A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where multiple experts' trajectories are available. We formulate representation learning as a bi-level optimization problem where the "outer" optimization tries to learn the joint representation and the "inner" optimization encodes the imitation learning setup and tries to learn task-specific parameters. We instantiate this framework for the imitation learning settings of behavior cloning and observation-alone. Theoretically, we show using our framework that representation learning can provide sample complexity benefits for imitation learning in both settings. We also provide proof-of-concept experiments to verify our theory.
In imitation learning, it is common to learn a behavior policy to match an unknown target policy via max-likelihood training on a collected set of target demonstrations. In this work, we consider using offline experience datasets - potentially far from the target distribution - to learn low-dimensional state representations that provably accelerate the sample-efficiency of downstream imitation learning. A central challenge in this setting is that the unknown target policy itself may not exhibit low-dimensional behavior, and so there is a potential for the representation learning objective to a…
Nanjing University（南京大学）；the University of Iowa（爱荷华大学）
NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable co…
Due to recent empirical successes, the options framework for hierarchical reinforcement learning is gaining increasing popularity. Rather than learning from rewards which suffers from the curse of dimensionality, we consider learning an options-type hierarchical policy from expert demonstrations. Such a problem is referred to as hierarchical imitation learning. Converting this problem to parameter inference in a latent variable model, we theoretically characterize the EM approach proposed by Daniel et al. (2016). The population level algorithm is analyzed as an intermediate step, which is nont…
the University of Iowa（爱荷华大学）；Google Research（谷歌研究院）；Nanjing University（南京大学）
In this paper, we study contrastive learning from an optimization perspective, aiming to analyze and address a fundamental issue of existing contrastive learning methods that either rely on a large batch size or a large dictionary of feature vectors. We consider a global objective for contrastive learning, which contrasts each positive pair with all negative pairs for an anchor point. From the optimization perspective, we explain why existing methods such as SimCLR require a large batch size in order to achieve a satisfactory result. In order to remove such requirement, we propose a memory-eff…
University of Southern California（南加州大学）；Princeton University（普林斯顿大学）；University of Minnesota（明尼苏达大学）
We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other. However, since the factors are a priori unknown, the corresponding optimization problems are inherently non-convex. The existing guaranteed algorithms which handle this non-convexity incur an irreducible error (bias), and only apply to cases where all factors have the same structure. To this end, w…
University of Pittsburgh（匹兹堡大学）；UPMC Hillman Cancer Center（匹兹堡大学医学中心希尔曼癌症中心）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other nonconvex methods require the rank or sparsity to be known a priori, we use nonconvex regularizers to minimize the rank and $l_0$ norm without the estimator bias from the convex relaxation. We present a novel analysis of the alternating proximal gradient descent algorithm applied to such problems, and bound the error between the iterates and the ground trut…
Imitation-regularized Optimal Transport on Networks: Provable Robustness and Application to Logistics Planning
Toyota Central R&D Labs., Inc.（丰田中央研究实验室有限公司）；Graduate School of Informatics, Kyoto University（京都大学信息科学研究生院）；Frontier Research Center, Toyota Motor Corporation（丰田电机公司前沿研究中心）
Stanford University（斯坦福大学）；Facebook AI Research（Facebook人工智能研究院）；DeepMind（深度思维）
We study risk-sensitive imitation learning where the agent's goal is to perform at least as well as the expert in terms of a risk profile. We first formulate our risk-sensitive imitation learning setting. We consider the generative adversarial approach to imitation learning (GAIL) and derive an optimization problem for our formulation, which we call it risk-sensitive GAIL (RS-GAIL). We then derive two different versions of our RS-GAIL optimization problem that aim at matching the risk profiles of the agent and the expert w.r.t. Jensen-Shannon (JS) divergence and Wasserstein distance, and devel…
Québec AI institute (Mila)（魁北克人工智能研究所（Mila））；McGill University（麦吉尔大学）；Polytechnique Montréal（蒙特利尔理工学院）；Facebook AI Research（Facebook人工智能研究院）；Element AI；Ubisoft Montreal’s La Forge R&D laboratory（育碧蒙特利尔La Forge研发实验室）
Adversarial Imitation Learning alternates between learning a discriminator -- which tells apart expert's demonstrations from generated ones -- and a generator's policy to produce trajectories that can fool this discriminator. This alternated optimization is known to be delicate in practice since it compounds unstable adversarial training with brittle and sample-inefficient reinforcement learning. We propose to remove the burden of the policy optimization steps by leveraging a novel discriminator formulation. Specifically, our discriminator is explicitly conditioned on two policies: the one fro…
In imitation learning, an agent learns how to behave in an environment with an unknown cost function by mimicking expert demonstrations. Existing imitation learning algorithms typically involve solving a sequence of planning or reinforcement learning problems. Such algorithms are therefore not directly applicable to large, high-dimensional environments, and their performance can significantly degrade if the planning problems are not solved to optimality. Under the apprenticeship learning formalism, we develop alternative model-free algorithms for finding a parameterized stochastic policy that …
