Large Language Models (LLMs) have demonstrated remarkable capabilities in complex reasoning tasks, yet generating reliable reasoning processes remains a significant challenge. We present a unified probabilistic framework that formalizes LLM reasoning through a novel graphical model incorporating latent thinking processes and evaluation signals. Our framework addresses two critical questions: (1) how to generate high-quality reasoning processes during inference automatically, and (2) how to integrate these processes into post-training. We propose the Bootstrapping Reinforced Thinking Process (BRiTE) algorithm and demonstrate its theoretical convergence at a rate of $1/T$, where $T$ is the number of iterations. The algorithm operates in two steps. First, it generates high-quality rationales by approximating the desired posterior distribution using a reinforcement learning approach with a novel reward shaping mechanism. Second, it fine-tunes the base LLM by maximizing the joint probability of rationale generation with respect to LLM parameters. Empirical evaluation on GSM8K and MATH benchmarks demonstrates that our approach consistently improves performance across different model sizes without requiring human-annotated thinking processes, outperforming standard chain-of-thought prompting while enhancing existing post-training methods.

Large language models (LLMs) demonstrate impressive reasoning abilities, but translating reasoning into actions in the real world remains challenging. In particular, it is unclear how to complete a given task provably within a minimum number of interactions with the external environment, e.g., through an internal mechanism of reasoning. To this end, we propose the first framework with provable regret guarantees to orchestrate reasoning and acting, which we call reason for future, act for now (RAFA). Specifically, we design a prompt template for reasoning that learns from the memory buffer and plans a future trajectory over a long horizon (reason for future). At each step, the LLM agent takes the initial action of the planned trajectory (act for now), stores the collected feedback in the memory buffer, and reinvokes the reasoning routine to replan the future trajectory from the new state. The key idea is to cast reasoning in LLMs as learning and planning in Bayesian adaptive Markov decision processes (MDPs). Correspondingly, we prompt LLMs with the memory buffer to estimate the unknown environment (learning) and generate an optimal trajectory for multiple future steps that maximize a value function (planning). The learning and planning subroutines are performed in an in-context manner to emulate the actor-critic update for MDPs. Our theoretical analysis establishes a $\sqrt{T}$ regret, while our experimental validation demonstrates superior empirical performance.

Aligning generative models with human preference via RLHF typically suffers from overoptimization, where an imperfectly learned reward model can misguide the generative model to output even undesired responses. We investigate this problem in a principled manner by identifying the source of the issue as the distributional shift and uncertainty of human preference in dataset. To mitigate overoptimization, we first propose a theoretical algorithm which optimizes the policy against an adversarially chosen reward model, one that simultaneously minimizes its MLE loss and a reward penalty term. The penalty pessimistically biases the uncertain rewards so as to prevent the policy from choosing actions with spursiouly high proxy rewards, resulting in provable sample efficiency of the algorithm under a partial coverage style condition. Moving from theory to practice, the proposed algorithm further enjoys an equivalent but surprisingly easy to implement form. With a clever usage of the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines (i) a preference optimization loss that directly aligns the policy with human preference, and (ii) a supervised learning loss which explicitly imitates the policy with a baseline distribution. In the context of aligning large language models (LLM), this objective fuses the direct preference optimization (DPO) loss with the supervised fune-tuning (SFT) loss to help mitigate the overoptimization towards undesired responses, for which we name the algorithm Regularized Preference Optimization (RPO). Experiments of aligning LLMs demonstrate the improved performance of our method when compared with DPO baselines. Our work sheds light on the interplay between preference optimization and SFT in tuning LLMs with both theoretical guarantees and empirical evidence.

