Junyu Zhang

Liang Pan, Jingbo Wang, Buzhen Huang et al.

We present a physics-based character control framework for synthesizing human-scene interactions. Recent advances adopt physics simulation to mitigate artifacts produced by data-driven kinematic approaches. However, existing physics-based methods mainly focus on single-object environments, resulting in limited applicability in realistic 3D scenes with multi-objects. To address such challenges, we propose a framework that enables physically simulated characters to perform long-term interaction tasks in diverse, cluttered, and unseen 3D scenes. The key idea is to decouple human-scene interactions into two fundamental processes, Interacting and Navigating, which motivates us to construct two reusable Controllers, namely InterCon and NavCon. Specifically, InterCon uses two complementary policies to enable characters to enter or leave the interacting state with a particular object (e.g., sitting on a chair or getting up). To realize navigation in cluttered environments, we introduce NavCon, where a trajectory following policy enables characters to track pre-planned collision-free paths. Benefiting from the divide and conquer strategy, we can train all policies in simple environments and directly apply them in complex multi-object scenes through coordination from a rule-based scheduler. Video and code are available at https://github.com/liangpan99/InterScene.

Fan Chen, Junyu Zhang, Zaiwen Wen

As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish an $Ω\left(\frac{\min\left\{|\mathcal{S}||\mathcal{A}|,|\mathcal{S}|+I\right\} C^*}{(1-γ)^3ε^2}\right)$ sample complexity lower bound for the offline CMDP problem, where $I$ stands for the number of constraints. By introducing a simple but novel deviation control mechanism, we propose a near-optimal primal-dual learning algorithm called DPDL. This algorithm provably guarantees zero constraint violation and its sample complexity matches the above lower bound except for an $\tilde{\mathcal{O}}((1-γ)^{-1})$ factor. Comprehensive discussion on how to deal with the unknown constant $C^*$ and the potential asynchronous structure on the offline dataset are also included.

Junyu Zhang, Feihong Yang, Jian Wang et al.

The Policy-Space Response Oracles (PSRO) framework scales equilibrium computation to large zero-sum games by iteratively expanding a restricted strategy set using deep reinforcement learning (DRL). A central challenge is to construct, under limited computational budgets, a small strategy population whose induced game well approximates the full game. Existing PSRO variants typically expand the population using best responses to meta-strategies computed from restricted-game payoffs, which can lead to inefficient expansions that provide limited global improvement. We propose to guide population expansion by directly evaluating the post-expansion population quality. Specifically, we adopt Population Exploitability (PE) to measure how well a restricted strategy set represents the full game, and introduce a two-phase exploration--selection framework that explicitly minimizes PE during expansion. We instantiate this framework as Global PSRO, a practical DRL-based algorithm that efficiently generates candidate responses and estimates PE via parameter-sharing conditional neural networks. Experiments across multiple two-player zero-sum games show that Global PSRO achieves lower exploitability and approximates Nash equilibria with significantly fewer policy iterations than prior PSRO methods.

Rui Yang, Hanyang Chen, Junyu Zhang et al.

Leveraging Multi-modal Large Language Models (MLLMs) to create embodied agents offers a promising avenue for tackling real-world tasks. While language-centric embodied agents have garnered substantial attention, MLLM-based embodied agents remain underexplored due to the lack of comprehensive evaluation frameworks. To bridge this gap, we introduce EmbodiedBench, an extensive benchmark designed to evaluate vision-driven embodied agents. EmbodiedBench features: (1) a diverse set of 1,128 testing tasks across four environments, ranging from high-level semantic tasks (e.g., household) to low-level tasks involving atomic actions (e.g., navigation and manipulation); and (2) six meticulously curated subsets evaluating essential agent capabilities like commonsense reasoning, complex instruction understanding, spatial awareness, visual perception, and long-term planning. Through extensive experiments, we evaluated 24 leading proprietary and open-source MLLMs within EmbodiedBench. Our findings reveal that: MLLMs excel at high-level tasks but struggle with low-level manipulation, with the best model, GPT-4o, scoring only 28.9\% on average. EmbodiedBench provides a multifaceted standardized evaluation platform that not only highlights existing challenges but also offers valuable insights to advance MLLM-based embodied agents. Our code and dataset are available at https://embodiedbench.github.io.

