We study the statistical limits of Imitation Learning (IL) in episodic Markov Decision Processes (MDPs) with a state space $\mathcal{S}$. We focus on the known-transition setting where the learner is provided a dataset of $N$ length-$H$ trajectories from a deterministic expert policy and knows the MDP transition. We establish an upper bound $O(|\mathcal{S}|H^{3/2}/N)$ for the suboptimality using the Mimic-MD algorithm in Rajaraman et al (2020) which we prove to be computationally efficient. In contrast, we show the minimax suboptimality grows as $Ω( H^{3/2}/N)$ when $|\mathcal{S}|\geq 3$ while the unknown-transition setting suffers from a larger sharp rate $Θ(|\mathcal{S}|H^2/N)$ (Rajaraman et al (2020)). The lower bound is established by proving a two-way reduction between IL and the value estimation problem of the unknown expert policy under any given reward function, as well as building connections with linear functional estimation with subsampled observations. We further show that under the additional assumption that the expert is optimal for the true reward function, there exists an efficient algorithm, which we term as Mimic-Mixture, that provably achieves suboptimality $O(1/N)$ for arbitrary 3-state MDPs with rewards only at the terminal layer. In contrast, no algorithm can achieve suboptimality $O(\sqrt{H}/N)$ with high probability if the expert is not constrained to be optimal. Our work formally establishes the benefit of the expert optimal assumption in the known transition setting, while Rajaraman et al (2020) showed it does not help when transitions are unknown.
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Center for Data Science, New York University（纽约大学数据科学中心）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）
Domain adaptation in imitation learning represents an essential step towards improving generalizability. However, even in the restricted setting of third-person imitation where transfer is between isomorphic Markov Decision Processes, there are no strong guarantees on the performance of transferred policies. We present problem-dependent, statistical learning guarantees for third-person imitation from observation in an offline setting, and a lower bound on performance in the online setting.
Carnegie Mellon University（卡内基梅隆大学）；Georgia Institute of Technology（佐治亚理工学院）；Aurora Innovation（Aurora创新公司）
We study Imitation Learning (IL) from Observations alone (ILFO) in large-scale MDPs. While most IL algorithms rely on an expert to directly provide actions to the learner, in this setting the expert only supplies sequences of observations. We design a new model-free algorithm for ILFO, Forward Adversarial Imitation Learning (FAIL), which learns a sequence of time-dependent policies by minimizing an Integral Probability Metric between the observation distributions of the expert policy and the learner. FAIL is the first provably efficient algorithm in ILFO setting, which learns a near-optimal po…
Imitation learning trains a policy from expert demonstrations. Imitation learning approaches have been designed from various principles, such as behavioral cloning via supervised learning, apprenticeship learning via inverse reinforcement learning, and GAIL via generative adversarial learning. In this paper, we propose a framework to analyze the theoretical property of imitation learning approaches based on discrepancy propagation analysis. Under the infinite-horizon setting, the framework leads to the value discrepancy of behavioral cloning in an order of O((1-γ)^{-2}). We also show that the …
Nanjing University（南京大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Polixir Technologies（波利克斯尔科技）
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 transiti…
We propose a new framework for Imitation Learning (IL) via density estimation of the expert's occupancy measure followed by Maximum Occupancy Entropy Reinforcement Learning (RL) using the density as a reward. Our approach maximizes a non-adversarial model-free RL objective that provably lower bounds reverse Kullback-Leibler divergence between occupancy measures of the expert and imitator. We present a practical IL algorithm, Neural Density Imitation (NDI), which obtains state-of-the-art demonstration efficiency on benchmark control tasks.
