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Researcher profile

Tian Xu

Tian Xu contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningmath.DGmath.APComputer VisionArtificial Intelligenceeess.IV

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Published work

14 published item(s)

preprint2026arXiv

Adversarial Imitation Learning with General Function Approximation: Theoretical Analysis and Practical Algorithms

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.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Constructions of Delaunay-type solutions for the spinorial Yamabe equation on spheres

In this paper we construct singular solutions to the critical Dirac equation on spheres. More precisely, first we construct solutions admitting two points singularities that we call Delaunay-type solutions because of their similarities with the Delaunay solutions constructed for the singular Yamabe problem in \cite{MP1 , Schoen1989}. Then we construct another kind of singular solutions admitting a great circle as a singular set. These solutions are the building blocks for singular solutions on a general Spin manifold.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Curvature effect in the spinorial Yamabe problem on product manifolds

Let $(M_1,\textit{g}^{(1)})$, $(M_2,\textit{g}^{(2)})$ be closed Riemannian spin manifolds. We study the existence of solutions of the spinorial Yamabe problem on the product $M_1\times M_2$ equipped with a family of metrics $\varepsilon^{-2}\textit{g}^{(1)}\oplus\textit{g}^{(2)}$, $\varepsilon>0$. Via variational methods and blow-up techniques, we prove the existence of solutions which depend only on the factor $M_1$, and which exhibit a spike layer as $\varepsilon\to0$. Moreover, we locate the asymptotic position of the peak points of the solutions in terms of the curvature tensor on $(M_1,\textit{g}^{(1)})$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Survey on Model-based Reinforcement Learning

Reinforcement learning (RL) solves sequential decision-making problems via a trial-and-error process interacting with the environment. While RL achieves outstanding success in playing complex video games that allow huge trial-and-error, making errors is always undesired in the real world. To improve the sample efficiency and thus reduce the errors, model-based reinforcement learning (MBRL) is believed to be a promising direction, which builds environment models in which the trial-and-errors can take place without real costs. In this survey, we take a review of MBRL with a focus on the recent progress in deep RL. For non-tabular environments, there is always a generalization error between the learned environment model and the real environment. As such, it is of great importance to analyze the discrepancy between policy training in the environment model and that in the real environment, which in turn guides the algorithm design for better model learning, model usage, and policy training. Besides, we also discuss the recent advances of model-based techniques in other forms of RL, including offline RL, goal-conditioned RL, multi-agent RL, and meta-RL. Moreover, we discuss the applicability and advantages of MBRL in real-world tasks. Finally, we end this survey by discussing the promising prospects for the future development of MBRL. We think that MBRL has great potential and advantages in real-world applications that were overlooked, and we hope this survey could attract more research on MBRL.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Conformal embeddings of $S^2\to\mathbb{R}^3$ with prescribed mean curvature: A variational approach

Motivated by recent progress on a spinorial analogue of the Yamabe problem in the geometric literature, we study a conformally invariant spinor field equation on the $m$-sphere, $m\geq2$. Via variational methods and the spinorial Weierstraß representation, we study the problem of prescribing mean curvature for the immersion $S^2\to\mathbb{R}^3$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Model Generation with Provable Coverability for Offline Reinforcement Learning

Model-based offline optimization with dynamics-aware policy provides a new perspective for policy learning and out-of-distribution generalization, where the learned policy could adapt to different dynamics enumerated at the training stage. But due to the limitation under the offline setting, the learned model could not mimic real dynamics well enough to support reliable out-of-distribution exploration, which still hinders policy to generalize well. To narrow the gap, previous works roughly ensemble randomly initialized models to better approximate the real dynamics. However, such practice is costly and inefficient, and provides no guarantee on how well the real dynamics could be approximated by the learned models, which we name coverability in this paper. We actively address this issue by generating models with provable ability to cover real dynamics in an efficient and controllable way. To that end, we design a distance metric for dynamic models based on the occupancy of policies under the dynamics, and propose an algorithm to generate models optimizing their coverage for the real dynamics. We give a theoretical analysis on the model generation process and proves that our algorithm could provide enhanced coverability. As a downstream task, we train a dynamics-aware policy with minor or no conservative penalty, and experiments demonstrate that our algorithm outperforms prior offline methods on existing offline RL benchmarks. We also discover that policies learned by our method have better zero-shot transfer performance, implying their better generalization.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On Generalization of Adversarial Imitation Learning and Beyond

