Robust Preference Optimization through Reward Model Distillation

Language model (LM) post-training (or alignment) involves maximizing a reward function that is derived from preference annotations. Direct Preference Optimization (DPO) is a popular offline alignment method that trains a policy directly on preference data without the need to train a reward model or apply reinforcement learning. However, typical preference datasets have only a single, or at most a few, annotation per preference pair, which causes DPO to overconfidently assign rewards that trend towards infinite magnitude. This frequently leads to degenerate policies, sometimes causing even the probabilities of the preferred generations to go to zero. In this work, we analyze this phenomenon and propose distillation to get a better proxy for the true preference distribution over generation pairs: we train the LM to produce probabilities that match the distribution induced by a reward model trained on the preference data. Moreover, to account for uncertainty in the reward model we are distilling from, we optimize against a family of reward models that, as a whole, is likely to include at least one reasonable proxy for the preference distribution. Our results show that distilling from such a family of reward models leads to improved robustness to distribution shift in preference annotations, while preserving the simple supervised nature of DPO.

Offline Imitation Learning from Multiple Baselines with Applications to Compiler Optimization

This work studies a Reinforcement Learning (RL) problem in which we are given a set of trajectories collected with K baseline policies. Each of these policies can be quite suboptimal in isolation, and have strong performance in complementary parts of the state space. The goal is to learn a policy which performs as well as the best combination of baselines on the entire state space. We propose a simple imitation learning based algorithm, show a sample complexity bound on its accuracy and prove that the the algorithm is minimax optimal by showing a matching lower bound. Further, we apply the algorithm in the setting of machine learning guided compiler optimization to learn policies for inlining programs with the objective of creating a small binary. We demonstrate that we can learn a policy that outperforms an initial policy learned via standard RL through a few iterations of our approach.

Stochastic Gradient Succeeds for Bandits

We show that the \emph{stochastic gradient} bandit algorithm converges to a \emph{globally optimal} policy at an $O(1/t)$ rate, even with a \emph{constant} step size. Remarkably, global convergence of the stochastic gradient bandit algorithm has not been previously established, even though it is an old algorithm known to be applicable to bandits. The new result is achieved by establishing two novel technical findings: first, the noise of the stochastic updates in the gradient bandit algorithm satisfies a strong ``growth condition'' property, where the variance diminishes whenever progress becomes small, implying that additional noise control via diminishing step sizes is unnecessary; second, a form of ``weak exploration'' is automatically achieved through the stochastic gradient updates, since they prevent the action probabilities from decaying faster than $O(1/t)$, thus ensuring that every action is sampled infinitely often with probability $1$. These two findings can be used to show that the stochastic gradient update is already ``sufficient'' for bandits in the sense that exploration versus exploitation is automatically balanced in a manner that ensures almost sure convergence to a global optimum. These novel theoretical findings are further verified by experimental results.

More Benefits of Being Distributional: Second-Order Bounds for Reinforcement Learning

In this paper, we prove that Distributional Reinforcement Learning (DistRL), which learns the return distribution, can obtain second-order bounds in both online and offline RL in general settings with function approximation. Second-order bounds are instance-dependent bounds that scale with the variance of return, which we prove are tighter than the previously known small-loss bounds of distributional RL. To the best of our knowledge, our results are the first second-order bounds for low-rank MDPs and for offline RL. When specializing to contextual bandits (one-step RL problem), we show that a distributional learning based optimism algorithm achieves a second-order worst-case regret bound, and a second-order gap dependent bound, simultaneously. We also empirically demonstrate the benefit of DistRL in contextual bandits on real-world datasets. We highlight that our analysis with DistRL is relatively simple, follows the general framework of optimism in the face of uncertainty and does not require weighted regression. Our results suggest that DistRL is a promising framework for obtaining second-order bounds in general RL settings, thus further reinforcing the benefits of DistRL.

A Minimaximalist Approach to Reinforcement Learning from Human Feedback

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

Theoretical guarantees on the best-of-n alignment policy

A simple and effective method for the alignment of generative models is the best-of-$n$ policy, where $n$ samples are drawn from a base policy, and ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-$n$ policy and the base policy is equal to $\log (n) - (n-1)/n.$ We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes. Finally, we propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.

Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking

Reward models play a key role in aligning language model applications towards human preferences. However, this setup creates an incentive for the language model to exploit errors in the reward model to achieve high estimated reward, a phenomenon often termed \emph{reward hacking}. A natural mitigation is to train an ensemble of reward models, aggregating over model outputs to obtain a more robust reward estimate. We explore the application of reward ensembles to alignment at both training time (through reinforcement learning) and inference time (through reranking). First, we show that reward models are \emph{underspecified}: reward models that perform similarly in-distribution can yield very different rewards when used in alignment, due to distribution shift. Second, underspecification results in overoptimization, where alignment to one reward model does not improve reward as measured by another reward model trained on the same data. Third, overoptimization is mitigated by the use of reward ensembles, and ensembles that vary by their \emph{pretraining} seeds lead to better generalization than ensembles that differ only by their \emph{fine-tuning} seeds, with both outperforming individual reward models. However, even pretrain reward ensembles do not eliminate reward hacking: we show several qualitative reward hacking phenomena that are not mitigated by ensembling because all reward models in the ensemble exhibit similar error patterns.

Efficient End-to-End Visual Document Understanding with Rationale Distillation

Understanding visually situated language requires recognizing text and visual elements, and interpreting complex layouts. State-of-the-art methods commonly use specialized pre-processing tools, such as optical character recognition (OCR) systems, that map document image inputs to extracted information in the space of textual tokens, and sometimes also employ large language models (LLMs) to reason in text token space. However, the gains from external tools and LLMs come at the cost of increased computational and engineering complexity. In this paper, we ask whether small pretrained image-to-text models can learn selective text or layout recognition and reasoning as an intermediate inference step in an end-to-end model for pixel-level visual language understanding. We incorporate the outputs of such OCR tools, LLMs, and larger multimodal models as intermediate ``rationales'' on training data, and train a small student model to predict both rationales and answers for input questions based on those training examples. A student model based on Pix2Struct (282M parameters) achieves consistent improvements on three visual document understanding benchmarks representing infographics, scanned documents, and figures, with improvements of more than 4\% absolute over a comparable Pix2Struct model that predicts answers directly.

A Mechanism for Sample-Efficient In-Context Learning for Sparse Retrieval Tasks

We study the phenomenon of \textit{in-context learning} (ICL) exhibited by large language models, where they can adapt to a new learning task, given a handful of labeled examples, without any explicit parameter optimization. Our goal is to explain how a pre-trained transformer model is able to perform ICL under reasonable assumptions on the pre-training process and the downstream tasks. We posit a mechanism whereby a transformer can achieve the following: (a) receive an i.i.d. sequence of examples which have been converted into a prompt using potentially-ambiguous delimiters, (b) correctly segment the prompt into examples and labels, (c) infer from the data a \textit{sparse linear regressor} hypothesis, and finally (d) apply this hypothesis on the given test example and return a predicted label. We establish that this entire procedure is implementable using the transformer mechanism, and we give sample complexity guarantees for this learning framework. Our empirical findings validate the challenge of segmentation, and we show a correspondence between our posited mechanisms and observed attention maps for step (c).

An Empirical Evaluation of Federated Contextual Bandit Algorithms

As the adoption of federated learning increases for learning from sensitive data local to user devices, it is natural to ask if the learning can be done using implicit signals generated as users interact with the applications of interest, rather than requiring access to explicit labels which can be difficult to acquire in many tasks. We approach such problems with the framework of federated contextual bandits, and develop variants of prominent contextual bandit algorithms from the centralized seting for the federated setting. We carefully evaluate these algorithms in a range of scenarios simulated using publicly available datasets. Our simulations model typical setups encountered in the real-world, such as various misalignments between an initial pre-trained model and the subsequent user interactions due to non-stationarity in the data and/or heterogeneity across clients. Our experiments reveal the surprising effectiveness of the simple and commonly used softmax heuristic in balancing the well-know exploration-exploitation tradeoff across the breadth of our settings.