Sample efficiency is critical in solving real-world reinforcement learning problems, where agent-environment interactions can be costly. Imitation learning from expert advice has proved to be an effective strategy for reducing the number of interactions required to train a policy. Online imitation learning, which interleaves policy evaluation and policy optimization, is a particularly effective technique with provable performance guarantees. In this work, we seek to further accelerate the convergence rate of online imitation learning, thereby making it more sample efficient. We propose two mod…
Non-Adversarial Imitation Learning Provably Free of Compounding Errors: The Value Flow Mechanism
National Key Laboratory for Novel Software Technology（新型软件技术国家实验室）；School of Artificial Intelligence, Nanjing University, China（南京大学人工智能学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）
This paper studies offline Imitation Learning (IL) where an agent learns to imitate an expert demonstrator without additional online environment interactions. Instead, the learner is presented with a static offline dataset of state-action-next state transition triples from a potentially less proficient behavior policy. We introduce Model-based IL from Offline data (MILO): an algorithmic framework that utilizes the static dataset to solve the offline IL problem efficiently both in theory and in practice. In theory, even if the behavior policy is highly sub-optimal compared to the expert, we sho…
Khoury College of Computer Sciences（库里计算机学院）；Northeastern University（东北大学）
Behavior cloning of expert demonstrations can speed up learning optimal policies in a more sample-efficient way over reinforcement learning. However, the policy cannot extrapolate well to unseen states outside of the demonstration data, creating covariate shift (agent drifting away from demonstrations) and compounding errors. In this work, we tackle this issue by extending the region of attraction around the demonstrations so that the agent can learn how to get back onto the demonstrated trajectories if it veers off-course. We train a generative backwards dynamics model and generate short imag…
While deep reinforcement learning has successfully solved many challenging control tasks, its real-world applicability has been limited by the inability to ensure the safety of learned policies. We propose an approach to verifiable reinforcement learning by training decision tree policies, which can represent complex policies (since they are nonparametric), yet can be efficiently verified using existing techniques (since they are highly structured). The challenge is that decision tree policies are difficult to train. We propose VIPER, an algorithm that combines ideas from model compression and…
Imitation learning (IL) is a general learning paradigm for tackling sequential decision-making problems. Interactive imitation learning, where learners can interactively query for expert demonstrations, has been shown to achieve provably superior sample efficiency guarantees compared with its offline counterpart or reinforcement learning. In this work, we study classification-based online imitation learning (abbrev. $\textbf{COIL}$) and the fundamental feasibility to design oracle-efficient regret-minimization algorithms in this setting, with a focus on the general nonrealizable case. We make …
The goal of imitation learning is for an apprentice to learn how to behave in a stochastic environment by observing a mentor demonstrating the correct behavior. Accurate prior knowledge about the correct behavior can reduce the need for demonstrations from the mentor. We present a novel approach to encoding prior knowledge about the correct behavior, where we assume that this prior knowledge takes the form of a Markov Decision Process (MDP) that is used by the apprentice as a rough and imperfect model of the mentor's behavior. Specifically, taking a Bayesian approach, we treat the value of a p…
Distributionally Robust Imitation Learning: Layered Control Architecture for Certifiable Autonomy
Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign（机械科学与工程系，伊利诺伊大学厄巴纳-香槟分校）；Department of Electrical and Systems Engineering, University of Pennsylvania（电气与系统工程系，宾夕法尼亚大学）；Mechanical and Civil Engineering, Control and Dynamical Systems, California Institute of Technology（机械与土木工程、控制与动态系统，加州理工学院）；Massachusetts Institute of Technology（麻省理工学院）；Advanced Technology Labs, Lockheed Martin（洛克希德·马丁高级技术实验室）
We consider imitation learning problems where the learner's ability to mimic the expert increases throughout the course of an episode as more information is revealed. One example of this is when the expert has access to privileged information: while the learner might not be able to accurately reproduce expert behavior early on in an episode, by considering the entire history of states and actions, they might be able to eventually identify the hidden context and act as the expert would. We prove that on-policy imitation learning algorithms (with or without access to a queryable expert) are bett…
