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Mengdi Xu

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11 papers

2 author rows

JMLR Journal 2024 Journal Article

Functional optimal transport: regularized map estimation and domain adaptation for functional data

Jiacheng Zhu
Aritra Guha
Dat Do
Mengdi Xu
XuanLong Nguyen
Ding Zhao

We introduce a formulation of regularized optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be approximated in terms of an (infinite-dimensional) Hilbert-Schmidt operator mapping a Hilbert space of functions to another. For numerous machine learning applications, data can be naturally viewed as samples drawn from spaces of functions, such as curves and surfaces, in high dimensions. Optimal transport for functional data analysis provides a useful framework of treatment for such domains. Since probability measures in infinite dimensional spaces generally lack absolute continuity (i.e., with respect to non-degenerate Gaussian measures), the Monge map in the standard optimal transport theory for finite dimensional spaces typically does not exist in the functional settings arising in such machine learning applications. This necessitates a suitable notion of approximation for the best pushforward measure to be obtained via a transport map. Indeed, our approach to the transportation problem in functional spaces is by a suitable regularization technique --- we restrict the class of transport maps to be a Hilbert-Schmidt space of operators.Within this regularization framework, we develop an efficient algorithm for finding the stochastic transport map between functional domains and provide theoretical guarantees on the existence, uniqueness, and consistency of our estimate for the Hilbert-Schmidt space of compact linear operators. We validate our method on synthetic datasets and examine the functional properties of the transport map. Experiments on real-world datasets of robot arm trajectories further demonstrate the effectiveness of our method on applications in domain adaptation. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2024. ( edit, beta )

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UAI Conference 2023 Conference Paper

A trajectory is worth three sentences: multimodal transformer for offline reinforcement learning

Yiqi Wang
Mengdi Xu
Laixi Shi
Yuejie Chi

Transformers hold tremendous promise in solving offline reinforcement learning (RL) by formulating it as a sequence modeling problem inspired by language modeling (LM). Prior works using transformers model a sample (trajectory) of RL as one sequence analogous to a sequence of words (one sentence) in LM, despite the fact that each trajectory includes tokens from three diverse modalities: state, action, and reward, while a sentence contains words only. Rather than taking a modality-agnostic approach which uniformly models the tokens from different modalities as one sequence, we propose a multimodal sequence modeling approach in which a trajectory (one “sentence”) of three modalities (state, action, reward) is disentangled into three unimodal ones (three “sentences”). We investigate the correlation of different modalities during sequential decision-making and use the insights to design a multimodal transformer, named Decision Transducer (DTd). DTd outperforms prior art in offline RL on the conducted D4RL benchmarks and enjoys better sample efficiency and algorithm flexibility. Our code is made publicly here.

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NeurIPS Conference 2023 Conference Paper

Adaptive Online Replanning with Diffusion Models

Siyuan Zhou
Yilun Du
Shun Zhang
Mengdi Xu
Yikang Shen
Wei Xiao
Dit-Yan Yeung
Chuang Gan

Diffusion models have risen a promising approach to data-driven planning, and have demonstrated impressive robotic control, reinforcement learning, and video planning performance. Given an effective planner, an important question to consider is replanning -- when given plans should be regenerated due to both action execution error and external environment changes. Direct plan execution, without replanning, is problematic as errors from individual actions rapidly accumulate and environments are partially observable and stochastic. Simultaneously, replanning at each timestep incurs a substantial computational cost, and may prevent successful task execution, as different generated plans prevent consistent progress to any particular goal. In this paper, we explore how we may effectively replan with diffusion models. We propose a principled approach to determine when to replan, based on the diffusion model's estimated likelihood of existing generated plans. We further present an approach to replan existing trajectories to ensure that new plans follow the same goal state as the original trajectory, which may efficiently bootstrap off previously generated plans. We illustrate how a combination of our proposed additions significantly improves the performance of diffusion planners leading to 38\% gains over past diffusion planning approaches on Maze2D and further enables handling of stochastic and long-horizon robotic control tasks.

