Imitation learning (IL) learns a policy from expert trajectories, serving as a fundamental paradigm in both large language model training and embodied AI. This process is challenging due to the nature of sequential decision-making where errors can accumulate and distributions may shift over horizons. However, it has been found that a kind of IL approach, adversarial imitation learning (AIL), can have exceptional empirical performance. With just one expert trajectory, AIL often matches the expert performance even in a long horizon, on tasks such as robotic locomotion control. There are two fundamental yet unsolved questions: why does AIL perform well with so few trajectories, and why does it maintain good performance over long horizons? Previous theoretical results fail to answer these questions as they are meaningful only in large sample regime (i.e., lots of expert trajectories) and have dependence on the decision horizon. In this paper, we analyze a total-variation-distance-based AIL (called TV-AIL), showing a horizon-free imitation gap ${\mathcal {O}}(\min \lbrace 1, \sqrt{|{\mathcal {S}}|/N} \rbrace )$O(min{1,|S|/N}) on a class of instances abstracted from robotic locomotion control tasks. Here $|{\mathcal {S}}|$|S| is the state space size for a Markov Decision Process (MDP), and $N$N is the number of expert trajectories. We emphasize two important features of our bound. First, this bound is meaningful in both small and large sample regimes. Second, this bound suggests that the imitation gap of TV-AIL does not increase with the decision horizon. Together, our bound can therefore explain the empirical observations and provide insights into how AIL addresses the distribution shift issue. Our analysis leverages the multi-stage policy optimization structure in TV-AIL and presents a new stage-coupled analysis. This tool also helps analyze the worst-case imitation gap of TV-AIL, disclosing its limitations in general MDPs.

Adversarial imitation learning (AIL), a prominent approach in imitation learning, has achieved significant practical success powered by neural network approximation. However, existing theoretical analyses of AIL are primarily confined to simplified settings-such as tabular and linear function approximation-and involve complex algorithmic designs that impede practical implementation. This creates a substantial gap between theory and practice. This paper bridges this gap by exploring the theoretical underpinnings of online AIL with general function approximation. We introduce a novel framework called optimization-based AIL (OPT-AIL), which performs online optimization for reward learning coupled with optimism-regularized optimization for policy learning. Within this framework, we develop two concrete methods: model-free OPT-AIL and model-based OPT-AIL. Our theoretical analysis demonstrates that both variants achieve polynomial expert sample complexity and interaction complexity for learning near-expert policies. To the best of our knowledge, they represent the first provably efficient AIL methods under general function approximation. From a practical standpoint, OPT-AIL requires only the approximate optimization of two objectives, thereby facilitating practical implementation. Empirical studies demonstrate that OPT-AIL outperforms previous state-of-the-art deep AIL methods across several challenging tasks.

Large Language Models (LLMs) typically rely on Supervised Fine-Tuning (SFT) to specialize in downstream tasks, with the Cross Entropy (CE) loss being the de facto choice. However, CE maximizes the likelihood of observed data without accounting for alternative possibilities. As such, CE usually leads to reduced diversity in the model's outputs, which hinders further development that requires sampling to explore better responses. To address this limitation, this paper introduces a new game-theoretic formulation for SFT. In this framework, an auxiliary variable is introduced to regulate the learning process. We prove that the proposed game-theoretic approach connects to the problem of reverse KL minimization with entropy regularization. This regularization prevents over-memorization of training data and promotes output diversity. To implement this framework, we develop GEM, a new training algorithm that is computationally efficient as CE by leveraging some unique properties of LLMs. Empirical studies of pre-trained models from 3B to 70B parameters show that GEM achieves comparable downstream performance to CE while significantly enhancing output diversity. This increased diversity translates to performance gains in test-time compute scaling for chat and code generation tasks. Moreover, we observe that preserving output diversity has the added benefit of mitigating forgetting, as maintaining diverse outputs encourages models to retain pre-trained knowledge throughout the training process.

In sequential decision-making, the reward function serves as the primary supervision signal, guiding agents to acquire the desired behaviors. Traditional reward modeling methods rely heavily on human expertise, limiting their scalability. Automated preference generation from suboptimal demonstrations has emerged as a promising alternative to address this limitation. This approach first generates preference data from suboptimal demonstrations and then trains reward models based on these preferences. Despite its potential, existing methods often struggle to generate preference data with sufficient coverage, limiting the accuracy and generalizability of the resulting reward models. To overcome this limitation, we propose APEC (Automated Preference generation with Enhanced Coverage), a novel method that improves the coverage of preference data. APEC achieves this by selecting policy pairs with significantly different iteration indices from the whole adversarial imitation learning process. We provide a theoretical analysis to validate that the selected policy pairs provably hold preference relationships. Experimental results demonstrate that APEC consistently outperforms baseline methods in generating preferences with broader coverage across both vector-based and pixel-based control tasks. Consequently, the reward models trained with APEC align more closely with ground-truth rewards, deriving improved policy performance.

