational resources, we didn’t extend our experiments to stronger policy models such as LLaMA2-Chat-70B to provide a clear landscape of the scalability of SePO.

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 3
presentation: 3
questions: 1. How performance when comparing win rates to the trained models themselves.
2. The model used for the experiment is a bit old and SePO needs to prove its performance on newer open source models.
3. The theoretical part needs to be further refined, and would like to see a discussion on whether DPO credit assignments need to be constructed through token-level weighted training, and that there should exist better ideas to take advantage of this feature of the DPO reward format.
soundness: 2
strengths: SePO offers a cost-efficient alignment strategy by focusing on a subset of high-reward tokens, which reduces annotation costs.
The method demonstrates better performance on several benchmarks, surpassing existing token-level and response-level alignment methods.
SePO’s weak-to-strong generalization enables effective supervision from smaller, weaker oracle models, showing scalability across varying model sizes.
summary: The paper introduces Selective Preference Optimization (SePO), a novel strategy for aligning large language models (LLMs) at the token level by selectively optimizing only on key tokens. Leveraging Direct Preference Optimization (DPO), SePO identifies and optimizes high-impact tokens, reducing supervision costs while improving alignment performance on benchmarks.
weaknesses: 1. The method is limited by the requirement that oracle and policy models share the same vocabulary and tokenizer, which reduces flexibility across different model architectures.
2. The use of the DPO reward format as an automated credit assignment behaviour has been attempted by other works, and the paper's contribution is weaker as only quantifies the results of this assignment to the weights of the DPO loss.
3. Suppose the confidence given by the Oracle model is used as the gold label for the credit distribution. In that case, we do not need dpo to fit the reward distribution given by the optimal policy (https://arxiv.org/abs/2404.12358, https://arxiv.org/abs/2408.14874). Alternatively, the paper needs to discuss the error problems associated with this approximation in the method to validate the need for SePO further.
4. Performance increases are relatively minor in the experiments, and the comparison model used is GPT-4-0314 (not the current optimal model, but again, not compared to the model untrained itself to provide a more intuitive increase)

---

confidence: 3
contribution: 3
initial_rating: 5
presentation: 3
questions: How does SePO scale with very large policy models?

How to decide the token selection threshold more smartly on different datasets and models?
soundness: 3
strengths: This paper introduces a novel token-level reward function estimator using DPO.

SePO reduces the need for extensive token optimization, demonstrating improved alignment performance while training on only 30% of tokens. This is valuable for scaling LLMs and reducing computational overhead.

The weak-to-strong generalization capability of SePO allows smaller models to supervise larger ones.
summary: This paper introduces Selective Preference Optimization (SePO) which optimizes model performance by selectively training only on key tokens with high token-level reward values using Direct Preference Optimization (DPO). 

This approach significantly reduces the data requirements by focusing on 30% of the tokens, avoiding noise from less informative tokens and improving computational efficiency.

Additionally, this paper also explores weak-to-strong generalization, demonstrating that weaker oracle models can provide useful supervision for larger, more powerful policy models. 

Experimental results across three benchmarks show that SePO outperforms baseline methods in alignment tasks, supporting its effectiveness and adaptability.
weaknesses: The experiments primarily involve relatively moderate-sized models. Testing SePO on stronger models, such as LLaMA2-Chat-70B, would provide further insights into its scalability and potential bottlenecks, especially for the weak-to-strong generalization experiment.

Compared to other methods, the improvement seems to be slight.

---

confidence: 4
contribution: 2
initial_rating: 3
presentation: 2
questions: See weaknesses
soundness: 2
strengths: - The idea is clear and novel.
- The reported results indicate the promise of the approach.
summary: The authors propose SePO—a method that utilizes selected tokens from an oracle model to perform preference optimization. The approach is evaluated across a wide range of models and general assistant benchmarks. The authors report that by optimizing only 30% of the tokens, they were able to surpass other methods for preference optimization.
weaknesses: - The proof of Theorem 1, which asserts that after training a DPO, the reward function can be expressed as a decoupled reward $\hat{r}$, inherits this property (Line 810) from the assumption that the reward can be written in such a manner (Assumption 1). This raises the question of whether all reward functions can be expressed in a decoupled way. From a naive perspective, a decoupled reward is not normalized, and longer texts might have larger absolute values of reward. In my attempts to learn reward models in online settings using a decoupled approach, I found that without normalization, their accuracy dramatically reduced. Normalizing the sum of small rewards over tokens led to improvements. Therefore, I strongly feel that not all rewards can be expressed in this way. Moreover, the training objective (Equation 11) uses a normalized reward, making it unclear why Theorem 1 was presented.
- Some of the writing is ambiguous. The SePO objective (Equation 11) is hard to parse visually and would benefit from a human-understandable explanation before the equation.
- The experiments lacked exploration of the dependence of performance on the KL divergence with the reference policy. It is evident that training a policy with the SePO objective could cause it to diverge significantly. This is similar to observations in Rafailov et al. [1]. For instance, could selecting a lower $\beta$ value enable DPO or other baselines to perform better than SePO?

[1] Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms

---

confidence: 4
contribution: 2
initial_rating: 3
presentation: 3
questions: See weakness section
soundness: 2
strengths: The strengths of this paper are listed as follows

1. This paper observes that the total reward of a generated utterance is usually dominated by a few tokens. This observation is interesting and motivate the method well

2. This paper propose a token-selection-based training method, which is new and interesting to me

3. The experiments are comprehensive and results look good.
summary: This paper propose selective preference optimization (SePO). SePO select the top-k token that dominate the final reward and train DPO on these tokens to eliminate noise and improve efficiency. Experiments shows that SePO outperforms a bunch of direct -preference learning methods.
weaknesses: My concerns are listed as follows:

1. My major concern is about the token selection mechanism. The motivation behind using $\hat{r}(s_t,a_t)$ as the proxy of the reward is unclear to me. Theorem 1 only proved that $\sum \hat{r} (s_t, a_t) + V^{*}(s_1) = \sum r(s_t, a_t)$, which only guarantees that the sum of $\hat{r}$ and the sum of $r$ is the same (up to a constant). However, the value distribution of $r$ and $\hat{r}$ might still be drastically different. Therefore, the token selection based on $\hat{r}=\log \pi_{\theta} / \log \pi_{\text{ref}}$ does not make sense given the current illustration. 

2. It looks like that that SePO is quite sensitive to the parameter $\gamma$. The search space of $\gamma=\{2.1, ...,2.5\}$ looks weird and it seems that there is a fluctuate of performance when $\gamma$ varies in this set. This makes a issue give that the improvement over baseline is not that significant.

3. (Minor issue): The $\propto$ in equation (6) looks like a typo