Distributional Preference Learning: Understanding and Accounting for Hidden Context in RLHF

• "The example...just underscores that different groups or populations have different preferences and one needs to obtain RLHF training data on a sufficiently large population reflecting what a model will be tested...one may also need to learn different sub-clusters." Just adding more diversity to RLHF training data might not help, since the way that the annotations from these diverse annotators are combined can lead to unexpected or harmful outcomes. We describe such cases in our theoretical results in Section 3. For instance, Proposition 3.3 shows that even when the majority of annotators prefer one alternative to another, preference learning may not output a utility function which agrees with the majority.

  With regards to modeling subgroups, we agree that this can be useful when there is detailed data available about which groups each annotator is a part of. However, this becomes impossible when some information is not present in the training data. For instance, perhaps information about annotators' genders, ages, and races is collected, but not about their income level; if there are differences in preferences across income levels, then these cannot be modeled without that data. In contrast, DPL can work without the need to collect this additional data, and so it can always model differences between annotators which have not been explicitly recorded. Furthermore, it also works with other types of hidden context, like irrationality, partial observability, and multiple objectives.

• Artificialness of competing objectives in RLHF: We argue that our case study is actually quite realistic, since this approach was used in practice to train LLM chatbots like Claude [2]. Although it not the best experiment design, it is crucial to understand the use of competing objectives in RLHF since they lead to real vulnerabilities in deployed models [3]. Furthermore, this setting is also reflective of actual populations of people which may have similar objectives but weight them quite differently from each other. Even if an AI system designer asks annotators to compare outputs based on helpfulness and harmlessness, each annotator will each probably choose a different weighting of the two objectives. Thus, we respectfully disagree that the case study on competing objectives is artificial.

• Choice of quantile for risk-sensitive optimization: We picked this based on trying various quantiles and seeing when the jailbreak rate decreased. However, we find that our results are not particular sensitive to the exact quantile chosen, as long as it is below around 0.02. See the table below for results at other quantiles.

  	Jailbreak rate	Accuracy on HH-RLHF helpfulness test set
  Normal preference learning	25.1%	68.2%
  Mean & var. DPL (0.02 quantile)	21.4%	66.7%
  Mean & var. DPL (0.01 quantile)	20.3%	66.4%
  Mean & var. DPL (0.001 quantile)	17.1%	65.8%
  Mean & var. DPL (0.0001 quantile)	15.0%	65.8%
  Categorical DPL (0.02 quantile)	13.9%	66.2%
  Categorical DPL (0.01 quantile)	13.4%	66.2%
  Categorical DPL (0.001 quantile)	13.4%	66.2%
  Categorical DPL (0.0001 quantile)	13.4%	66.2%

• Other writing suggestions: Thank you for catching these typos; we will fix them.

[2] Bai et al. Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback.

[3] Wei et al. Jailbroken: How does LLM Safety Training Fail? NeurIPS 2023.

We thank the reviewer for their careful reading of the paper and extensive comments. We have addressed their questions below.

• Are single utility functions too simplistic to be useful? While we agree that a single utility function is too simplistic to model preference data in practice, there are a couple of reasons we analyze preference learning that outputs a single utility function. First, we want to understand what happens when current preference learning methods—ones that are unaware of hidden context—are applied to settings where there is hidden context. In this case, preference learning methods implicitly aggregate over the hidden context and return a single utility function. Second, preference learning is generally used to estimate a utility function which can later be optimized, e.g., by the RL phase of RLHF. Since a system designer must eventually choose a single optimization objective, it makes sense to study ways of aggregating preference data into a single utility function.

  We do think that explicitly modeling multiple utility functions through DPL is a superior solution compared to methods that just estimate a single utility function. While clustering could be a useful approach for modeling disagreement in preference comparisons, it is quite difficult to perform clustering based solely on anonymous comparisons, since each comparison only provides a single label. In contrast, we show that DPL can effectively estimate disagreement between annotators, or arising from other sources of hidden context, even without annotator identities.

• Uniqueness of the utility function: In Proposition A.1, we show that the loss function in Equation 1 is strongly convex for $\lambda > 0$ and thus has a unique minimum; that is, there is a unique best utility function that minimizes equation (1) as long as $\lambda > 0$. Intuitively, in the case the reviewer brought up, the regularization prefers smaller and smaller $\hat{u}(a)$ and $\hat{u}(b)$, but the other loss term prefers them to be farther and farther apart. Thus, the two terms balance each other out at some point and that is the unique minimum. We will reference Proposition A.1 in Section 2 so it is clear that there is a unique minimum of the preference learning loss function.

