Xun Yu Zhou

Yanwei Jia, Xun Yu Zhou

We study the continuous-time counterpart of Q-learning for reinforcement learning (RL) under the entropy-regularized, exploratory diffusion process formulation introduced by Wang et al. (2020). As the conventional (big) Q-function collapses in continuous time, we consider its first-order approximation and coin the term ``(little) q-function". This function is related to the instantaneous advantage rate function as well as the Hamiltonian. We develop a ``q-learning" theory around the q-function that is independent of time discretization. Given a stochastic policy, we jointly characterize the associated q-function and value function by martingale conditions of certain stochastic processes, in both on-policy and off-policy settings. We then apply the theory to devise different actor-critic algorithms for solving underlying RL problems, depending on whether or not the density function of the Gibbs measure generated from the q-function can be computed explicitly. One of our algorithms interprets the well-known Q-learning algorithm SARSA, and another recovers a policy gradient (PG) based continuous-time algorithm proposed in Jia and Zhou (2022b). Finally, we conduct simulation experiments to compare the performance of our algorithms with those of PG-based algorithms in Jia and Zhou (2022b) and time-discretized conventional Q-learning algorithms.

Xuefeng Gao, Xun Yu Zhou

We consider reinforcement learning for continuous-time Markov decision processes (MDPs) in the infinite-horizon, average-reward setting. In contrast to discrete-time MDPs, a continuous-time process moves to a state and stays there for a random holding time after an action is taken. With unknown transition probabilities and rates of exponential holding times, we derive instance-dependent regret lower bounds that are logarithmic in the time horizon. Moreover, we design a learning algorithm and establish a finite-time regret bound that achieves the logarithmic growth rate. Our analysis builds upon upper confidence reinforcement learning, a delicate estimation of the mean holding times, and stochastic comparison of point processes.

Xuefeng Gao, Xun Yu Zhou

We study reinforcement learning for continuous-time Markov decision processes (MDPs) in the finite-horizon episodic setting. In contrast to discrete-time MDPs, the inter-transition times of a continuous-time MDP are exponentially distributed with rate parameters depending on the state--action pair at each transition. We present a learning algorithm based on the methods of value iteration and upper confidence bound. We derive an upper bound on the worst-case expected regret for the proposed algorithm, and establish a worst-case lower bound, both bounds are of the order of square-root on the number of episodes. Finally, we conduct simulation experiments to illustrate the performance of our algorithm.

Xia Han, Ruodu Wang, Xun Yu Zhou

We propose \emph{Choquet regularizers} to measure and manage the level of exploration for reinforcement learning (RL), and reformulate the continuous-time entropy-regularized RL problem of Wang et al. (2020, JMLR, 21(198)) in which we replace the differential entropy used for regularization with a Choquet regularizer. We derive the Hamilton--Jacobi--Bellman equation of the problem, and solve it explicitly in the linear--quadratic (LQ) case via maximizing statically a mean--variance constrained Choquet regularizer. Under the LQ setting, we derive explicit optimal distributions for several specific Choquet regularizers, and conversely identify the Choquet regularizers that generate a number of broadly used exploratory samplers such as $ε$-greedy, exponential, uniform and Gaussian.

Ronilo J. Ragodos, Tong Wang, Qihang Lin et al.

While deep reinforcement learning has proven to be successful in solving control tasks, the "black-box" nature of an agent has received increasing concerns. We propose a prototype-based post-hoc policy explainer, ProtoX, that explains a blackbox agent by prototyping the agent's behaviors into scenarios, each represented by a prototypical state. When learning prototypes, ProtoX considers both visual similarity and scenario similarity. The latter is unique to the reinforcement learning context, since it explains why the same action is taken in visually different states. To teach ProtoX about visual similarity, we pre-train an encoder using contrastive learning via self-supervised learning to recognize states as similar if they occur close together in time and receive the same action from the black-box agent. We then add an isometry layer to allow ProtoX to adapt scenario similarity to the downstream task. ProtoX is trained via imitation learning using behavior cloning, and thus requires no access to the environment or agent. In addition to explanation fidelity, we design different prototype shaping terms in the objective function to encourage better interpretability. We conduct various experiments to test ProtoX. Results show that ProtoX achieved high fidelity to the original black-box agent while providing meaningful and understandable explanations.

