Solving mathematics problems has been an intriguing capability of large language models, and many efforts have been made to improve reasoning by extending reasoning length, such as through self-correction and extensive long chain-of-thoughts. While promising in problem-solving, advanced long reasoning chain models exhibit an undesired single-modal behavior, where trivial questions require unnecessarily tedious long chains of thought. In this work, we propose a way to allow models to be aware of inference budgets by formulating it as utility maximization with respect to an inference budget constraint, hence naming our algorithm Inference Budget-Constrained Policy Optimization (IBPO). In a nutshell, models fine-tuned through IBPO learn to ``understand'' the difficulty of queries and allocate inference budgets to harder ones. With different inference budgets, our best models are able to have a $4.14$\% and $5.74$\% absolute improvement ($8.08$\% and $11.2$\% relative improvement) on MATH500 using $2.16$x and $4.32$x inference budgets respectively, relative to LLaMA3.1 8B Instruct. These improvements are approximately $2$x those of self-consistency under the same budgets.

Modern recommendation systems can be broadly divided into two key stages: the ranking stage, where the system predicts various user engagements (e.g., click-through rate, like rate, follow rate, watch time), and the value model stage, which aggregates these predictive scores through a function (e.g., a linear combination defined by a weight vector) to measure the value of each content by a single numerical score. Both stages play roughly equally important roles in real industrial systems; however, how to optimize the model weights for the second stage still lacks systematic study. This paper focuses on optimizing the second stage through auto-tuning technology. Although general auto-tuning systems and solutions - both from established production practices and open-source solutions - can address this problem, they typically require weeks or even months to identify a feasible solution. Such prolonged tuning processes are unacceptable in production environments for recommendation systems, as suboptimal value models can severely degrade user experience. An effective auto-tuning solution is required to identify a viable model within 2-3 days, rather than the extended timelines typically associated with existing approaches. In this paper, we introduce a practical auto-tuning system named HyperZero that addresses these time constraints while effectively solving the unique challenges inherent in modern recommendation systems. Moreover, this framework has the potential to be expanded to broader tuning tasks within recommendation systems.

Large language models (LLMs) have recently shown remarkable capabilities in reasoning-intensive tasks such as coding (Chen et al., 2021; Li et al., 2022; Rozière et al., 2023) and solving complex mathematical problems (Shao et al., 2024; Azerbayev et al., 2024). Prompting strategies like chain-of-thought prompting (Nye et al., 2021; Wei et al., 2022; Kojima et al., 2022; Adolphs et al., 2022) and self-consistency sampling (Wang et al., 2023) enhance these models' final-answer accuracy by encouraging them to articulate intermediate reasoning steps. However, a significant issue remains: even when these methods boost final-answer correctness, the internal reasoning steps are often unreliable or logically inconsistent (Uesato et al., 2022; Lightman et al., 2024). This discrepancy between correct final answers and flawed intermediate reasoning limits our ability to trust LLMs in scenarios where transparency and correctness of each reasoning stage are crucial (Lanham et al., 2023). For example, in mathematical problem-solving, a model might produce the right answer for the wrong reasons (Lyu et al., 2023; Zheng et al., 2024), confounding our understanding of its true capabilities (Turpin et al., 2023).

Large Language Models (LLMs) have demonstrated impressive capabilities in various tasks, including instruction following, which is crucial for aligning model outputs with user expectations. However, evaluating LLMs' ability to follow instructions remains challenging due to the complexity and subjectivity of human language. Current benchmarks primarily focus on single-turn, monolingual instructions, which do not adequately reflect the complexities of real-world applications that require handling multi-turn and multilingual interactions. To address this gap, we introduce Multi-IF, a new benchmark designed to assess LLMs' proficiency in following multi-turn and multilingual instructions. Multi-IF, which utilizes a hybrid framework combining LLM and human annotators, expands upon the IFEval by incorporating multi-turn sequences and translating the English prompts into another 7 languages, resulting in a dataset of 4,501 multilingual conversations, where each has three turns. Our evaluation of 14 state-of-the-art LLMs on Multi-IF reveals that it presents a significantly more challenging task than existing benchmarks. All the models tested showed a higher rate of failure in executing instructions correctly with each additional turn. For example, o1-preview drops from 0.877 at the first turn to 0.707 at the third turn in terms of average accuracy over all languages. Moreover, languages with non-Latin scripts (Hindi, Russian, and Chinese) generally exhibit higher error rates, suggesting potential limitations in the models' multilingual capabilities. We release Multi-IF prompts and the evaluation code base to encourage further research in this critical area.