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 AIL may generalize poorly even on visited states from the expert demonstrations. For another class of MDPs, vanilla AIL is proved to generalize well even on non-visited states. Interestingly, its sample complexity is horizon-free, which provably beats BC by a wide margin. Finally, we establish a framework in the unknown transition scenario, which allows AIL to explore via reward-free exploration strategies. Compared with the best-known online apprenticeship learning algorithm, the resulting algorithm improves the sample complexity and interaction complexity.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Rethinking ValueDice: Does It Really Improve Performance?

Since the introduction of GAIL, adversarial imitation learning (AIL) methods attract lots of research interests. Among these methods, ValueDice has achieved significant improvements: it beats the classical approach Behavioral Cloning (BC) under the offline setting, and it requires fewer interactions than GAIL under the online setting. Are these improvements benefited from more advanced algorithm designs? We answer this question by the following conclusions. First, we show that ValueDice could reduce to BC under the offline setting. Second, we verify that overfitting exists and regularization matters in the low-data regime. Specifically, we demonstrate that with weight decay, BC also nearly matches the expert performance as ValueDice does. The first two claims explain the superior offline performance of ValueDice. Third, we establish that ValueDice does not work when the expert trajectory is subsampled. Instead, the mentioned success of ValueDice holds when the expert trajectory is complete, in which ValueDice is closely related to BC that performs well as mentioned. Finally, we discuss the implications of our research for imitation learning studies beyond ValueDice.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Generating Multi-scale Maps from Remote Sensing Images via Series Generative Adversarial Networks

Considering the success of generative adversarial networks (GANs) for image-to-image translation, researchers have attempted to translate remote sensing images (RSIs) to maps (rs2map) through GAN for cartography. However, these studies involved limited scales, which hinders multi-scale map creation. By extending their method, multi-scale RSIs can be trivially translated to multi-scale maps (multi-scale rs2map translation) through scale-wise rs2map models trained for certain scales (parallel strategy). However, this strategy has two theoretical limitations. First, inconsistency between various spatial resolutions of multi-scale RSIs and object generalization on multi-scale maps (RS-m inconsistency) increasingly complicate the extraction of geographical information from RSIs for rs2map models with decreasing scale. Second, as rs2map translation is cross-domain, generators incur high computation costs to transform the RSI pixel distribution to that on maps. Thus, we designed a series strategy of generators for multi-scale rs2map translation to address these limitations. In this strategy, high-resolution RSIs are inputted to an rs2map model to output large-scale maps, which are translated to multi-scale maps through series multi-scale map translation models. The series strategy avoids RS-m inconsistency as inputs are high-resolution large-scale RSIs, and reduces the distribution gap in multi-scale map generation through similar pixel distributions among multi-scale maps. Our experimental results showed better quality multi-scale map generation with the series strategy, as shown by average increases of 11.69%, 53.78%, 55.42%, and 72.34% in the structural similarity index, edge structural similarity index, intersection over union (road), and intersection over union (water) for data from Mexico City and Tokyo at zoom level 17-13.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A variational analysis of the spinorial Yamabe equation on product manifolds

This work is devoted to the analysis of the Yamabe problem on Spin manifolds and some applications to CMC immersions. Despite the efforts of many authors, very little is known on the existence of Yamabe metrics on general Spin manifolds. Motivated to bubbling phenomena for the Riemannian problem and recent multiplicity results in this setting, we investigate special spinorial Yamabe metrics on product manifolds developing a bubbling analysis which has independent interest in the present setting.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Investigating Bias and Fairness in Facial Expression Recognition