Hanqing Jin, Zuo Quan Xu, Xun Yu Zhou

A continuous-time financial portfolio selection model with expected utility maximization typically boils down to solving a (static) convex stochastic optimization problem in terms of the terminal wealth, with a budget constraint. In literature the latter is solved by assuming {\it a priori} that the problem is well-posed (i.e., the supremum value is finite) and a Lagrange multiplier exists (and as a consequence the optimal solution is attainable). In this paper it is first shown, via various counter-examples, neither of these two assumptions needs to hold, and an optimal solution does not necessarily exist. These anomalies in turn have important interpretations in and impacts on the portfolio selection modeling and solutions. Relations among the non-existence of the Lagrange multiplier, the ill-posedness of the problem, and the non-attainability of an optimal solution are then investigated. Finally, explicit and easily verifiable conditions are derived which lead to finding the unique optimal solution.

Minghao Zhu, Zhengpu Wang, Mengxian Hu et al.

Transferring visual-language knowledge from large-scale foundation models for video recognition has proved to be effective. To bridge the domain gap, additional parametric modules are added to capture the temporal information. However, zero-shot generalization diminishes with the increase in the number of specialized parameters, making existing works a trade-off between zero-shot and close-set performance. In this paper, we present MoTE, a novel framework that enables generalization and specialization to be balanced in one unified model. Our approach tunes a mixture of temporal experts to learn multiple task views with various degrees of data fitting. To maximally preserve the knowledge of each expert, we propose \emph{Weight Merging Regularization}, which regularizes the merging process of experts in weight space. Additionally with temporal feature modulation to regularize the contribution of temporal feature during test. We achieve a sound balance between zero-shot and close-set video recognition tasks and obtain state-of-the-art or competitive results on various datasets, including Kinetics-400 \& 600, UCF, and HMDB. Code is available at \url{https://github.com/ZMHH-H/MoTE}.

Xuefeng Gao, Jiale Zha, Xun Yu Zhou

We propose a new reinforcement learning (RL) formulation for training continuous-time score-based diffusion models for generative AI to generate samples that maximize reward functions while keeping the generated distributions close to the unknown target data distributions. Different from most existing studies, ours does not involve any pretrained model for the unknown score functions of the noise-perturbed data distributions, nor does it attempt to learn the score functions. Instead, we formulate the problem as entropy-regularized continuous-time RL and show that the optimal stochastic policy has a Gaussian distribution with a known covariance matrix. Based on this result, we parameterize the mean of Gaussian policies and develop an actor--critic type (little) q-learning algorithm to solve the RL problem. A key ingredient in our algorithm design is to obtain noisy observations from the unknown score function via a ratio estimator. Our formulation can also be adapted to solve pure score-matching and fine-tuning pretrained models. Numerically, we show the effectiveness of our approach by comparing its performance with two state-of-the-art RL methods that fine-tune pretrained models on several generative tasks including high-dimensional image generations. Finally, we discuss extensions of our RL formulation to probability flow ODE implementation of diffusion models and to conditional diffusion models.

Min Dai, Yuchao Dong, Yanwei Jia et al.

We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. The agent under consideration is a price taker who has access only to the stock and factor value processes and the instantaneous volatility. We propose an auxiliary problem in which the agent can invoke policy randomization according to a specific class of Gaussian distributions, and prove that the mean of its optimal Gaussian policy solves the original Merton problem. With randomized policies, we are in the realm of continuous-time reinforcement learning (RL) recently developed in Wang et al. (2020) and Jia and Zhou (2022a, 2022b, 2023), enabling us to solve the auxiliary problem in a data-driven way without having to estimate the model primitives. Specifically, we establish a policy improvement theorem based on which we design both online and offline actor-critic RL algorithms for learning Merton's strategies. A key insight from this study is that RL in general and policy randomization in particular are useful beyond the purpose for exploration -- they can be employed as a technical tool to solve a problem that cannot be otherwise solved by mere deterministic policies. At last, we carry out both simulation and empirical studies in a stochastic volatility environment to demonstrate the decisive outperformance of the devised RL algorithms in comparison to the conventional model-based, plug-in method.