Reinforcement learning (RL) has demonstrated impressive performance in decision-making tasks like embodied control, autonomous driving, and financial trading. In many decision-making tasks, the agents often encounter the problem of executing actions under limited budgets. However, classic RL methods typically overlook the challenges posed by such sparse-executing actions. They operate under the assumption that all actions can be taken for an unlimited number of times, both in the formulation of the problem and in the development of effective algorithms. To tackle the issue of limited action execution in RL, this article first formalizes the problem as a sparse action Markov decision process (SA-MDP), in which specific actions in the action space can only be executed for a limited time. Then, we propose a policy optimization algorithm, Action Sparsity REgularization (ASRE), which adaptively handles each action with a distinct preference. ASRE operates through two steps. First, ASRE evaluates action sparsity by constrained action sampling. Following this, ASRE incorporates the sparsity evaluation into policy learning by way of an action distribution regularization. We provide theoretical identification that validates the convergence of ASRE to a regularized optimal value function. Experiments on tasks with known sparse-executing actions, where classical RL algorithms struggle to train policy efficiently, show that ASRE effectively constrains the action sampling and outperforms baselines. Moreover, we present that ASRE can generally improve the performance in Atari games, demonstrating its broad applicability.

Human beings can make adaptive decisions in a preparatory manner, i.e., by making preparations in advance, which offers significant advantages in scenarios where both online and offline experiences are expensive and limited. Meanwhile, current reinforcement learning methods commonly rely on numerous environment interactions but hardly obtain generalizable policies. In this paper, we introduce the idea of \textit{rehearsal} into policy optimization, where the agent plans for all possible outcomes in mind and acts adaptively according to actual responses from the environment. To effectively rehearse, we propose ReDM, an algorithm that generates a diverse and eligible set of dynamics models and then rehearse the policy via adaptive training on the generated model set. Rehearsal enables the policy to make decision plans for various hypothetical dynamics and to naturally generalize to previously unseen environments. Our experimental results demonstrate that ReDM is capable of learning a valid policy solely through rehearsal, even with \emph{zero} interaction data. We further extend ReDM to scenarios where limited or mismatched interaction data is available, and our experimental results reveal that ReDM produces high-performing policies compared to other offline RL baselines.

Learning a precise dynamics model can be crucial for offline reinforcement learning, which, unfortunately, has been found to be quite challenging. Dynamics models that are learned by fitting historical transitions often struggle to generalize to unseen transitions. In this study, we identify a hidden but pivotal factor termed dynamics reward that remains consistent across transitions, offering a pathway to better generalization. Therefore, we propose the idea of reward-consistent dynamics models: any trajectory generated by the dynamics model should maximize the dynamics reward derived from the data. We implement this idea as the MOREC (Model-based Offline reinforcement learning with Reward Consistency) method, which can be seamlessly integrated into previous offline model-based reinforcement learning (MBRL) methods. MOREC learns a generalizable dynamics reward function from offline data, which is subsequently employed as a transition filter in any offline MBRL method: when generating transitions, the dynamics model generates a batch of transitions and selects the one with the highest dynamics reward value. On a synthetic task, we visualize that MOREC has a strong generalization ability and can surprisingly recover some distant unseen transitions. On 21 offline tasks in D4RL and NeoRL benchmarks, MOREC improves the previous state-of-the-art performance by a significant margin, i.e., 4.6\% on D4RL tasks and 25.9\% on NeoRL tasks. Notably, MOREC is the first method that can achieve above 95\% online RL performance in 6 out of 12 D4RL tasks and 3 out of 9 NeoRL tasks. Code is available at https://github.com/polixir/morec.

Imitation learning mimics high-quality policies from expert data for sequential decision-making tasks. However, its efficacy is hindered in scenarios where optimal demonstrations are unavailable, and only imperfect demonstrations are present. To address this issue, introducing additional limited human preferences is a suitable approach as it can be obtained in a human-friendly manner, offering a promising way to learn the policy that exceeds the performance of imperfect demonstrations. In this paper, we propose a novel imitation learning (IL) algorithm, Preference Aided Imitation Learning from imperfect demonstrations (PAIL). Specifically, PAIL learns a preference reward by querying experts for limited preferences from imperfect demonstrations. This serves two purposes during training: 1) Reweighting imperfect demonstrations with the preference reward for higher quality. 2) Selecting explored trajectories with high cumulative preference rewards to augment imperfect demonstrations. The dataset with continuously improving quality empowers the performance of PAIL to transcend the initial demonstrations. Comprehensive empirical results across a synthetic task and two locomotion benchmarks show that PAIL surpasses baselines by 73.2% and breaks through the performance bottleneck of imperfect demonstrations.