Zhifa Ke, Junyu Zhang, Zaiwen Wen

In this paper, a Gauss-Newton Temporal Difference (GNTD) learning method is proposed to solve the Q-learning problem with nonlinear function approximation. In each iteration, our method takes one Gauss-Newton (GN) step to optimize a variant of Mean-Squared Bellman Error (MSBE), where target networks are adopted to avoid double sampling. Inexact GN steps are analyzed so that one can safely and efficiently compute the GN updates by cheap matrix iterations. Under mild conditions, non-asymptotic finite-sample convergence to the globally optimal Q function is derived for various nonlinear function approximations. In particular, for neural network parameterization with relu activation, GNTD achieves an improved sample complexity of $\tilde{\mathcal{O}}(\varepsilon^{-1})$, as opposed to the $\mathcal{\mathcal{O}}(\varepsilon^{-2})$ sample complexity of the existing neural TD methods. An $\tilde{\mathcal{O}}(\varepsilon^{-1.5})$ sample complexity of GNTD is also established for general smooth function approximations. We validate our method via extensive experiments in several RL benchmarks, where GNTD exhibits both higher rewards and faster convergence than TD-type methods.

Heng Dong, Junyu Zhang, Chongjie Zhang

Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these approaches often optimize robots directly in the vast design space, resulting in robots with complicated morphologies that are hard to control. In response, this paper presents a novel coarse-to-fine method for designing multi-cellular robots. Initially, this strategy seeks optimal coarse-grained robots and progressively refines them. To mitigate the challenge of determining the precise refinement juncture during the coarse-to-fine transition, we introduce the Hyperbolic Embeddings for Robot Design (HERD) framework. HERD unifies robots of various granularity within a shared hyperbolic space and leverages a refined Cross-Entropy Method for optimization. This framework enables our method to autonomously identify areas of exploration in hyperbolic space and concentrate on regions demonstrating promise. Finally, the extensive empirical studies on various challenging tasks sourced from EvoGym show our approach's superior efficiency and generalization capability.

Junyu Zhang, Yipeng Kang, Jiong Guo et al.

Do large language models (LLMs) genuinely understand abstract concepts, or merely manipulate them as statistical patterns? We introduce an abstraction-grounding framework that decomposes conceptual understanding into three capacities: interpretation of abstract concepts (Abstract-Abstract, A-A), grounding of abstractions in concrete events (Abstract-Concrete, A-C), and application of abstract principles to regulate concrete decisions (Concrete-Concrete, C-C). Using human values as a testbed - given their semantic richness and centrality to alignment - we employ probing (detecting value traces in internal activations) and steering (modifying representations to shift behavior). Across six open-source LLMs and ten value dimensions, probing shows that diagnostic probes trained solely on abstract value descriptions reliably detect the same values in concrete event narratives and decision reasoning, demonstrating cross-level transfer. Steering reveals an asymmetry: intervening on value representations causally shifts concrete judgments and decisions (A-C, C-C), yet leaves abstract interpretations unchanged (A-A), suggesting that encoded abstract values function as stable anchors rather than malleable activations. These findings indicate LLMs maintain structured value representations that bridge abstraction and action, providing a mechanistic and operational foundation for building value-driven autonomous AI systems with more transparent, generalizable alignment and control.

Jinbiao Chen, Shuang Jin, Guoyun Zhang et al.

Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its practical use is often limited by the need to manually reformulate uncertain optimization models into tractable deterministic counterparts. Recent large language models (LLMs) have been shown promising for automating optimization formulation, yet RO reformulation remains challenging because it requires precise multi-step reasoning and mathematically consistent transformations. To facilitate systematic evaluation of LLM-based reformulation, for which no dedicated benchmark currently exists, we develop AutoRO-Bench, a benchmark featuring an automated data generation pipeline for the core RO reformulation task and a curated dataset for the RO application task. To address the reformulation challenge, we propose Automated Reformulation with Experience Memory (AutoREM), a tuning-free memory-augmented framework that autonomously builds a structured textual experience memory by reflecting on past failed trajectories through a tailored offline adaptation procedure. AutoREM requires neither domain-specific expert knowledge nor parameter updates, and the resulting memory readily transfers across different base LLMs. Experimental results show that AutoREM consistently improves the accuracy and efficiency of RO reformulation across in-distribution datasets, out-of-distribution datasets, and diverse base LLMs.

Junwen Qiu, Leilei Mei, Junyu Zhang

The global Lipschitz smoothness condition underlies most convergence and complexity analyses via two key consequences: the descent lemma and the gradient Lipschitz continuity. How to study the performance of optimization algorithms in the absence of Lipschitz smoothness remains an active area. The relative smoothness framework from Bauschke-Bolte-Teboulle (2017) and Lu-Freund-Nesterov (2018) provides an extended descent lemma, ensuring convergence of Bregman-based proximal gradient methods and their vanilla stochastic counterparts. However, many widely used techniques (e.g., momentum schemes, random reshuffling, and variance reduction) additionally require the Lipschitz-type bound for gradient deviations, leaving their analysis under relative smoothness an open area. To resolve this issue, we introduce the dual kernel conditioning (DKC) regularity condition to regulate the local relative curvature of the kernel functions. Combined with the relative smoothness, DKC provides a dual Lipschitz continuity for gradients: even though the gradient mapping is not Lipschitz in the primal space, it preserves Lipschitz continuity in the dual space induced by a mirror map. We verify that DKC is widely satisfied by popular kernels and is closed under affine composition and conic combination. With these novel tools, we establish the first complexity bounds as well as the iterate convergence of random reshuffling mirror descent for constrained nonconvex relative smooth problems.

Xuekai Wei, Junyu Zhang, Qinlin Hu et al.

Current full-reference image quality assessment (FR-IQA) methods often fuse features from reference and distorted images, overlooking that color and luminance distortions occur mainly at low frequencies, whereas edge and texture distortions occur at high frequencies. This work introduces a pioneering training-free FR-IQA method that accurately predicts image quality in alignment with the human visual system (HVS) by leveraging a novel perceptual degradation modelling approach to address this limitation. First, a collaborative feature refinement module employs a carefully designed wavelet transform to extract perceptually relevant features, capturing multiscale perceptual information and mimicking how the HVS analyses visual information at various scales and orientations in the spatial and frequency domains. Second, a Hausdorff distance-based distribution similarity measurement module robustly assesses the discrepancy between the feature distributions of the reference and distorted images, effectively handling outliers and variations while mimicking the ability of HVS to perceive and tolerate certain levels of distortion. The proposed method accurately captures perceptual quality differences without requiring training data or subjective quality scores. Extensive experiments on multiple benchmark datasets demonstrate superior performance compared with existing state-of-the-art approaches, highlighting its ability to correlate strongly with the HVS.\footnote{The code is available at \url{https://anonymous.4open.science/r/CVPR2025-F339}.}

Chengke Zou, Xingang Guo, Rui Yang et al.

The rapid advancements in Vision-Language Models (VLMs) have shown great potential in tackling mathematical reasoning tasks that involve visual context. Unlike humans who can reliably apply solution steps to similar problems with minor modifications, we found that SOTA VLMs like GPT-4o can consistently fail in these scenarios, revealing limitations in their mathematical reasoning capabilities. In this paper, we investigate the mathematical reasoning robustness in VLMs and evaluate how well these models perform under different variants of the same question, such as changes in visual numerical values or function graphs. While several vision-based math benchmarks have been developed to assess VLMs' problem-solving capabilities, these benchmarks contain only static sets of problems and cannot easily evaluate mathematical reasoning robustness. To fill this gap, we introduce DynaMath, a dynamic visual math benchmark designed for in-depth assessment of VLMs. DynaMath includes 501 high-quality, multi-topic seed questions, each represented as a Python program. Those programs are carefully designed and annotated to enable the automatic generation of a much larger set of concrete questions, including many different types of visual and textual variations. DynaMath allows us to evaluate the generalization ability of VLMs, by assessing their performance under varying input conditions of a seed question. We evaluated 14 SOTA VLMs with 5,010 generated concrete questions. Our results show that the worst-case model accuracy, defined as the percentage of correctly answered seed questions in all 10 variants, is significantly lower than the average-case accuracy. Our analysis emphasizes the need to study the robustness of VLMs' reasoning abilities, and DynaMath provides valuable insights to guide the development of more reliable models for mathematical reasoning.