Siyi Zhou, Yiquan Zhou, Yi He et al.

Existing autoregressive large-scale text-to-speech (TTS) models have advantages in speech naturalness, but their token-by-token generation mechanism makes it difficult to precisely control the duration of synthesized speech. This becomes a significant limitation in applications requiring strict audio-visual synchronization, such as video dubbing. This paper introduces IndexTTS2, which proposes a novel, general, and autoregressive model-friendly method for speech duration control. The method supports two generation modes: one explicitly specifies the number of generated tokens to precisely control speech duration; the other freely generates speech in an autoregressive manner without specifying the number of tokens, while faithfully reproducing the prosodic features of the input prompt. Furthermore, IndexTTS2 achieves disentanglement between emotional expression and speaker identity, enabling independent control over timbre and emotion. In the zero-shot setting, the model can accurately reconstruct the target timbre (from the timbre prompt) while perfectly reproducing the specified emotional tone (from the style prompt). To enhance speech clarity in highly emotional expressions, we incorporate GPT latent representations and design a novel three-stage training paradigm to improve the stability of the generated speech. Additionally, to lower the barrier for emotional control, we designed a soft instruction mechanism based on text descriptions by fine-tuning Qwen3, effectively guiding the generation of speech with the desired emotional orientation. Finally, experimental results on multiple datasets show that IndexTTS2 outperforms state-of-the-art zero-shot TTS models in terms of word error rate, speaker similarity, and emotional fidelity. Audio samples are available at: https://index-tts.github.io/index-tts2.github.io/

Peng Tu, Xun Zhou, Mingming Wang et al.

Neural Radiance Fields (NeRF) have emerged as a paradigm-shifting methodology for the photorealistic rendering of objects and environments, enabling the synthesis of novel viewpoints with remarkable fidelity. This is accomplished through the strategic utilization of object-centric camera poses characterized by significant inter-frame overlap. This paper explores a compelling, alternative utility of NeRF: the derivation of point clouds from aggregated urban landscape imagery. The transmutation of street-view data into point clouds is fraught with complexities, attributable to a nexus of interdependent variables. First, high-quality point cloud generation hinges on precise camera poses, yet many datasets suffer from inaccuracies in pose metadata. Also, the standard approach of NeRF is ill-suited for the distinct characteristics of street-view data from autonomous vehicles in vast, open settings. Autonomous vehicle cameras often record with limited overlap, leading to blurring, artifacts, and compromised pavement representation in NeRF-based point clouds. In this paper, we present NeRF2Points, a tailored NeRF variant for urban point cloud synthesis, notable for its high-quality output from RGB inputs alone. Our paper is supported by a bespoke, high-resolution 20-kilometer urban street dataset, designed for point cloud generation and evaluation. NeRF2Points adeptly navigates the inherent challenges of NeRF-based point cloud synthesis through the implementation of the following strategic innovations: (1) Integration of Weighted Iterative Geometric Optimization (WIGO) and Structure from Motion (SfM) for enhanced camera pose accuracy, elevating street-view data precision. (2) Layered Perception and Integrated Modeling (LPiM) is designed for distinct radiance field modeling in urban environments, resulting in coherent point cloud representations.

Xun Zhou, Charlie Ruan, Zihe Zhao et al.

We present the MIDInfinite, a web application capable of generating symbolic music using a large-scale generative AI model locally on commodity hardware. Creating this demo involved porting the Anticipatory Music Transformer, a large language model (LLM) pre-trained on the Lakh MIDI dataset, to the Machine Learning Compilation (MLC) framework. Once the model is ported, MLC facilitates inference on a variety of runtimes including C++, mobile, and the browser. We envision that MLC has the potential to bridge the gap between the landscape of increasingly capable music AI models and technology more familiar to music software developers. As a proof of concept, we build a web application that allows users to generate endless streams of multi-instrumental MIDI in the browser, either from scratch or conditioned on a prompt. On commodity hardware (an M3 Macbook Pro), our demo can generate 51 notes per second, which is faster than real-time playback for 72.9% of generations, and increases to 86.3% with 2 seconds of upfront buffering.