• Annotators cooperating and/or not show their true beliefs:" To be clear, in Example 1.1, we are not assuming that annotators are manipulating the preference learning process. Instead, we assume they are annotating according to their true preferences: high income users don’t want to see Pell Grant info while low income users do want to see it. Later, in Section 3.2, we discuss annotators having incentives for manipulation. We agree that this will not always happen in practice and most annotators will probably report their true preferences. However, there are examples of coordinated attacks on ML systems [1] and it is useful to know what it is possible for malicious actors to accomplish. Furthermore, annotators do not necessarily need to cooperate—even a single annotator may be able to successfully alter the outcome of preference learning

• Modeling comparison outcomes as probabilities: We agree that we could do a better job of motivating why to model comparison choices as probablistic earlier in Section 2. We will take the reviewer's suggestion to mention noisy annotators earlier to motivate our choice of modeling annotations as stochastic instead of deterministic.

[1] Shan et al. Glaze: Protecting Artists from Style Mimicry by Text-to-Image Models. USENIX Security Symposium, 2023.

We thank the reviewer for their comments. We appreciate that they found the paper "original" and "reasonably significant."

The reviewer asked when our approach to modeling irrationality as hidden context fails. While in theory our model can capture many types of irrationality, it is most useful when the irrationality can be represented by latent noise variables affecting decision making which are unobserved. For instance, the Thurstone-Mosteller model we mention consists of latent noise which affects the annotator’s evaluations of the alternatives they are comparing. In Theorem 3.2, we show that for cases like Thurstone-Mosteller, reference learning will converge to a learned utility function that agrees with the annotator’s true utility function.

When irrationality is more systematic, such as consistent undervaluing or overvaluing of certain alternatives relative to the annotator’s true utility function, then it may be much harder to recover that true utility function. Preference learning might produce an estimated utility function which also undervalues and overvalues the same alternatives. In this case, it might be necessary to more precisely characterize the systematic irrationality and build this into preference learning in other ways, e.g., [1]. Otherwise, our theory suggests that it is hopeless to recover a systematically irrational annotator's true utility function using normal Bradley-Terry-Luce (BTL) preference learning.

We will more carefully describe in the final paper when our model is useful for different types of irrationality.

[1] Jeon et al. Reward-rational (implicit) choice. NeurIPS 2020.

• How the implications of our results depend on the source of the hidden context:" Depending on the source of the hidden context, the implications of preference learning may vary. For instance, when hidden context arises from a population with diverse preferences, then in Section 3.2 we show that preference learning is akin to a social welfare functional, i.e., a method of aggregating multiple people's preferences into one. We find that "participants may have an incentive to misreport their preferences," which is a particular implication of our results specifically in the case of learning from a population. When hidden context arises from partial observability, decision theory suggests that ideally one should maximize expected utility. In Section 3.1, we discuss when preference learning's output will agree with expected utility, which is particularly relevant in this setting of partial observability.

  The fact that these implications differ depending on the source of the hidden context is why we "encourage qualitative analysis of alternatives where DPL suggests there are significant effects of hidden context;" determining the source of the disagreement in the data affects how a system designer should proceed. If annotators are misreporting their preferences, for instance, this requires a quite different response than if annotators merely differ in their honest judgements. Possible responses to hidden context that a system designer could employ include collecting more data, making hidden context explicit (i.e., including it as an input to the preference model), choosing an alternative aggregation mechanism, or personalizing the preference model to individual users. We will include more discussion of how the implications of hidden context can vary in the final paper.

• "Does your analysis suggest any new insights about voting rules or mechanisms given unknown/diverse preferences?" In Section 3.2, we introduce proportion-representable social welfare functionals (SWFs), which are a novel class of SWFs that arise specifically from our analysis of preference learning with diverse preferences. This class of SWFs encompasses those which can be implemented with only access to anonymous binary comparisons, and to the best of our knowledge has not appeared in the literature previously.

We thank the reviewer for their thoughtful comments. We are glad they found our paper "makes an original contribution" and that its "technical quality is high." Below we have the addressed the weaknesses and questions raised by the reviewer.

• Concerns about the scale of experiments: We worked hard to evaluate DPL in a large scale setting, given our resources and the available preference datasets. In all our experiments in Section 5 we finetuned Llama-7B, a 7 billion parameter language model, on the HH-RLHF dataset, which has over 78,000 preference comparisons. We may not have communicated this clearly enough, so we will make sure to emphasize that our experiments are conducted in a realistic, high dimensional setting with large amounts of training data. If the reviewer thinks that this is small scale or low dimensional, is there an alternative dataset or model that they recommend we use?

• Detecting other types of hidden context with DPL: Our goal with the experiments in Section 5 was to determine if DPL can reliably find hidden context. Experimentally, this means that we need a setting where we know the 'ground truth' of hidden context that is unobserved. This is why we elected to run our experiment with the HH-RLHF dataset, as it provides a clear evaluation of the method. We agree that it will be important to investigate the ability of DPL to identify hidden context in other settings. However, we believe that would be best left for a future paper, as this one already: 1) defines the problem of hidden context; 2) theoretically analyzes its implications; 3) contributes a new preference modeling method; and 4) experimentally validates the method in a large experiment with real-world data.