Despite its promise, reinforcement learning's real-world adoption has been hampered by the need for costly exploration to learn a good policy. Imitation learning (IL) mitigates this shortcoming by using an oracle policy during training as a bootstrap to accelerate the learning process. However, in many practical situations, the learner has access to multiple suboptimal oracles, which may provide conflicting advice in a state. The existing IL literature provides a limited treatment of such scenarios. Whereas in the single-oracle case, the return of the oracle's policy provides an obvious benchm…
Nanjing University（南京大学）；The University of Hong Kong（香港大学）；Peng Cheng Laboratory（鹏城实验室）
Imitation learning aims to mimic the behavior of experts without explicit reward signals. Passive imitation learning methods which use static expert datasets typically suffer from compounding error, low sample efficiency, and high hyper-parameter sensitivity. In contrast, active imitation learning methods solicit expert interventions to address the limitations. However, recent active imitation learning methods are designed based on human intuitions or empirical experience without theoretical guarantee. In this paper, we propose a novel active imitation learning framework based on a teacher-stu…
Princeton University（普林斯顿大学）；University of California, Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）
Imitation learning, followed by reinforcement learning algorithms, is a promising paradigm to solve complex control tasks sample-efficiently. However, learning from demonstrations often suffers from the covariate shift problem, which results in cascading errors of the learned policy. We introduce a notion of conservatively-extrapolated value functions, which provably lead to policies with self-correction. We design an algorithm Value Iteration with Negative Sampling (VINS) that practically learns such value functions with conservative extrapolation. We show that VINS can correct mistakes of th…
Sequence prediction models can be learned from example sequences with a variety of training algorithms. Maximum likelihood learning is simple and efficient, yet can suffer from compounding error at test time. Reinforcement learning such as policy gradient addresses the issue but can have prohibitively poor exploration efficiency. A rich set of other algorithms such as RAML, SPG, and data noising, have also been developed from different perspectives. This paper establishes a formal connection between these algorithms. We present a generalized entropy regularized policy optimization formulation,…
Imitation learning is the task of replicating expert policy from demonstrations, without access to a reward function. This task becomes particularly challenging when the expert exhibits a mixture of behaviors. Prior work has introduced latent variables to model variations of the expert policy. However, our experiments show that the existing works do not exhibit appropriate imitation of individual modes. To tackle this problem, we adopt an encoder-free generative model for behavior cloning (BC) to accurately distinguish and imitate different modes. Then, we integrate it with GAIL to make the le…
Provably Efficient Off-Policy Adversarial Imitation Learning with Convergence Guarantees
Division of Systems Engineering（系统工程系）；Department of Computer Science（计算机科学系）；Amazon Robotics（亚马逊机器人）；Department of Electrical and Computer Engineering（电气与计算机工程系）
We provide a unifying view of a large family of previous imitation learning algorithms through the lens of moment matching. At its core, our classification scheme is based on whether the learner attempts to match (1) reward or (2) action-value moments of the expert's behavior, with each option leading to differing algorithmic approaches. By considering adversarially chosen divergences between learner and expert behavior, we are able to derive bounds on policy performance that apply for all algorithms in each of these classes, the first to our knowledge. We also introduce the notion of moment r…
Although Behavioral Cloning (BC) in theory suffers compounding errors, its scalability and simplicity still makes it an attractive imitation learning algorithm. In contrast, imitation approaches with adversarial training typically does not share the same problem, but necessitates interactions with the environment. Meanwhile, most imitation learning methods only utilises optimal datasets, which could be significantly more expensive to obtain than its suboptimal counterpart. A question that arises is, can we utilise the suboptimal dataset in a principled manner, which otherwise would have been i…
We tackle a common scenario in imitation learning (IL), where agents try to recover the optimal policy from expert demonstrations without further access to the expert or environment reward signals. Except the simple Behavior Cloning (BC) that adopts supervised learning followed by the problem of compounding error, previous solutions like inverse reinforcement learning (IRL) and recent generative adversarial methods involve a bi-level or alternating optimization for updating the reward function and the policy, suffering from high computational cost and training instability. Inspired by recent p…
