Statistical estimation often involves tradeoffs between expensive, high-quality measurements and a variety of lower-quality proxies. We introduce Multiple-Prediction-Powered Inference (MultiPPI): a general framework for constructing statistically efficient estimates by optimally allocating resources across these diverse data sources. This work provides theoretical guarantees about the minimax optimality, finite-sample performance, and asymptotic normality of the MultiPPI estimator. Through experiments across three diverse large language model (LLM) evaluation scenarios, we show that MultiPPI consistently achieves lower estimation error than existing baselines. This advantage stems from its budget-adaptive allocation strategy, which strategically combines subsets of models by learning their complex cost and correlation structures.

A core challenge in modern AI model development is obtaining high-quality evaluation metrics in a cost-effective way. Such evaluation often involves tradeoffs between expensive, high-quality measurements and a variety of lower-quality proxies. We introduce Multiple-Prediction-Powered Inference (MultiPPI), a general framework for constructing statistically efficient estimates by optimally allocating resources across these diverse data sources. We provide theoretical guarantees about the minimax optimality, finite-sample performance, and asymptotic normality of the MultiPPI estimator. Through experiments across three diverse large language model (LLM) evaluation scenarios, we show that MultiPPI consistently achieves lower estimation error than existing baselines. This advantage stems from its budget-adaptive allocation strategy, which strategically combines subsets of models by learning their complex cost and correlation structures.

Evaluating generative AI models is a routine, but resource-intensive, process that is conducted over and over again during the course of model development. In this work, we propose Collaborative Evaluation (CollabEval), a simple, effective, and principled method for exploiting dependencies between historical runs of different models on the same tasks to improve statistical efficiency. Specifically, our approach treats model evaluation as a matrix completion problem over an M × N matrix of evaluation scores, where M is the total number of models and N is the total number of evaluation prompts. We assume that a subset of these M models are targeted for evaluation. For these target models only a small fraction, p, of prompts has been annotated with evaluation scores. Leveraging recent results in prediction-powered inference, we build a low-rank approximation of the score matrix, and use the reconstructed values as control variates in a manner that guarantees unbiased estimates of the true evaluation metric mean, in addition to statistically valid confidence intervals. Empirically, across a wide range of datasets, models, and sparsity levels p, we find that CollabEval substantially reduces the mean confidence interval size, and the mean squared error of the point estimate, compared to baseline methods at the same annotation budget.

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.

A simple and effective method for the inference-time alignment and scaling test-time compute of generative models is best-of-n sampling, where n samples are drawn from a reference policy, 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 reference 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, and propose a new estimator for the KL divergence and empirically show that it provides a tight approximation. We also show that the win rate of the best-of-n policy against the reference policy is upper bounded by n/(n + 1) and derive bounds on the tightness of this characterization. We conclude with analyzing the tradeoffs between win rate and KL divergence of the best-of-n alignment policy, which demonstrate that very good tradeoffs are achievable with n < 1000.

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, 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. With the goal of using PRMs to improve a *base* policy via test-time search and 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, as measured under a *prover* policy distinct from the base policy. Such progress values can {distinguish} good and bad steps generated by the base policy, even though the base policy itself cannot. Theoretically, we show that even weaker provers can improve the base policy, as long as they distinguish steps without being too misaligned with the base policy. Our results show that process rewards defined as progress under such provers improve the efficiency of exploration during test-time search and online RL. We empirically validate our claims by training **process advantage verifiers (PAVs)** to measure progress under such provers and show that compared to ORM, they are >8% more accurate, and 1.5-5x more compute-efficient. Equipped with these insights, our PAVs enable **one of the first results** showing a 6x gain in sample efficiency for a policy trained using online RL with PRMs vs. ORMs.

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.

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.

The development lifecycle of generative AI systems requires continual evaluation, data acquisition, and annotation, which is costly in both resources and time. In practice, rapid iteration often makes it necessary to rely on synthetic annotation data because of the low cost, despite the potential for substantial bias. In this paper, we develop novel, cost-aware methods for actively balancing the use of a cheap, but often inaccurate, weak rater – such as a model-based autorater that is designed to automatically assess the quality of generated content – with a more expensive, but also more accurate, strong rater alternative such as a human. More specifically, the goal of our approach is to produce a low variance, unbiased estimate of the mean of the target "strong" rating, subject to some total annotation budget. Building on recent work in active and prediction-powered statistical inference, we derive a family of cost-optimal policies for allocating a given annotation budget between weak and strong raters so as to maximize statistical efficiency. Using synthetic and real-world data, we empirically characterize the conditions under which these policies yield improvements over prior methods. We find that, especially in tasks where there is high variability in the difficulty of examples, our policies can achieve the same estimation precision at a far lower total annotation budget than standard evaluation methods.