Junyu Zhang, Yifan Sun, Tianang Leng et al.

Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper presents the Laws of Reasoning (LoRe), a unified framework that characterizes intrinsic reasoning patterns in LRMs. We first propose compute law with the hypothesis that the reasoning compute should scale linearly with question complexity. Beyond compute, we extend LoRe with a supplementary accuracy law. Since the question complexity is difficult to quantify in practice, we examine these hypotheses by two properties of the laws, monotonicity and compositionality. We therefore introduce LoRe-Bench, a benchmark that systematically measures these two tractable properties for large reasoning models. Evaluation shows that most reasoning models exhibit reasonable monotonicity but lack compositionality. In response, we develop an effective finetuning approach that enforces compute-law compositionality. Extensive empirical studies demonstrate that better compliance with compute laws yields consistently improved reasoning performance on multiple benchmarks, and uncovers synergistic effects across properties and laws. Project page: https://lore-project.github.io/

Yin Liu, Qiming Dai, Junyu Zhang et al.

Reinforcement learning (RL) has gained attention for aligning large language models (LLMs) via reinforcement learning from human feedback (RLHF). The actor-only variants of Proximal Policy Optimization (PPO) are widely applied for their efficiency. These algorithms incorporate a clipping mechanism to improve stability. Besides, a regularization term, such as the reverse KL-divergence or a more general \(f\)-divergence, is introduced to prevent policy drift. Despite their empirical success, a rigorous theoretical understanding of the problem and the algorithm's properties is limited. This paper advances the theoretical foundations of the PPO-Clip algorithm by analyzing a deterministic actor-only PPO algorithm within the general RL setting with \(f\)-divergence regularization under the softmax policy parameterization. We derive a non-uniform Lipschitz smoothness condition and a Łojasiewicz inequality for the considered problem. Based on these, a non-asymptotic linear convergence rate to the globally optimal policy is established for the forward KL-regularizer. Furthermore, stationary convergence and local linear convergence are derived for the reverse KL-regularizer.

Junyu Zhang, Runpei Dong, Han Wang et al.

This paper presents AlphaOne ($α$1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. $α$1 first introduces $α$ moment, which represents the scaled thinking phase with a universal parameter $α$. Within this scaled pre-$α$ moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the $α$ moment, $α$1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate $α$1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

Daochang Liu, Junyu Zhang, Anh-Dung Dinh et al.

Generative Artificial Intelligence (AI) has rapidly advanced the field of computer vision by enabling machines to create and interpret visual data with unprecedented sophistication. This transformation builds upon a foundation of generative models to produce realistic images, videos, and 3D/4D content. Conventional generative models primarily focus on visual fidelity while often neglecting the physical plausibility of the generated content. This gap limits their effectiveness in applications that require adherence to real-world physical laws, such as robotics, autonomous systems, and scientific simulations. As generative models evolve to increasingly integrate physical realism and dynamic simulation, their potential to function as "world simulators" expands. Therefore, the field of physics-aware generation in computer vision is rapidly growing, calling for a comprehensive survey to provide a structured analysis of current efforts. To serve this purpose, the survey presents a systematic review, categorizing methods based on how they incorporate physical knowledge, either through explicit simulation or implicit learning. It also analyzes key paradigms, discusses evaluation protocols, and identifies future research directions. By offering a comprehensive overview, this survey aims to help future developments in physically grounded generation for computer vision. The reviewed papers are summarized at https://tinyurl.com/Physics-Aware-Generation.