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ICLR Conference 2023 Conference Paper

Hyper-Decision Transformer for Efficient Online Policy Adaptation

Mengdi Xu
Yuchen Lu
Yikang Shen
Shun Zhang
Ding Zhao
Chuang Gan 0001

Decision Transformers (DT) have demonstrated strong performances in offline reinforcement learning settings, but quickly adapting to unseen novel tasks remains challenging. To address this challenge, we propose a new framework, called Hyper-Decision Transformer (HDT), that can generalize to novel tasks from a handful of demonstrations in a data- and parameter-efficient manner. To achieve such a goal, we propose to augment the base DT with an adaptation module, whose parameters are initialized by a hyper-network. When encountering unseen tasks, the hyper-network takes a handful of demonstrations as inputs and initializes the adaptation module accordingly. This initialization enables HDT to efficiently adapt to novel tasks by only fine-tuning the adaptation module. We validate HDT's generalization capability on object manipulation tasks. We find that with a single expert demonstration and fine-tuning only 0.5% of DT parameters, HDT adapts faster to unseen tasks than fine-tuning the whole DT model. Finally, we explore a more challenging setting where expert actions are not available, and we show that HDT outperforms state-of-the-art baselines in terms of task success rates by a large margin. Demos are available on our project page: https://sites.google.com/view/hdtforiclr2023/home.

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NeurIPS Conference 2022 Conference Paper

Curriculum Reinforcement Learning using Optimal Transport via Gradual Domain Adaptation

Peide Huang
Mengdi Xu
Jiacheng Zhu
Laixi Shi
Fei Fang
Ding Zhao

Curriculum Reinforcement Learning (CRL) aims to create a sequence of tasks, starting from easy ones and gradually learning towards difficult tasks. In this work, we focus on the idea of framing CRL as interpolations between a source (auxiliary) and a target task distribution. Although existing studies have shown the great potential of this idea, it remains unclear how to formally quantify and generate the movement between task distributions. Inspired by the insights from gradual domain adaptation in semi-supervised learning, we create a natural curriculum by breaking down the potentially large task distributional shift in CRL into smaller shifts. We propose GRADIENT which formulates CRL as an optimal transport problem with a tailored distance metric between tasks. Specifically, we generate a sequence of task distributions as a geodesic interpolation between the source and target distributions, which are actually the Wasserstein barycenter. Different from many existing methods, our algorithm considers a task-dependent contextual distance metric and is capable of handling nonparametric distributions in both continuous and discrete context settings. In addition, we theoretically show that GRADIENT enables smooth transfer between subsequent stages in the curriculum under certain conditions. We conduct extensive experiments in locomotion and manipulation tasks and show that our proposed GRADIENT achieves higher performance than baselines in terms of learning efficiency and asymptotic performance.

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ICML Conference 2022 Conference Paper

Prompting Decision Transformer for Few-Shot Policy Generalization

Mengdi Xu
Yikang Shen
Shun Zhang
Yuchen Lu
Ding Zhao
Joshua B. Tenenbaum
Chuang Gan 0001

Human can leverage prior experience and learn novel tasks from a handful of demonstrations. In contrast to offline meta-reinforcement learning, which aims to achieve quick adaptation through better algorithm design, we investigate the effect of architecture inductive bias on the few-shot learning capability. We propose a Prompt-based Decision Transformer (Prompt-DT), which leverages the sequential modeling ability of the Transformer architecture and the prompt framework to achieve few-shot adaptation in offline RL. We design the trajectory prompt, which contains segments of the few-shot demonstrations, and encodes task-specific information to guide policy generation. Our experiments in five MuJoCo control benchmarks show that Prompt-DT is a strong few-shot learner without any extra finetuning on unseen target tasks. Prompt-DT outperforms its variants and strong meta offline RL baselines by a large margin with a trajectory prompt containing only a few timesteps. Prompt-DT is also robust to prompt length changes and can generalize to out-of-distribution (OOD) environments. Project page: \href{https: //mxu34. github. io/PromptDT/}{https: //mxu34. github. io/PromptDT/}.

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IJCAI Conference 2022 Conference Paper

Robust Reinforcement Learning as a Stackelberg Game via Adaptively-Regularized Adversarial Training

Peide Huang
Mengdi Xu
Fei Fang
Ding Zhao

Robust Reinforcement Learning (RL) focuses on improving performances under model errors or adversarial attacks, which facilitates the real-life deployment of RL agents. Robust Adversarial Reinforcement Learning (RARL) is one of the most popular frameworks for robust RL. However, most of the existing literature models RARL as a zero-sum simultaneous game with Nash equilibrium as the solution concept, which could overlook the sequential nature of RL deployments, produce overly conservative agents, and induce training instability. In this paper, we introduce a novel hierarchical formulation of robust RL -- a general-sum Stackelberg game model called RRL-Stack -- to formalize the sequential nature and provide extra flexibility for robust training. We develop the Stackelberg Policy Gradient algorithm to solve RRL-Stack, leveraging the Stackelberg learning dynamics by considering the adversary's response. Our method generates challenging yet solvable adversarial environments which benefit RL agents' robust learning. Our algorithm demonstrates better training stability and robustness against different testing conditions in the single-agent robotics control and multi-agent highway merging tasks.