Xuefeng Gao, Jiale Zha, Xun Yu Zhou

This paper introduces a new approach to generating sample paths of unknown stochastic differential equations (SDEs) using diffusion models, a class of generative AI models commonly employed in image and video applications. Unlike the traditional Monte Carlo methods for simulating SDEs, which require explicit specifications of the drift and diffusion coefficients, our method takes a model-free, data-driven approach. Given a finite set of sample paths from an SDE, we utilize conditional diffusion models to generate new, synthetic paths of the same SDE. To demonstrate the effectiveness of our approach, we conduct a simulation experiment to compare our method with alternative benchmark ones including neural SDEs. Furthermore, in an empirical study we leverage these synthetically generated sample paths to enhance the performance of reinforcement learning algorithms for continuous-time mean-variance portfolio selection, hinting promising applications of diffusion models in financial analysis and decision-making.

Chen Zheng, Yiyuan Ma, Yuan Yang et al.

The development of alignment and reasoning capabilities in large language models has seen remarkable progress through two paradigms: instruction tuning and reinforcement learning from human feedback (RLHF) alignment paradigm, and distillation-based reasoning fine-tuning paradigm. While both approaches prove effective independently, the third paradigm of applying RLHF to distillation-trained models presents significant challenges. Our investigation reveals two critical phenomena that emerge in this paradigm: Sequence Length Collapse, where language generation dramatically reduces during early RLHF training, and the Reward Hockey Stick Curve, featuring severe reward score drops followed by gradual recovery. These instabilities fundamentally compromise the model's alignment and reasoning capabilities. To address these challenges, we propose Balanced Actor Initialization (BAI), a two-stage weighted model merging approach. BAI first merges instruction-following and distillation-based reasoning fine-tuned models, then further combines this intermediate model with the pretrained model to preserve foundational knowledge. Through comprehensive experiments across diverse benchmarks and detailed analysis of training experiments, we demonstrate that BAI resolves Sequence Length Collapse, mitigates the Reward Hockey Stick Curve, and enables continuous sequence length improvement during training. Additionally, our analysis reveals that balanced merging ratios achieve optimal trade-offs between training stability and reasoning capability preservation. Our work provides the effective solution for stable training in this third paradigm, enabling more capable reasoning models that combine distillation efficiency with RLHF alignment.

Bang An, Xun Zhou, Amin Vahedian et al.

Traffic accident forecasting is an important task for intelligent transportation management and emergency response systems. However, this problem is challenging due to the spatial heterogeneity of the environment. Existing data-driven methods mostly focus on studying homogeneous areas with limited size (e.g. a single urban area such as New York City) and fail to handle the heterogeneous accident patterns over space at different scales. Recent advances (e.g. spatial ensemble) utilize pre-defined space partitions and learn multiple models to improve prediction accuracy. However, external knowledge is required to define proper space partitions before training models and pre-defined partitions may not necessarily reduce the heterogeneity. To address this issue, we propose a novel Learning-Integrated Space Partition Framework (LISA) to simultaneously learn partitions while training models, where the partitioning process and learning process are integrated in a way that partitioning is guided explicitly by prediction accuracy rather than other factors. Experiments using real-world datasets, demonstrate that our work can capture underlying heterogeneous patterns in a self-guided way and substantially improve baseline networks by an average of 13.0%.

Bang An, Xun Zhou, Zirui Zhou et al.

The problem of forecasting spatiotemporal events such as crimes and accidents is crucial to public safety and city management. Besides accuracy, interpretability is also a key requirement for spatiotemporal forecasting models to justify the decisions. Interpretation of the spatiotemporal forecasting mechanism is, however, challenging due to the complexity of multi-source spatiotemporal features, the non-intuitive nature of spatiotemporal patterns for non-expert users, and the presence of spatial heterogeneity in the data. Currently, no existing deep learning model intrinsically interprets the complex predictive process learned from multi-source spatiotemporal features. To bridge the gap, we propose GeoPro-Net, an intrinsically interpretable spatiotemporal model for spatiotemporal event forecasting problems. GeoPro-Net introduces a novel Geo-concept convolution operation, which employs statistical tests to extract predictive patterns in the input as Geo-concepts, and condenses the Geo-concept-encoded input through interpretable channel fusion and geographic-based pooling. In addition, GeoPro-Net learns different sets of prototypes of concepts inherently, and projects them to real-world cases for interpretation. Comprehensive experiments and case studies on four real-world datasets demonstrate that GeoPro-Net provides better interpretability while still achieving competitive prediction performance compared with state-of-the-art baselines.

