Optimizing Pre-Training Data Mixtures with Mixtures of Data Expert Models

We propose a method to optimize language model pre-training data mixtures through efficient approximation of the cross-entropy loss corresponding to each candidate mixture via a Mixture of Data Experts (MDE). We use this approximation as a source of additional features in a regression model, trained from observations of model loss for a small number of mixtures. Experiments with Transformer decoder-only language models in the range of 70M to 1B parameters on the SlimPajama dataset show that our method achieves significantly better performance than approaches that train regression models using only the mixture rates as input features. Combining this improved optimization method with an objective that takes into account cross-entropy on end task data leads to superior performance on few-shot downstream evaluations. We also provide theoretical insights on why aggregation of data expert predictions can provide good approximations to model losses for data mixtures.

Small steps no more: Global convergence of stochastic gradient bandits for arbitrary learning rates

We provide a new understanding of the stochastic gradient bandit algorithm by showing that it converges to a globally optimal policy almost surely using \emph{any} constant learning rate. This result demonstrates that the stochastic gradient algorithm continues to balance exploration and exploitation appropriately even in scenarios where standard smoothness and noise control assumptions break down. The proofs are based on novel findings about action sampling rates and the relationship between cumulative progress and noise, and extend the current understanding of how simple stochastic gradient methods behave in bandit settings.

Design Considerations in Offline Preference-based RL

Offline algorithms for Reinforcement Learning from Human Preferences (RLHF), which use only a fixed dataset of sampled responses given an input, and preference feedback among these responses, have gained increasing prominence in the literature on aligning language models. In this paper, we study how the different design choices made in methods such as DPO, IPO, SLiC and many variants influence the quality of the learned policy, from a theoretical perspective. Our treatment yields insights into the choices of loss function, the policy which is used to normalize log-likelihoods, and also the role of the data sampling policy. Notably, our results do not rely on the standard reparameterization-style arguments used to motivate some of the algorithms in this family, which allows us to give a unified treatment to a broad class of methods. We also conduct a small empirical study to verify some of the theoretical findings on a standard summarization benchmark.

Catoni Contextual Bandits are Robust to Heavy-tailed Rewards

Typical contextual bandit algorithms assume that the rewards at each round lie in some fixed range $[0, R]$, and their regret scales polynomially with this reward range $R$. However, many practical scenarios naturally involve heavy-tailed rewards or rewards where the worst-case range can be substantially larger than the variance. In this paper, we develop an algorithmic approach building on Catoni's estimator from robust statistics, and apply it to contextual bandits with general function approximation. When the variance of the reward at each round is known, we use a variance-weighted regression approach and establish a regret bound that depends only on the cumulative reward variance and logarithmically on the reward range $R$ as well as the number of rounds $T$. For the unknown-variance case, we further propose a careful peeling-based algorithm and remove the need for cumbersome variance estimation. With additional dependence on the fourth moment, our algorithm also enjoys a variance-based bound with logarithmic reward-range dependence. Moreover, we demonstrate the optimality of the leading-order term in our regret bound through a matching lower bound.

Preserving Expert-Level Privacy in Offline Reinforcement Learning

The offline reinforcement learning (RL) problem aims to learn an optimal policy from historical data collected by one or more behavioural policies (experts) by interacting with an environment. However, the individual experts may be privacy-sensitive in that the learnt policy may retain information about their precise choices. In some domains like personalized retrieval, advertising and healthcare, the expert choices are considered sensitive data. To provably protect the privacy of such experts, we propose a novel consensus-based expert-level differentially private offline RL training approach compatible with any existing offline RL algorithm. We prove rigorous differential privacy guarantees, while maintaining strong empirical performance. Unlike existing work in differentially private RL, we supplement the theory with proof-of-concept experiments on classic RL environments featuring large continuous state spaces, demonstrating substantial improvements over a natural baseline across multiple tasks.

Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is $>8\%$ more accurate, and $1.5-5\times$ more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with $5-6\times$ gain in sample efficiency, and $>6\%$ gain in accuracy, over ORMs.

Conditioned Language Policy: A General Framework for Steerable Multi-Objective Finetuning

Reward-based finetuning is crucial for aligning language policies with intended behaviors (e.g., creativity and safety). A key challenge here is to develop steerable language models that trade-off multiple (conflicting) objectives in a flexible and efficient manner. This paper presents Conditioned Language Policy (CLP), a general framework for finetuning language models on multiple objectives. Building on techniques from multi-task training and parameter-efficient finetuning, CLP can learn steerable models that effectively trade-off conflicting objectives at inference time. Notably, this does not require training or maintaining multiple models to achieve different trade-offs between the objectives. Through an extensive set of experiments and ablations, we show that the CLP framework learns steerable models that outperform and Pareto-dominate the current state-of-the-art approaches for multi-objective finetuning.

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.