Reinforcement Learning from Human Feedback (RLHF) is key to aligning Large Language Models (LLMs), typically paired with the Proximal Policy Optimization (PPO) algorithm. While PPO is a powerful method designed for general reinforcement learning tasks, it is overly sophisticated for LLMs, leading to laborious hyper-parameter tuning and significant computation burdens. To make RLHF efficient, we present ReMax, which leverages 3 properties of RLHF: fast simulation, deterministic transitions, and trajectory-level rewards. These properties are not exploited in PPO, making it less suitable for RLHF. Building on the renowned REINFORCE algorithm, ReMax does not require training an additional value model as in PPO and is further enhanced with a new variance reduction technique. ReMax offers several benefits over PPO: it is simpler to implement, eliminates more than 4 hyper-parameters in PPO, reduces GPU memory usage, and shortens training time. ReMax can save about 46% GPU memory than PPO when training a 7B model and enables training on A800-80GB GPUs without the memory-saving offloading technique needed by PPO. Applying ReMax to a Mistral-7B model resulted in a 94.78% win rate on the AlpacaEval leaderboard and a 7.739 score on MT-bench, setting a new SOTA for open-source 7B models. These results show the effectiveness of ReMax while addressing the limitations of PPO in LLMs.

Imitation learning (IL) algorithms excel in acquiring high-quality policies from expert data for sequential decision-making tasks. But, their effectiveness is hampered when faced with limited expert data. To tackle this challenge, a novel framework called (offline) IL with supplementary data has been proposed, which enhances learning by incorporating an additional yet imperfect dataset obtained inexpensively from sub-optimal policies. Nonetheless, learning becomes challenging due to the potential inclusion of out-of-expert-distribution samples. In this work, we propose a mathematical formalization of this framework, uncovering its limitations. Our theoretical analysis reveals that a naive approach—applying the behavioral cloning (BC) algorithm concept to the combined set of expert and supplementary data—may fall short of vanilla BC, which solely relies on expert data. This deficiency arises due to the distribution shift between the two data sources. To address this issue, we propose a new importance-sampling-based technique for selecting data within the expert distribution. We prove that the proposed method eliminates the gap of the naive approach, highlighting its efficacy when handling imperfect data. Empirical studies demonstrate that our method outperforms previous state-of-the-art methods in tasks including robotic locomotion control, Atari video games, and image classification. Overall, our work underscores the potential of improving IL by leveraging diverse data sources through effective data selection.

Imitation learning (IL) has proven to be an effective method for learning good policies from expert demonstrations. Adversarial imitation learning (AIL), a subset of IL methods, is particularly promising, but its theoretical foundation in the presence of unknown transitions has yet to be fully developed. This paper explores the theoretical underpinnings of AIL in this context, where the stochastic and uncertain nature of environment transitions presents a challenge. We examine the expert sample complexity and interaction complexity required to recover good policies. To this end, we establish a framework connecting reward-free exploration and AIL, and propose an algorithm, MB-TAIL, that achieves the minimax optimal expert sample complexity of $\widetilde{\mathcal{O}} (H^{3/2} |\mathcal{S}|/\varepsilon)$ and interaction complexity of $\widetilde{\mathcal{O}} (H^{3} |\mathcal{S}|^2 |\mathcal{A}|/\varepsilon^2)$. Here, $H$ represents the planning horizon, $|\mathcal{S}|$ is the state space size, $|\mathcal{A}|$ is the action space size, and $\varepsilon$ is the desired imitation gap. MB-TAIL is the first algorithm to achieve this level of expert sample complexity in the unknown transition setting and improves upon the interaction complexity of the best-known algorithm, OAL, by $\mathcal{O} (H)$. Additionally, we demonstrate the generalization ability of MB-TAIL by extending it to the function approximation setting and proving that it can achieve expert sample and interaction complexity independent of $|\mathcal{S}|$.

In sequential decision-making, imitation learning (IL) trains a policy efficiently by mimicking expert demonstrations. Various imitation methods were proposed and empirically evaluated, meanwhile, their theoretical understandings need further studies, among which the compounding error in long-horizon decisions is a major issue. In this paper, we first analyze the value gap between the expert policy and imitated policies by two imitation methods, behavioral cloning (BC) and generative adversarial imitation. The results support that generative adversarial imitation can reduce the compounding error compared to BC. Furthermore, we establish the lower bounds of IL under two settings, suggesting the significance of environment interactions in IL. By considering the environment transition model as a dual agent, IL can also be used to learn the environment model. Therefore, based on the bounds of imitating policies, we further analyze the performance of imitating environments. The results show that environment models can be more effectively imitated by generative adversarial imitation than BC. Particularly, we obtain a policy evaluation error that is linear with the effective planning horizon w.r.t. the model bias, suggesting a novel application of adversarial imitation for model-based reinforcement learning (MBRL). We hope these results could inspire future advances in IL and MBRL.

Imitation learning trains a policy by mimicking expert demonstrations. Various imitation methods were proposed and empirically evaluated, meanwhile, their theoretical understanding needs further studies. In this paper, we firstly analyze the value gap between the expert policy and imitated policies by two imitation methods, behavioral cloning and generative adversarial imitation. The results support that generative adversarial imitation can reduce the compounding errors compared to behavioral cloning, and thus has a better sample complexity. Noticed that by considering the environment transition model as a dual agent, imitation learning can also be used to learn the environment model. Therefore, based on the bounds of imitating policies, we further analyze the performance of imitating environments. The results show that environment models can be more effectively imitated by generative adversarial imitation than behavioral cloning, suggesting a novel application of adversarial imitation for model-based reinforcement learning. We hope these results could inspire future advances in imitation learning and model-based reinforcement learning.