Haizhou Ge, Ruixiang Wang, Zhu-ang Xu et al.

Advanced imitation learning with structures like the transformer is increasingly demonstrating its advantages in robotics. However, deploying these large-scale models on embedded platforms remains a major challenge. In this paper, we propose a pipeline that facilitates the migration of advanced imitation learning algorithms to edge devices. The process is achieved via an efficient model compression method and a practical asynchronous parallel method Temporal Ensemble with Dropped Actions (TEDA) that enhances the smoothness of operations. To show the efficiency of the proposed pipeline, large-scale imitation learning models are trained on a server and deployed on an edge device to complete various manipulation tasks.

Junwen Qiu, Ziyang Zeng, Leilei Mei et al.

Existing convergence of distributed optimization methods in non-Euclidean geometries typically rely on kernel assumptions: (i) global Lipschitz smoothness and (ii) bi-convexity of the associated Bregman divergence function. Unfortunately, these conditions are violated by nearly all kernels used in practice, leaving a huge theory-practice gap. This work closes this gap by developing a unified analytical tool that guarantees convergence under mild conditions. Specifically, we introduce Hessian relative uniform continuity (HRUC), a regularity satisfied by nearly all standard kernels. Importantly, HRUC is closed under concatenation, positive scaling, composition, and various kernel combinations. Leveraging the geometric structure induced by HRUC, we derive convergence guarantees for mirror descent-based gradient tracking without imposing any restrictive assumptions. More broadly, our analysis techniques extend seamlessly to other decentralized optimization methods in genuinely non-Euclidean and non-Lipschitz settings.

Gang Li, Jie Lin, Yining Tang et al.

Multi-agent social interaction has clearly benefited from Large Language Models. However, current simulation systems still face challenges such as difficulties in scaling to diverse scenarios and poor reusability due to a lack of modular design. To address these issues, we designed and developed a modular, object-oriented framework that organically integrates various base classes through a hierarchical structure, harvesting scalability and reusability. We inherited the framework to realize common derived classes. Additionally, a memory summarization mechanism is proposed to filter and distill relevant information from raw memory data, prioritizing contextually salient events and interactions. By selecting and combining some necessary derived classes, we customized a specific simulated environment. Utilizing this simulated environment, we successfully simulated human interactions on social media, replicating real-world online social behaviors. The source code for the project will be released and evolve.

Younghyun Kim, Geunmin Hwang, Junyu Zhang et al.

Large-scale generative models, such as text-to-image diffusion models, have garnered widespread attention across diverse domains due to their creative and high-fidelity image generation. Nonetheless, existing large-scale diffusion models are confined to generating images of up to 1K resolution, which is far from meeting the demands of contemporary commercial applications. Directly sampling higher-resolution images often yields results marred by artifacts such as object repetition and distorted shapes. Addressing the aforementioned issues typically necessitates training or fine-tuning models on higher-resolution datasets. However, this poses a formidable challenge due to the difficulty in collecting large-scale high-resolution images and substantial computational resources. While several preceding works have proposed alternatives to bypass the cumbersome training process, they often fail to produce convincing results. In this work, we probe the generative ability of diffusion models at higher resolution beyond their original capability and propose a novel progressive approach that fully utilizes generated low-resolution images to guide the generation of higher-resolution images. Our method obviates the need for additional training or fine-tuning which significantly lowers the burden of computational costs. Extensive experiments and results validate the efficiency and efficacy of our method. Project page: https://yhyun225.github.io/DiffuseHigh/

Zhifa Ke, Zaiwen Wen, Junyu Zhang

Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general $L$-layer neural network. New proof techniques are developed and an improved new $\tilde{\mathcal{O}}(ε^{-1})$ sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an $\tilde{\mathcal{O}}(ε^{-1})$ complexity under the Markovian sampling, as opposed to the best known $\tilde{\mathcal{O}}(ε^{-2})$ complexity in the existing literature.