• Comparison to other methods for handling disagreement: There are a few reasons that did not compare to other methods for handling annotator disagreement. First, the preference learning dataset we used, HH-RLHF, does not include multiple annotations per comparison, so it impossible to directly apply many methods for measuring or modeling annotator disagreement. Furthermore, the dataset does not contain features of annotators (like demographics), meaning we can't use methods that require these like [1]. In comparison, DPL is able to model variation in the data arising from hidden context without needing any additional information, like multiple annotations or annotator identity. We will add a discussion of alternative methods for handling annotator diagreement and describe how DPL can complement them in the final version.

• Ordinal rating setting: First, we would like to note that collecting data via binary comparisons is becoming more and more common in training the most advanced AI models, like GPT-4 and Claude. Thus, while ordinal ratings are also a common way of collecting human feedback, we believe it is paramount to understand preference learning from comparisons. When collecting preference data with ordinal ratings (e.g., 1-5 or 1-10 scales), the most common way of learning from this data is via utility regression, which we compare to in Section 3.1. Proposition A.2, referenced in that section, shows that utility regression from ordinal ratings handles hidden context gracefully, since it converges to the expected utility at each alternative given enough data. The remainder of Section 3.1 discusses when preference learning from binary comparisons produces similar results. We show that often the results can diverge between learning from binary comparisons and regressing from ordinal ratings quite sharply. Thus, we believe that the paper already covers theoretical results on learning from ordinal ratings.

  Additionally, our DPL method can also model variation arising from hidden context in the ordinal rating setting. This just requires replacing the least-squares loss in utility regression with the negative log-likelihood of an ordinal rating being produced from some parameterized distribution.

[1] Fleisig et al. When the Majority is Wrong: Modeling Annotator Disagreement for Subjective Tasks.

We thank the reviewer for their comments, and we are glad they found our paper "tackles an interesting and important problem." Below we have responded to their questions and criticisms.

• Theoretical issues: We apologize for our confusing notation in the proofs. We have fixed the issues mentioned and generally clarified Appendix A.

• Missing objective function for DPL: We agree that we should have included this in the paper explicitly. We have now added it to Section 4 and quoted it here as well:

  Our alternative preference learning methods, which we call distributional preference learning (DPL), output a distribution over possible utilities for each alternative rather than a single value. In particular, we learn a mapping $\hat{\mathcal{D}}: \mathcal{A} \to \Delta(\mathbb{R})$ from alternatives to distributions over utilities to estimate the distribution of $u(a, z)$ when $u \sim \mathcal{D}_z$. We consider two variants, each of which parameterizes the distribution $\hat{\mathcal{D}}(a)$ in a different way.

  First, the mean-and-variance model learns two functions $\hat{\mu}: \mathcal{A} \to \mathbb{R}$ and $\hat{\sigma}: \mathcal{A} \to [0, \infty)$, parameterizing the distribution over utilities as $\hat{\mathcal{D}}(a) = \mathcal{N}\left(\hat{\mu}(a), \hat{\sigma}(a)^2\right)$. We train the distributional preference models by maximizing the likelihood of the data given the model $p_{\hat{\mathcal{D}}} (a, b) = \mathbb{E}[O (u_a, u_b)]$ where $u_a \sim \hat{\mathcal{D}}(a)$ and $u_b \sim \hat{\mathcal{D}}(b)$. Concretely, for the mean-and-variance model, the loss for a single preference comparison where alternative $a$ is preferred to $b$ is the negative log probability that $u_a - u_b > 0$: $- \log \Phi\left(\frac{\hat{\mu}(a) - \hat{\mu}(b)}{\sqrt{\hat{\sigma}(a)^2 + \hat{\sigma}(b)^2}} \right).$ We also consider a second DPL variant: in the categorical model, we choose $n$ evenly spaced utility values $u_1 < u_2 < \dots < u_n$, and then parameterize the distribution as the probabilities of each of those utilities $\hat{p}(u_i \mid a)$ for $i \in \{1, \dots, n\}$. In this case, the equivalent loss is

  $$$$

   1/2 & \quad u_i = u_j \\\\
  

   \mathbf{1} \\{ u_i > u_j \\} & \quad u_i \neq u_j.
  

  \end{cases}$$

• Training a language model using the utility functions: We agree that this is an interesting and important direction. However, we believe that experiments on training language models with DPL would be best left for a future paper, as this one already: 1) defines the problem of hidden context; 2) theoretically analyzes its implications; 3) contributes a new preference modeling method; and 4) experimentally validates the method in a large experiment with real-world data.

  Furthermore, we argue that our main conclusions are well supported by our experiments with just training utility functions. First, our results on detecting when hidden context is present via the $r^2$ metric clearly do not require training a language model. Training an LLM is more relevant to our results on preventing jailbreaks. However, if a learned utility function assigns higher utility to jailbroken responses than the safe ones, then we expect using that utility function to train an LLM assistant via RLHF would lead to the assistant outputting the jailbroken response. Thus, we believe our metric for evaluating utility functions—the proportion of jailbreak prompts where the utility function prefers jailbroken responses—corresponds closely to how an LLM assistant would behave if trained with the utility function, and thus explicitly training the LLM is not necessary.