University of Science and Technology of China（中国科学技术大学）；Northwestern University（西北大学）；Princeton University（普林斯顿大学）
In generative adversarial imitation learning (GAIL), the agent aims to learn a policy from an expert demonstration so that its performance cannot be discriminated from the expert policy on a certain predefined reward set. In this paper, we study GAIL in both online and offline settings with linear function approximation, where both the transition and reward function are linear in the feature maps. Besides the expert demonstration, in the online setting the agent can interact with the environment, while in the offline setting the agent only accesses an additional dataset collected by a prior. F…
This paper studies Imitation Learning from Observations alone (ILFO) where the learner is presented with expert demonstrations that consist only of states visited by an expert (without access to actions taken by the expert). We present a provably efficient model-based framework MobILE to solve the ILFO problem. MobILE involves carefully trading off strategic exploration against imitation - this is achieved by integrating the idea of optimism in the face of uncertainty into the distribution matching imitation learning (IL) framework. We provide a unified analysis for MobILE, and demonstrate tha…
Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested structure: the inner loop finds the optimal policy given parametrized rewards while the outer loop updates the estimates towards optimizing a measure of fit. For high dimensional environments such nested-loop structure entails a significant computational burden. To reduce the computational burden of a nested loop, novel methods such as SQIL [1] and IQ-Learn […
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学新型软件技术国家重点实验室）；Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）深圳大数据研究院）
Despite massive empirical evaluations, one of the fundamental questions in imitation learning is still not fully settled: does AIL (adversarial imitation learning) provably generalize better than BC (behavioral cloning)? We study this open problem with tabular and episodic MDPs. For vanilla AIL that uses the direct maximum likelihood estimation, we provide both negative and positive answers under the known transition setting. For some MDPs, we show that vanilla AIL has a worse sample complexity than BC. The key insight is that the state-action distribution matching principle is weak so that AI…
Tsinghua University（清华大学）；THU-Bosch JCML center（清华-博世机器学习联合中心）；University of California, Los Angeles（加州大学洛杉矶分校）；Bytedance AI Lab（字节跳动人工智能实验室）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
It has been a challenge to learning skills for an agent from long-horizon unannotated demonstrations. Existing approaches like Hierarchical Imitation Learning(HIL) are prone to compounding errors or suboptimal solutions. In this paper, we propose Option-GAIL, a novel method to learn skills at long horizon. The key idea of Option-GAIL is modeling the task hierarchy by options and train the policy via generative adversarial optimization. In particular, we propose an Expectation-Maximization(EM)-style algorithm: an E-step that samples the options of expert conditioned on the current learned polic…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Amazon（亚马逊）
The current paper studies sample-efficient Reinforcement Learning (RL) in settings where only the optimal value function is assumed to be linearly-realizable. It has recently been understood that, even under this seemingly strong assumption and access to a generative model, worst-case sample complexities can be prohibitively (i.e., exponentially) large. We investigate the setting where the learner additionally has access to interactive demonstrations from an expert policy, and we present a statistically and computationally efficient algorithm (Delphi) for blending exploration with expert queri…
Georgia Tech（佐治亚理工学院）；University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an ex…
University of Pennsylvania（宾夕法尼亚大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Google Brain Robotics（谷歌大脑机器人）
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert - a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a hum…
The aim in imitation learning is to learn effective policies by utilizing near-optimal expert demonstrations. However, high-quality demonstrations from human experts can be expensive to obtain in large numbers. On the other hand, it is often much easier to obtain large quantities of suboptimal or task-agnostic trajectories, which are not useful for direct imitation, but can nevertheless provide insight into the dynamical structure of the environment, showing what could be done in the environment even if not what should be done. We ask the question, is it possible to utilize such suboptimal off…