In reinforcement learning, unsupervised skill discovery aims to learn diverse skills without extrinsic rewards. Previous methods discover skills by maximizing the mutual information (MI) between states and skills. However, such an MI objective tends to learn simple and static skills and may hinder exploration. In this paper, we propose a novel unsupervised skill discovery method through contrastive learning among behaviors, which makes the agent produce similar behaviors for the same skill and diverse behaviors for different skills. Under mild assumptions, our objective maximizes the MI between different behaviors based on the same skill, which serves as an upper bound of the previous MI objective. Meanwhile, our method implicitly increases the state entropy to obtain better state coverage. We evaluate our method on challenging mazes and continuous control tasks. The results show that our method generates diverse and far-reaching skills, and also obtains competitive performance in downstream tasks compared to the state-of-the-art methods.

We study offline reinforcement learning (RL) for partially observable Markov decision processes (POMDPs) with possibly infinite state and observation spaces. Under the undercompleteness assumption, the optimal policy in such POMDPs are characterized by a class of finite-memory Bellman operators. In the offline setting, estimating these operators directly is challenging due to (i) the large observation space and (ii) insufficient coverage of the offline dataset. To tackle these challenges, we propose a novel algorithm that constructs confidence regions for these Bellman operators via offline estimation of their RKHS embeddings, and returns the final policy via pessimistic planning within the confidence regions. We prove that the proposed algorithm attains an \(\epsilon\)-optimal policy using an offline dataset containing \(\tilde\cO(1 / \epsilon^2)\){episodes}, provided that the behavior policy has good coverage over the optimal trajectory. To our best knowledge, our algorithm is the first provably sample efficient offline algorithm for POMDPs without uniform coverage assumptions.

We study the global convergence and global optimality of the actor-critic algorithm applied for the zero-sum two-player stochastic games in a decentralized manner. We focus on the single-timescale setting where the critic is updated by applying the Bellman operator only once and the actor is updated by policy gradient with the information from the critic. Our algorithm is in a decentralized manner, as we assume that each player has no access to the actions of the other one, which, in a way, protects the privacy of both players. Moreover, we consider linear function approximations for both actor and critic, and we prove that the sequence of joint policy generated by our decentralized linear algorithm converges to the minimax equilibrium at a sublinear rate \(\cO(\sqrt{K})\), where \(K\){is} the number of iterations. To the best of our knowledge, we establish the global optimality and convergence of decentralized actor-critic algorithm on zero-sum two-player stochastic games with linear function approximations for the first time.

Most existing policy learning solutions require the learning agents to receive high-quality supervision signals, e.g., rewards in reinforcement learning (RL) or high-quality expert demonstrations in behavioral cloning (BC). These quality supervisions are either infeasible or prohibitively expensive to obtain in practice. We aim for a unified framework that leverages the available cheap weak supervisions to perform policy learning efficiently. To handle this problem, we treat the weak supervision'' as imperfect information coming from a peer agent, and evaluate the learning agent's policy based on a correlated agreement'' with the peer agent's policy (instead of simple agreements). Our approach explicitly punishes a policy for overfitting to the weak supervision. In addition to theoretical guarantees, extensive evaluations on tasks including RL with noisy reward, BC with weak demonstrations, and standard policy co-training (RL + BC) show that our method leads to substantial performance improvements, especially when the complexity or the noise of the learning environments is high.

Learning with noisy labels is a common challenge in supervised learning. Existing approaches often require practitioners to specify noise rates, i.e., a set of parameters controlling the severity of label noises in the problem, and the specifications are either assumed to be given or estimated using additional steps. In this work, we introduce a new family of loss functions that we name as peer loss functions, which enables learning from noisy labels and does not require a priori specification of the noise rates. Peer loss functions work within the standard empirical risk minimization (ERM) framework. We show that, under mild conditions, performing ERM with peer loss functions on the noisy data leads to the optimal or a near-optimal classifier as if performing ERM over the clean training data, which we do not have access to. We pair our results with an extensive set of experiments. Peer loss provides a way to simplify model development when facing potentially noisy training labels, and can be promoted as a robust candidate loss function in such situations.