Recognition of expressions of emotions and affect from facial images is a well-studied research problem in the fields of affective computing and computer vision with a large number of datasets available containing facial images and corresponding expression labels. However, virtually none of these datasets have been acquired with consideration of fair distribution across the human population. Therefore, in this work, we undertake a systematic investigation of bias and fairness in facial expression recognition by comparing three different approaches, namely a baseline, an attribute-aware and a disentangled approach, on two well-known datasets, RAF-DB and CelebA. Our results indicate that: (i) data augmentation improves the accuracy of the baseline model, but this alone is unable to mitigate the bias effect; (ii) both the attribute-aware and the disentangled approaches fortified with data augmentation perform better than the baseline approach in terms of accuracy and fairness; (iii) the disentangled approach is the best for mitigating demographic bias; and (iv) the bias mitigation strategies are more suitable in the existence of uneven attribute distribution or imbalanced number of subgroup data.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Strongly localized semiclassical states for nonlinear Dirac equations

We study semiclassical states of the nonlinear Dirac equation \[ -i\hbar\partial_tψ= ic\hbar\sum_{k=1}^3α_k\partial_kψ- mc^2βψ- M(x)ψ+ f(|ψ|)ψ,\quad t\in\mathbb{R},\ x\in\mathbb{R}^3, \] where $V$ is a bounded continuous potential function and the nonlinear term $f(|ψ|)ψ$ is superlinear, possibly of critical growth. Our main result deals with standing wave solutions that concentrate near a critical point of the potential. Standard methods applicable to nonlinear Schrödinger equations, like Lyapunov-Schmidt reduction or penalization, do not work, not even for the homogeneous nonlinearity $f(s)=s^p$. We develop a variational method for the strongly indefinite functional associated to the problem.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent

Let $(M,\textit{g},σ)$ be a compact Riemannian spin manifold of dimension $m\geq2$, let $\mathbb{S}(M)$ denote the spinor bundle on $M$, and let $D$ be the Atiyah-Singer Dirac operator acting on spinors $ψ:M\to\mathbb{S}(M)$. We study the existence of solutions of the nonlinear Dirac equation with critical exponent \[ Dψ= λψ+ f(|ψ|)ψ+ |ψ|^{\frac2{m-1}}ψ\tag{NLD} \] where $λ\in\mathbb{R}$ and $f(|ψ|)ψ$ is a subcritical nonlinearity in the sense that $f(s)=o\big(s^{\frac2{m-1}}\big)$ as $s\to\infty$. A model nonlinearity is $f(s)=αs^{p-2}$ with $2<p<\frac{2m}{m-1}$, $α\in\mathbb{R}$. In particular we study the nonlinear Dirac equation \[ Dψ=λψ+|ψ|^{\frac2{m-1}}ψ, \quad λ\in\mathbb{R}. \tag{BND} \] This equation is a spinorial analogue of the Brezis-Nirenberg problem. As corollary of our main results we obtain the existence of least energy solutions $(λ,ψ)$ of (BND) and (NLD) for every $λ>0$, even if $λ$ is an eigenvalue of $D$. For some classes of nonlinearities $f$ we also obtain solutions of (NLD) for every $λ\in\mathbb{R}$, except for non-positive eigenvalues. If $m\not\equiv3$ (mod 4) we obtain solutions of (NLD) for every $λ\in\mathbb{R}$, except for a finite number of non-positive eigenvalues. In certain parameter ranges we obtain multiple solutions of (NLD) and (BND), some near the trivial branch, others away from it. The proofs of our results are based on variational methods using the strongly indefinite energy functional associated to (NLD).

0 citations0 reviewsNo code linkedOpen access