This thesis rigorously studies fundamental reinforcement learning (RL) methods in modern practical considerations, including robust RL, distributional RL, and offline RL with neural function approximation. The thesis first prepares the readers with an overall overview of RL and key technical background in statistics and optimization. In each of the settings, the thesis motivates the problems to be studied, reviews the current literature, provides computationally efficient algorithms with provable efficiency guarantees, and concludes with future research directions. The thesis makes fundamental…
Imitation learning can reproduce policies by observing experts, which poses a problem regarding policy privacy. Policies, such as human, or policies on deployed robots, can all be cloned without consent from the owners. How can we protect against external observers cloning our proprietary policies? To answer this question we introduce a new reinforcement learning framework, where we train an ensemble of near-optimal policies, whose demonstrations are guaranteed to be useless for an external observer. We formulate this idea by a constrained optimization problem, where the objective is to improv…
Northwestern University（西北大学）；University of Minnesota Twin Cities（明尼苏达大学双城分校）；Georgia Institute of Technology（佐治亚理工学院）
We study the global convergence of generative adversarial imitation learning for linear quadratic regulators, which is posed as minimax optimization. To address the challenges arising from non-convex-concave geometry, we analyze the alternating gradient algorithm and establish its Q-linear rate of convergence to a unique saddle point, which simultaneously recovers the globally optimal policy and reward function. We hope our results may serve as a small step towards understanding and taming the instability in imitation learning as well as in more general non-convex-concave alternating minimax o…
Recent progress in state-only imitation learning extends the scope of applicability of imitation learning to real-world settings by relieving the need for observing expert actions. However, existing solutions only learn to extract a state-to-action mapping policy from the data, without considering how the expert plans to the target. This hinders the ability to leverage demonstrations and limits the flexibility of the policy. In this paper, we introduce Decoupled Policy Optimization (DePO), which explicitly decouples the policy as a high-level state planner and an inverse dynamics model. With e…
Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective optimization, where $f(x)$ outputs a vector of possibly competing objectives and the goal is to converge to the Pareto frontier. Quantitatively, we wish to maximize the standard hypervolume indicator metric, which measures the dominated hypervolume of the entire set of chosen inputs. In this paper, we introduce a novel scalarization function, which we term the hyper…
University of California, Berkeley（加州大学伯克利分校）；University of New Hampshire（新罕布什尔大学）
The difficulty in specifying rewards for many real-world problems has led to an increased focus on learning rewards from human feedback, such as demonstrations. However, there are often many different reward functions that explain the human feedback, leaving agents with uncertainty over what the true reward function is. While most policy optimization approaches handle this uncertainty by optimizing for expected performance, many applications demand risk-averse behavior. We derive a novel policy gradient-style robust optimization approach, PG-BROIL, that optimizes a soft-robust objective that b…
ETH Zurich（苏黎世联邦理工学院）；Shanghai Jiao Tong University（上海交通大学）
Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we investigate the role of submodularity in provable non-convex optimization and validation of algorithms. A profound understanding which classes of functions can be tractably optimized remains a central challenge for non-convex optimization. By advancing the notion of submodularity to continuous domains (termed "continuous submodularity"), we characterize a clas…
We study the problem of meta-learning through the lens of online convex optimization, developing a meta-algorithm bridging the gap between popular gradient-based meta-learning and classical regularization-based multi-task transfer methods. Our method is the first to simultaneously satisfy good sample efficiency guarantees in the convex setting, with generalization bounds that improve with task-similarity, while also being computationally scalable to modern deep learning architectures and the many-task setting. Despite its simplicity, the algorithm matches, up to a constant factor, a lower boun…
Google AI Princeton（谷歌AI普林斯顿）；Princeton University（普林斯顿大学）
The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network architecture, initialization procedure, and other factors tie together and are all components of its success. This presents theoretical challenges for analyzing state-based and/or online deep learning. Motivated by applications in control, we give a general black-box reduction from deep learning to online convex optimization. This allows us to decouple optimization…
Active-GRPO: Adaptive Imitation and Self-Improving Reasoning for Molecular Optimization
School of Medicine, Stanford University（斯坦福大学医学院）；Data Science Institute, University of Chicago（芝加哥大学数据科学研究所）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普利兹克分子工程学院）；Department of Computer Science, University of Chicago（芝加哥大学计算机科学系）；Argonne National Laboratory（阿贡国家实验室）
Beijing Institute of Technology（北京理工大学）；McGill University（麦吉尔大学）