Heng Dong, Junyu Zhang, Tonghan Wang et al.

Robot design aims at learning to create robots that can be easily controlled and perform tasks efficiently. Previous works on robot design have proven its ability to generate robots for various tasks. However, these works searched the robots directly from the vast design space and ignored common structures, resulting in abnormal robots and poor performance. To tackle this problem, we propose a Symmetry-Aware Robot Design (SARD) framework that exploits the structure of the design space by incorporating symmetry searching into the robot design process. Specifically, we represent symmetries with the subgroups of the dihedral group and search for the optimal symmetry in structured subgroups. Then robots are designed under the searched symmetry. In this way, SARD can design efficient symmetric robots while covering the original design space, which is theoretically analyzed. We further empirically evaluate SARD on various tasks, and the results show its superior efficiency and generalizability.

Jianhao Wang, Jin Zhang, Haozhe Jiang et al.

Recent offline meta-reinforcement learning (meta-RL) methods typically utilize task-dependent behavior policies (e.g., training RL agents on each individual task) to collect a multi-task dataset. However, these methods always require extra information for fast adaptation, such as offline context for testing tasks. To address this problem, we first formally characterize a unique challenge in offline meta-RL: transition-reward distribution shift between offline datasets and online adaptation. Our theory finds that out-of-distribution adaptation episodes may lead to unreliable policy evaluation and that online adaptation with in-distribution episodes can ensure adaptation performance guarantee. Based on these theoretical insights, we propose a novel adaptation framework, called In-Distribution online Adaptation with uncertainty Quantification (IDAQ), which generates in-distribution context using a given uncertainty quantification and performs effective task belief inference to address new tasks. We find a return-based uncertainty quantification for IDAQ that performs effectively. Experiments show that IDAQ achieves state-of-the-art performance on the Meta-World ML1 benchmark compared to baselines with/without offline adaptation.

Amrit Singh Bedi, Anjaly Parayil, Junyu Zhang et al.

Reinforcement learning is a framework for interactive decision-making with incentives sequentially revealed across time without a system dynamics model. Due to its scaling to continuous spaces, we focus on policy search where one iteratively improves a parameterized policy with stochastic policy gradient (PG) updates. In tabular Markov Decision Problems (MDPs), under persistent exploration and suitable parameterization, global optimality may be obtained. By contrast, in continuous space, the non-convexity poses a pathological challenge as evidenced by existing convergence results being mostly limited to stationarity or arbitrary local extrema. To close this gap, we step towards persistent exploration in continuous space through policy parameterizations defined by distributions of heavier tails defined by tail-index parameter alpha, which increases the likelihood of jumping in state space. Doing so invalidates smoothness conditions of the score function common to PG. Thus, we establish how the convergence rate to stationarity depends on the policy's tail index alpha, a Holder continuity parameter, integrability conditions, and an exploration tolerance parameter introduced here for the first time. Further, we characterize the dependence of the set of local maxima on the tail index through an exit and transition time analysis of a suitably defined Markov chain, identifying that policies associated with Levy Processes of a heavier tail converge to wider peaks. This phenomenon yields improved stability to perturbations in supervised learning, which we corroborate also manifests in improved performance of policy search, especially when myopic and farsighted incentives are misaligned.

Junyu Zhang, Amrit Singh Bedi, Mengdi Wang et al.

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $ε$-stationarity in $\mathcal{O}(1/ε^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/ε^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

Junyu Zhang, Chengzhuo Ni, Zheng Yu et al.

Policy gradient (PG) gives rise to a rich class of reinforcement learning (RL) methods. Recently, there has been an emerging trend to accelerate the existing PG methods such as REINFORCE by the \emph{variance reduction} techniques. However, all existing variance-reduced PG methods heavily rely on an uncheckable importance weight assumption made for every single iteration of the algorithms. In this paper, a simple gradient truncation mechanism is proposed to address this issue. Moreover, we design a Truncated Stochastic Incremental Variance-Reduced Policy Gradient (TSIVR-PG) method, which is able to maximize not only a cumulative sum of rewards but also a general utility function over a policy's long-term visiting distribution. We show an $\tilde{\mathcal{O}}(ε^{-3})$ sample complexity for TSIVR-PG to find an $ε$-stationary policy. By assuming the overparameterizaiton of policy and exploiting the hidden convexity of the problem, we further show that TSIVR-PG converges to global $ε$-optimal policy with $\tilde{\mathcal{O}}(ε^{-2})$ samples.