Jie Chen, Xintian Han, Yu Ma et al.

Automatic code generation has been a longstanding research topic. With the advancement of general-purpose large language models (LLMs), the ability to code stands out as one important measure to the model's reasoning performance. Usually, a two-stage training paradigm is implemented to obtain a Code LLM, namely the pretraining and the fine-tuning. Within the fine-tuning, supervised fine-tuning (SFT), and reinforcement learning (RL) are often used to improve the model's zero-shot ability. A large number of work has been conducted to improve the model's performance on code-related benchmarks with either modifications to the algorithm or refinement of the dataset. However, we still lack a deep insight into the correlation between SFT and RL. For instance, what kind of dataset should be used to ensure generalization, or what if we abandon the SFT phase in fine-tuning. In this work, we make an attempt to understand the correlation between SFT and RL. To facilitate our research, we manually craft 100 basis python functions, called atomic functions, and then a synthesizing pipeline is deployed to create a large number of synthetic functions on top of the atomic ones. In this manner, we ensure that the train and test sets remain distinct, preventing data contamination. Through comprehensive ablation study, we find: (1) Both atomic and synthetic functions are indispensable for SFT's generalization, and only a handful of synthetic functions are adequate; (2) Through RL, the SFT's generalization to target domain can be greatly enhanced, even with the same training prompts; (3) Training RL from scratch can alleviate the over-fitting issue introduced in the SFT phase.

Yanwei Jia, Xun Yu Zhou

We study policy gradient (PG) for reinforcement learning in continuous time and space under the regularized exploratory formulation developed by Wang et al. (2020). We represent the gradient of the value function with respect to a given parameterized stochastic policy as the expected integration of an auxiliary running reward function that can be evaluated using samples and the current value function. This effectively turns PG into a policy evaluation (PE) problem, enabling us to apply the martingale approach recently developed by Jia and Zhou (2021) for PE to solve our PG problem. Based on this analysis, we propose two types of the actor-critic algorithms for RL, where we learn and update value functions and policies simultaneously and alternatingly. The first type is based directly on the aforementioned representation which involves future trajectories and hence is offline. The second type, designed for online learning, employs the first-order condition of the policy gradient and turns it into martingale orthogonality conditions. These conditions are then incorporated using stochastic approximation when updating policies. Finally, we demonstrate the algorithms by simulations in two concrete examples.

Yanwei Jia, Xun Yu Zhou

We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time and space. We show that PE is equivalent to maintaining the martingale condition of a process. From this perspective, we find that the mean--square TD error approximates the quadratic variation of the martingale and thus is not a suitable objective for PE. We present two methods to use the martingale characterization for designing PE algorithms. The first one minimizes a "martingale loss function", whose solution is proved to be the best approximation of the true value function in the mean--square sense. This method interprets the classical gradient Monte-Carlo algorithm. The second method is based on a system of equations called the "martingale orthogonality conditions" with test functions. Solving these equations in different ways recovers various classical TD algorithms, such as TD($λ$), LSTD, and GTD. Different choices of test functions determine in what sense the resulting solutions approximate the true value function. Moreover, we prove that any convergent time-discretized algorithm converges to its continuous-time counterpart as the mesh size goes to zero, and we provide the convergence rate. We demonstrate the theoretical results and corresponding algorithms with numerical experiments and applications.

Haoran Wang, Xun Yu Zhou

We approach the continuous-time mean-variance (MV) portfolio selection with reinforcement learning (RL). The problem is to achieve the best tradeoff between exploration and exploitation, and is formulated as an entropy-regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time-decaying variance. We then establish connections between the entropy-regularized MV and the classical MV, including the solvability equivalence and the convergence as exploration weighting parameter decays to zero. Finally, we prove a policy improvement theorem, based on which we devise an implementable RL algorithm. We find that our algorithm outperforms both an adaptive control based method and a deep neural networks based algorithm by a large margin in our simulations.