Reinforcement learning from human feedback (RLHF) has become the leading approach for fine-tuning large language models (LLM). However, RLHF has limitations in multi-task learning (MTL) due to challenges of reward hacking and extreme multi-objective optimization (i.e., trade-off of multiple and/or sometimes conflicting objectives). Applying RLHF for MTL currently requires careful tuning of the weights for reward model and data combinations. This is often done via human intuition and does not generalize. In this work, we introduce a novel post-training paradigm which we called Constrained Generative Policy Optimization (CGPO). The core of CGPO is Mixture of Judges (MoJ) with cost-efficient constrained policy optimization with stratification, which can identify the perfect blend in RLHF in a principled manner. It shows strong empirical results with theoretical guarantees, does not require extensive hyper-parameter tuning, and is plug-and-play in common post-training pipelines. Together, this can detect and mitigate reward hacking behaviors while reaching a pareto-optimal point across an extremely large number of objectives. Our empirical evaluations demonstrate that CGPO significantly outperforms standard RLHF algorithms like PPO and DPO across various tasks including general chat, STEM questions, instruction following, and coding. Specifically, CGPO shows improvements of 7.4% in AlpacaEval-2 (general chat), 12.5% in Arena-Hard (STEM & reasoning), and consistent gains in other domains like math and coding. Notably, PPO, while commonly used, is prone to severe reward hacking in popular coding benchmarks, which CGPO successfully addresses. This breakthrough in RLHF not only tackles reward hacking and extreme multi-objective optimization challenges but also advances the state-of-the-art in aligning general-purpose LLMs for diverse applications.

The remarkable success of reinforcement learning (RL) heavily relies on observing the reward of every visited state-action pair. In many real world applications, however, an agent can observe only a score that represents the quality of the whole trajectory, which is referred to as the {\em trajectory-wise reward}. In such a situation, it is difficult for standard RL methods to well utilize trajectory-wise reward, and large bias and variance errors can be incurred in policy evaluation. In this work, we propose a novel offline RL algorithm, called Pessimistic vAlue iteRaTion with rEward Decomposition (PARTED), which decomposes the trajectory return into per-step proxy rewards via least-squares-based reward redistribution, and then performs pessimistic value iteration based on the learned proxy reward. To ensure the value functions constructed by PARTED are always pessimistic with respect to the optimal ones, we design a new penalty term to offset the uncertainty of the proxy reward. For general episodic MDPs with large state space, we show that PARTED with overparameterized neural network function approximation achieves an $\tilde{\mathcal{O}}(D_{\text{eff}}H^2/\sqrt{N})$ suboptimality, where $H$ is the length of episode, $N$ is the total number of samples, and $D_{\text{eff}}$ is the effective dimension of the neural tangent kernel matrix. To further illustrate the result, we show that PARTED achieves an $\tilde{\mathcal{O}}(dH^3/\sqrt{N})$ suboptimality with linear MDPs, where $d$ is the feature dimension, which matches with that with neural network function approximation, when $D_{\text{eff}}=dH$. To the best of our knowledge, PARTED is the first offline RL algorithm that is provably efficient in general MDP with trajectory-wise reward.

As a major value function evaluation method, temporal difference (TD) learning (Sutton, 1988; Dayan, 1992) has been widely used in various planning problems in reinforcement learning. Although TD learning performs successfully in the on-policy settings, where an agent can interact with environments under the target policy, it can perform poorly or even diverge under the off-policy settings when the agent only has access to data sampled by a behavior policy (Baird, 1995; Tsitsiklis and Van Roy, 1997; Mahmood et al., 2015). To address such an issue, the gradient temporal-difference (GTD) (Sutton et al., 2008) and least-squares temporal difference (LSTD) (Yu, 2010) algorithms have been proposed, which have been shown to converge in the off-policy settings. However, since GTD and LSTD consider an objective function based on the behavior policy, their converging points can be largely biased from the true value function due to the distribution mismatch between the target and behavior policies, even when the express power of the function approximation class is arbitrarily large (Kolter, 2011). In order to provide a more accurate evaluation, Sutton et al. (2016) proposed the emphatic temporal difference (ETD) algorithm, which introduces the follow-on trace to address the distribution mismatch issue. The stability of ETD was then shown in Sutton et al. (2016); Mahmood et al. (2015), and the asymptotic convergence guarantee for ETD was established in Yu (2015), it has also achieved great success in many tasks (Ghiassian et al., 2016; Ni, 2021).