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IROS Conference 2022 Conference Paper

Scalable Safety-Critical Policy Evaluation with Accelerated Rare Event Sampling

Mengdi Xu
Peide Huang
Fengpei Li
Jiacheng Zhu
Xuewei Tony Qi
Kentaro Oguchi 0001
Zhiyuan Huang
Henry Lam

Evaluating rare but high-stakes events is one of the main challenges in obtaining reliable reinforcement learning policies, especially in large or infinite state/action spaces where limited scalability dictates a prohibitively large number of testing iterations. On the other hand, a biased or inaccurate policy evaluation in a safety-critical system could potentially cause unexpected catastrophic failures during deployment. This paper proposes the Accelerated Policy Evaluation (APE) method, which simultaneously uncovers rare events and estimates the rare event probability in Markov decision processes. The APE method treats the environment nature as an adversarial agent and learns towards, through adaptive importance sampling, the zero-variance sampling distribution for the policy evaluation. Moreover, APE is scalable to large discrete or continuous spaces by incorporating function approximators. We investigate the convergence property of APE in the tabular setting. Our empirical studies show that APE can estimate the rare event probability with a smaller bias while only using orders of magnitude fewer samples than baselines in multi-agent and single-agent environments.

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ICRA Conference 2021 Conference Paper

Context-Aware Safe Reinforcement Learning for Non-Stationary Environments

Baiming Chen
Zuxin Liu
Jiacheng Zhu
Mengdi Xu
Wenhao Ding
Liang Li 0004
Ding Zhao

Safety is a critical concern when deploying reinforcement learning agents for realistic tasks. Recently, safe reinforcement learning algorithms have been developed to optimize the agent’s performance while avoiding violations of safety constraints. However, few studies have addressed the nonstationary disturbances in the environments, which may cause catastrophic outcomes. In this paper, we propose the context-aware safe reinforcement learning (CASRL) method, a metal-earning framework to realize safe adaptation in non-stationary environments. We use a probabilistic latent variable model to achieve fast inference of the posterior environment transition distribution given the context data. Safety constraints are then evaluated with uncertainty-aware trajectory sampling. Prior safety constraints are formulated with domain knowledge to improve safety during exploration. The algorithm is evaluated in realistic safety-critical environments with non-stationary disturbances. Results show that the proposed algorithm significantly outperforms existing baselines in terms of safety and robustness.

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ICRA Conference 2020 Conference Paper

CMTS: A Conditional Multiple Trajectory Synthesizer for Generating Safety-Critical Driving Scenarios

Wenhao Ding
Mengdi Xu
Ding Zhao

Naturalistic driving trajectory generation is crucial for the development of autonomous driving algorithms. However, most of the data is collected in collision-free scenarios leading to the sparsity of the safety-critical cases. When considering safety, testing algorithms in near-miss scenarios that rarely show up in off-the-shelf datasets and are costly to accumulate is a vital part of the evaluation. As a remedy, we propose a safety-critical data synthesizing framework based on variational Bayesian methods and term it as Conditional Multiple Trajectory Synthesizer (CMTS). We extend a generative model to connect safe and collision driving data by representing their distribution in the latent space and use conditional probability to adapt to different maps. Sampling from the mixed distribution enables us to synthesize the safety-critical data not shown in the safe or collision datasets. Experimental results demonstrate that the generated dataset covers many different realistic scenarios, especially the near-misses. We conclude that the use of data generated by CMTS can improve the accuracy of trajectory predictions and autonomous vehicle safety.

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NeurIPS Conference 2020 Conference Paper

Task-Agnostic Online Reinforcement Learning with an Infinite Mixture of Gaussian Processes

Mengdi Xu
Wenhao Ding
Jiacheng Zhu
Zuxin Liu
Baiming Chen
Ding Zhao

Continuously learning to solve unseen tasks with limited experience has been extensively pursued in meta-learning and continual learning, but with restricted assumptions such as accessible task distributions, independently and identically distributed tasks, and clear task delineations. However, real-world physical tasks frequently violate these assumptions, resulting in performance degradation. This paper proposes a continual online model-based reinforcement learning approach that does not require pre-training to solve task-agnostic problems with unknown task boundaries. We maintain a mixture of experts to handle nonstationarity, and represent each different type of dynamics with a Gaussian Process to efficiently leverage collected data and expressively model uncertainty. We propose a transition prior to account for the temporal dependencies in streaming data and update the mixture online via sequential variational inference. Our approach reliably handles the task distribution shift by generating new models for never-before-seen dynamics and reusing old models for previously seen dynamics. In experiments, our approach outperforms alternative methods in non-stationary tasks, including classic control with changing dynamics and decision making in different driving scenarios.

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