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.

This work tackles the problem of overoptimization in reinforcement learning from human feedback (RLHF), a prevalent technique for aligning models with human preferences. RLHF relies on reward or preference models trained on \emph{fixed preference datasets}, and these models are unreliable when evaluated outside the support of this preference data, leading to the common reward or preference hacking phenomenon. We propose novel, pessimistic objectives for RLHF which are provably robust to overoptimization through the use of pessimism in the face of uncertainty, and design practical algorithms, P3O and PRPO, to optimize these objectives. Our approach is derived for the general preference optimization setting, but can be used with reward models as well. We evaluate P3O and PRPO on the tasks of fine-tuning language models for document summarization and creating helpful assistants, demonstrating remarkable resilience to overoptimization.

Policy gradient (PG) methods have played an essential role in the empirical successes of reinforcement learning. In order to handle large state-action spaces, PG methods are typically used with function approximation. In this setting, the approximation error in modeling problem-dependent quantities is a key notion for characterizing the global convergence of PG methods. We focus on Softmax PG with linear function approximation (referred to as ) and demonstrate that the approximation error is irrelevant to the algorithm's global convergence even for the stochastic bandit setting. Consequently, we first identify the necessary and sufficient conditions on the feature representation that can guarantee the asymptotic global convergence of . Under these feature conditions, we prove that T iterations of with a problem-specific learning rate result in an O(1/T) convergence to the optimal policy. Furthermore, we prove that with any arbitrary constant learning rate can ensure asymptotic global convergence to the optimal policy.

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.

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.

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.

Reward-based finetuning is crucial for aligning language policies with intended behaviors (e.g., creativity and safety). A key challenge is to develop steerable language models that trade-off multiple (conflicting) objectives in a flexible and efficient manner. This paper presents Conditional 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 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 extensive experiments and ablations on two summarization datasets, we show that CLP learns steerable language models that outperform and Pareto-dominate the existing approaches for multi-objective finetuning.

The low rank MDP has emerged as an important model for studying representation learning and exploration in reinforcement learning. With a known representation, several model-free exploration strategies exist. In contrast, all algorithms for the unknown representation setting are model-based, thereby requiring the ability to model the full dynamics. In this work, we present the first model-free representation learning algorithms for low rank MDPs. The key algorithmic contribution is a new minimax representation learning objective, for which we provide variants with differing tradeoffs in their statistical and computational properties. We interleave this representation learning step with an exploration strategy to cover the state space in a reward-free manner. The resulting algorithms are provably sample efficient and can accommodate general function approximation to scale to complex environments.

We propose a generalization of the classical G-optimal design concept to non-linear function classes. The criterion, termed F -design, coincides with G-design in the linear case. We compute the value of the optimal design, termed the F-condition number, for several non-linear function classes. We further provide algorithms to construct designs with a bounded F -condition number. Finally, we employ the F-design in a variety of interactive machine learning tasks, where the design is naturally useful for data collection or exploration. We show that in four diverse settings of confidence band construction, contextual bandits, model-free reinforcement learning, and active learning, F-design can be combined with existing approaches in a black-box manner to yield state-of-the-art results in known problem settings as well as to generalize to novel ones.

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.

The electromagnetic structure of Sc-45 at low excitation energy was investigated via low-energy Coulomb excitation at the Heavy Ion Laboratory (HIL) of the University of Warsaw and at the Inter-University Accelerator Centre (IUAC) in New Delhi. A set of reduced E2, E3, and M1 matrix elements was extracted from the collected data using the GOSIA code. The reduced transition probability B(E2; 11/2(-) -> 7/2(-)) has been determined, allowing us to deduce the lifetime of the 11/2(-) state at 1237 keV. In addition, the upper limit on the reduced transition probability B(E3; 7/2(-) -> 5/2(+)) has been determined for the first time. New large-scale shell-model and beyond-mean-field calculations were performed to interpret the structure of this nucleus.