Junyu Zhang, Alec Koppel, Amrit Singh Bedi et al.

In recent years, reinforcement learning (RL) systems with general goals beyond a cumulative sum of rewards have gained traction, such as in constrained problems, exploration, and acting upon prior experiences. In this paper, we consider policy optimization in Markov Decision Problems, where the objective is a general concave utility function of the state-action occupancy measure, which subsumes several of the aforementioned examples as special cases. Such generality invalidates the Bellman equation. As this means that dynamic programming no longer works, we focus on direct policy search. Analogously to the Policy Gradient Theorem \cite{sutton2000policy} available for RL with cumulative rewards, we derive a new Variational Policy Gradient Theorem for RL with general utilities, which establishes that the parametrized policy gradient may be obtained as the solution of a stochastic saddle point problem involving the Fenchel dual of the utility function. We develop a variational Monte Carlo gradient estimation algorithm to compute the policy gradient based on sample paths. We prove that the variational policy gradient scheme converges globally to the optimal policy for the general objective, though the optimization problem is nonconvex. We also establish its rate of convergence of the order $O(1/t)$ by exploiting the hidden convexity of the problem, and proves that it converges exponentially when the problem admits hidden strong convexity. Our analysis applies to the standard RL problem with cumulative rewards as a special case, in which case our result improves the available convergence rate.

Mingyi Hong, Siliang Zeng, Junyu Zhang et al.

We study a generic class of decentralized algorithms in which $N$ agents jointly optimize the non-convex objective $f(u):=1/N\sum_{i=1}^{N}f_i(u)$, while only communicating with their neighbors. This class of problems has become popular in modeling many signal processing and machine learning applications, and many efficient algorithms have been proposed. However, by constructing some counter-examples, we show that when certain local Lipschitz conditions (LLC) on the local function gradient $\nabla f_i$'s are not satisfied, most of the existing decentralized algorithms diverge, even if the global Lipschitz condition (GLC) is satisfied, where the sum function $f$ has Lipschitz gradient. This observation raises an important open question: How to design decentralized algorithms when the LLC, or even the GLC, is not satisfied? To address the above question, we design a first-order algorithm called Multi-stage gradient tracking algorithm (MAGENTA), which is capable of computing stationary solutions with neither the LLC nor the GLC. In particular, we show that the proposed algorithm converges sublinearly to certain $ε$-stationary solution, where the precise rate depends on various algorithmic and problem parameters. In particular, if the local function $f_i$'s are $Q$th order polynomials, then the rate becomes $\mathcal{O}(1/ε^{Q-1})$. Such a rate is tight for the special case of $Q=2$ where each $f_i$ satisfies LLC. To our knowledge, this is the first attempt that studies decentralized non-convex optimization problems with neither the LLC nor the GLC.

Junyu Zhang, Amrit Singh Bedi, Mengdi Wang et al.

We study the estimation of risk-sensitive policies in reinforcement learning problems defined by a Markov Decision Process (MDPs) whose state and action spaces are countably finite. Prior efforts are predominately afflicted by computational challenges associated with the fact that risk-sensitive MDPs are time-inconsistent. To ameliorate this issue, we propose a new definition of risk, which we call caution, as a penalty function added to the dual objective of the linear programming (LP) formulation of reinforcement learning. The caution measures the distributional risk of a policy, which is a function of the policy's long-term state occupancy distribution. To solve this problem in an online model-free manner, we propose a stochastic variant of primal-dual method that uses Kullback-Lieber (KL) divergence as its proximal term. We establish that the number of iterations/samples required to attain approximately optimal solutions of this scheme matches tight dependencies on the cardinality of the state and action spaces, but differs in its dependence on the infinity norm of the gradient of the risk measure. Experiments demonstrate the merits of this approach for improving the reliability of reward accumulation without additional computational burdens.