General Value Function (GVF) is a powerful tool to represent both the {\em predictive} and {\em retrospective} knowledge in reinforcement learning (RL). In practice, often multiple interrelated GVFs need to be evaluated jointly with pre-collected off-policy samples. In the literature, the gradient temporal difference (GTD) learning method has been adopted to evaluate GVFs in the off-policy setting, but such an approach may suffer from a large estimation error even if the function approximation class is sufficiently expressive. Moreover, none of the previous work have formally established the convergence guarantee to the ground truth GVFs under the function approximation settings. In this paper, we address both issues through the lens of a class of GVFs with causal filtering, which cover a wide range of RL applications such as reward variance, value gradient, cost in anomaly detection, stationary distribution gradient, etc. We propose a new algorithm called GenTD for off-policy GVFs evaluation and show that GenTD learns multiple interrelated multi-dimensional GVFs as efficiently as a single canonical scalar value function. We further show that unlike GTD, the learned GVFs by GenTD are guaranteed to converge to the ground truth GVFs as long as the function approximation power is sufficiently large. To our best knowledge, GenTD is the first off-policy GVF evaluation algorithm that has global optimality guarantee.

Designing off-policy reinforcement learning algorithms is typically a very challenging task, because a desirable iteration update often involves an expectation over an on-policy distribution. Prior off-policy actor-critic (AC) algorithms have introduced a new critic that uses the density ratio for adjusting the distribution mismatch in order to stabilize the convergence, but at the cost of potentially introducing high biases due to the estimation errors of both the density ratio and value function. In this paper, we develop a doubly robust off-policy AC (DR-Off-PAC) for discounted MDP, which can take advantage of learned nuisance functions to reduce estimation errors. Moreover, DR-Off-PAC adopts a single timescale structure, in which both actor and critics are updated simultaneously with constant stepsize, and is thus more sample efficient than prior algorithms that adopt either two timescale or nested-loop structure. We study the finite-time convergence rate and characterize the sample complexity for DR-Off-PAC to attain an $\epsilon$-accurate optimal policy. We also show that the overall convergence of DR-Off-PAC is doubly robust to the approximation errors that depend only on the expressive power of approximation functions. To the best of our knowledge, our study establishes the first overall sample complexity analysis for a single time-scale off-policy AC algorithm.

Safe reinforcement learning (SRL) problems are typically modeled as constrained Markov Decision Process (CMDP), in which an agent explores the environment to maximize the expected total reward and meanwhile avoids violating certain constraints on a number of expected total costs. In general, such SRL problems have nonconvex objective functions subject to multiple nonconvex constraints, and hence are very challenging to solve, particularly to provide a globally optimal policy. Many popular SRL algorithms adopt a primal-dual structure which utilizes the updating of dual variables for satisfying the constraints. In contrast, we propose a primal approach, called constraint-rectified policy optimization (CRPO), which updates the policy alternatingly between objective improvement and constraint satisfaction. CRPO provides a primal-type algorithmic framework to solve SRL problems, where each policy update can take any variant of policy optimization step. To demonstrate the theoretical performance of CRPO, we adopt natural policy gradient (NPG) for each policy update step and show that CRPO achieves an $\mathcal{O}(1/\sqrt{T})$ convergence rate to the global optimal policy in the constrained policy set and an $\mathcal{O}(1/\sqrt{T})$ error bound on constraint satisfaction. This is the first finite-time analysis of SRL algorithms with global optimality guarantee. Our empirical results demonstrate that CRPO can outperform the existing primal-dual baseline algorithms significantly.