Intelligent motion planning is one of the core components in automated vehicles, which has received extensive interests. Traditional motion planning methods suffer from several drawbacks in terms of optimality, efficiency and generalization capability. Sampling based methods cannot guarantee the optimality of the generated trajectories. Whereas the optimization-based methods are not able to perform motion planning in real-time, and limited by the simplified formalization. In this work, we propose a learning-based approach to handle those shortcomings. Mixed Integer Quadratic Problem based opti…
We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\mathcal{O}(1/\sqrt{T})$ global convergence rate for both the optimality gap and the constraint violation. We propose a new algorithm called policy mirror descent-primal dual (PMD-PD) algorithm that can provably achieve a faster $\mathcal{O}(\log(T)/T)$ convergence rate for both the optimality gap and the constraint violation. For the primal (policy) update, the PMD-PD algorithm uti…
While recent state-of-the-art results for adversarial imitation-learning algorithms are encouraging, recent works exploring the imitation learning from observation (ILO) setting, where trajectories \textit{only} contain expert observations, have not been met with the same success. Inspired by recent investigations of $f$-divergence manipulation for the standard imitation learning setting(Ke et al., 2019; Ghasemipour et al., 2019), we here examine the extent to which variations in the choice of probabilistic divergence may yield more performant ILO algorithms. We unfortunately find that $f$-div…
NVIDIA（英伟达）；Georgia Institute of Technology（佐治亚理工学院）；University of Washington（华盛顿大学）
Imitation learning (IL) is a frequently used approach for data-efficient policy learning. Many IL methods, such as Dataset Aggregation (DAgger), combat challenges like distributional shift by interacting with oracular experts. Unfortunately, assuming access to oracular experts is often unrealistic in practice; data used in IL frequently comes from offline processes such as lead-through or teleoperation. In this paper, we present a novel imitation learning technique called Collocation for Demonstration Encoding (CoDE) that operates on only a fixed set of trajectory demonstrations. We circumvent…
Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Kaiyuan International Mathematical Sciences Institute（开元国际数学科学研究院）
Direct Distributional Optimization for Provable Alignment of Diffusion Models
University of Tokyo（东京大学）；RIKEN（理化学研究所）；UC Berkeley（加州大学伯克利分校）；Agency for Science, Technology and Research (A⋆STAR)（新加坡科技研究局）；Nanyang Technological University（南洋理工大学）
Beihang University（北京航空航天大学）；Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
Combinatorial optimization problems have aroused extensive research interests due to its huge application potential. In practice, there are highly redundant patterns and characteristics during solving the combinatorial optimization problem, which can be captured by machine learning models. Thus, the 2021 NeurIPS Machine Learning for Combinatorial Optimization (ML4CO) competition is proposed with the goal of improving state-of-the-art combinatorial optimization solvers by replacing key heuristic components with machine learning techniques. This work presents our solution and insights gained by …
The use of machine learning models in consequential decision making often exacerbates societal inequity, in particular yielding disparate impact on members of marginalized groups defined by race and gender. The area under the ROC curve (AUC) is widely used to evaluate the performance of a scoring function in machine learning, but is studied in algorithmic fairness less than other performance metrics. Due to the pairwise nature of the AUC, defining an AUC-based group fairness metric is pairwise-dependent and may involve both \emph{intra-group} and \emph{inter-group} AUCs. Importantly, consideri…
Colorado School of Mines（科罗拉多矿业学院）；Johns Hopkins University（约翰斯·霍普金斯大学）
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to generalize the concept of Lipschitz smoothness condition to the relative smoothness condition, which is satisfied by any finite-order polynomial objective function. Further, this work develops new Bregman-divergence based algorithms that are guaranteed to converge to a second-order stationary point for any relatively smooth problem. In addition, the proposed…
We study the problem of alleviating the instability issue in the GAN training procedure via new architecture design. The discrepancy between the minimax and maximin objective values could serve as a proxy for the difficulties that the alternating gradient descent encounters in the optimization of GANs. In this work, we give new results on the benefits of multi-generator architecture of GANs. We show that the minimax gap shrinks to $ε$ as the number of generators increases with rate $\widetilde{O}(1/ε)$. This improves over the best-known result of $\widetilde{O}(1/ε^2)$. At the core of our tech…
University of Pennsylvania（宾夕法尼亚大学）；University of Melbourne（墨尔本大学）
We propose State Matching Offline DIstribution Correction Estimation (SMODICE), a novel and versatile regression-based offline imitation learning (IL) algorithm derived via state-occupancy matching. We show that the SMODICE objective admits a simple optimization procedure through an application of Fenchel duality and an analytic solution in tabular MDPs. Without requiring access to expert actions, SMODICE can be effectively applied to three offline IL settings: (i) imitation from observations (IfO), (ii) IfO with dynamics or morphologically mismatched expert, and (iii) example-based reinforcem…
Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate guarantee solving the constraints-free version of the problem by leveraging XOR-Sampling. However, the task becomes more difficult when additional equality and inequality constraints are needed to be satisfied. Here we propose XOR-PGD, a novel algorithm based on Projected Gradient Descent (PGD) coupled with the XOR sampler, which is guaranteed to solve the constra…