Junyu Zhang, Lin Xiao

We consider multi-level composite optimization problems where each mapping in the composition is the expectation over a family of random smooth mappings or the sum of some finite number of smooth mappings. We present a normalized proximal approximate gradient (NPAG) method where the approximate gradients are obtained via nested stochastic variance reduction. In order to find an approximate stationary point where the expected norm of its gradient mapping is less than $ε$, the total sample complexity of our method is $O(ε^{-3})$ in the expectation case, and $O(N+\sqrt{N}ε^{-2})$ in the finite-sum case where $N$ is the total number of functions across all composition levels. In addition, the dependence of our total sample complexity on the number of composition levels is polynomial, rather than exponential as in previous work.

Damek Davis, Dmitriy Drusvyatskiy, Lin Xiao et al.

Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. More nuanced high probability guarantees are rare, and typically either rely on "light-tail" noise assumptions or exhibit worse sample complexity. In this work, we show that a wide class of stochastic optimization algorithms for strongly convex problems can be augmented with high confidence bounds at an overhead cost that is only logarithmic in the confidence level and polylogarithmic in the condition number. The procedure we propose, called proxBoost, is elementary and builds on two well-known ingredients: robust distance estimation and the proximal point method. We discuss consequences for both streaming (online) algorithms and offline algorithms based on empirical risk minimization.

Junyu Zhang, Lin Xiao

We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic composite gradient method that employs an incremental variance-reduced estimator for both the inner vector mapping and its Jacobian. We show that this method achieves the same orders of complexity as the best known first-order methods for minimizing expected-value and finite-sum nonconvex functions, despite the additional outer composition which renders the composite gradient estimator biased. This finding enables a much broader range of applications in machine learning to benefit from the low complexity of incremental variance-reduction methods.

Jason Causey, Junyu Zhang, Shiqian Ma et al.

Computed tomography (CT) examinations are commonly used to predict lung nodule malignancy in patients, which are shown to improve noninvasive early diagnosis of lung cancer. It remains challenging for computational approaches to achieve performance comparable to experienced radiologists. Here we present NoduleX, a systematic approach to predict lung nodule malignancy from CT data, based on deep learning convolutional neural networks (CNN). For training and validation, we analyze >1000 lung nodules in images from the LIDC/IDRI cohort. All nodules were identified and classified by four experienced thoracic radiologists who participated in the LIDC project. NoduleX achieves high accuracy for nodule malignancy classification, with an AUC of ~0.99. This is commensurate with the analysis of the dataset by experienced radiologists. Our approach, NoduleX, provides an effective framework for highly accurate nodule malignancy prediction with the model trained on a large patient population. Our results are replicable with software available at http://bioinformatics.astate.edu/NoduleX.

Junyu Zhang, Shiqian Ma, Shuzhong Zhang

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing, image processing, and tensor PCA, among others. We develop an ADMM-like primal-dual approach based on decoupled solvable subroutines such as linearized proximal mappings. First, we introduce the optimality conditions for the afore-mentioned optimization models. Then, the notion of $ε$-stationary solutions is introduced as a result. The main part of the paper is to show that the proposed algorithms enjoy an iteration complexity of $O(1/ε^2)$ to reach an $ε$-stationary solution. For prohibitively large-size tensor or machine learning models, we present a sampling-based stochastic algorithm with the same iteration complexity bound in expectation. In case the subproblems are not analytically solvable, a feasible curvilinear line-search variant of the algorithm based on retraction operators is proposed. Finally, we show specifically how the algorithms can be implemented to solve a variety of practical problems such as the NP-hard maximum bisection problem, the $\ell_q$ regularized sparse tensor principal component analysis and the community detection problem. Our preliminary numerical results show great potentials of the proposed methods.