arXiv subjects

Haoyuan Sun

Publications and source records attributed to Haoyuan Sun.

36 records · Page 2Linked to original sources

arXiv2025

Meta-Learning for Adaptive Control with Automated Mirror Descent

Adaptive control achieves concurrent parameter learning and stable control under uncertainties that are linearly parameterized with known nonlinear features. Nonetheless, it is often difficult to obtain such nonlinear features. To address this difficulty, recent progress has been made in integrating meta-learning with adaptive control to learn such nonlinear features from data. However, these meta-learning-based control methods rely on classical adaptation laws using gradient descent, which is confined to the Euclidean geometry. In this paper, we propose a novel method that combines meta-learning and adaptation laws based on mirror descent, a popular generalization of gradient descent, which takes advantage of the potentially non-Euclidean geometry of the parameter space. In our approach, meta-learning not only learns the nonlinear features but also searches for a suitable mirror-descent potential function that optimizes control performance. Through numerical simulations, we demonstrate the effectiveness of the proposed method in learning efficient representations and real-time tracking control performance under uncertain dynamics.

eess.SY↗

arXiv2025

The Hidden Link Between RLHF and Contrastive Learning

Alignment of large language models (LLMs) with human values has recently garnered significant attention, with prominent examples including the canonical yet costly Reinforcement Learning from Human Feedback (RLHF) and the simple Direct Preference Optimization (DPO). In this work, we demonstrate that both RLHF and DPO can be interpreted from the perspective of mutual information (MI) maximization, uncovering a profound connection to contrastive learning. Within this framework, both RLHF and DPO can be interpreted as methods that performing contrastive learning based on the positive and negative samples derived from base model, leveraging the Donsker-Varadhan (DV) lower bound on MI (equivalently, the MINE estimator). Such paradigm further illuminates why RLHF may not intrinsically incentivize reasoning capacities in LLMs beyond what is already present in the base model. Building on the perspective, we replace the DV/MINE bound with the Jensen-Shannon (JS) MI estimator and propose the Mutual Information Optimization (MIO). Comprehensive theoretical analysis and extensive empirical evaluations demonstrate that MIO mitigates the late-stage decline in chosen-likelihood observed in DPO, achieving competitive or superior performance across various challenging reasoning and mathematical benchmarks.

cs.LG↗

arXiv2025

On the Role of Transformer Feed-Forward Layers in Nonlinear In-Context Learning

Transformer-based models demonstrate a remarkable ability for in-context learning (ICL), where they can adapt to unseen tasks from a few prompt examples without parameter updates. Recent research has illuminated how Transformers perform ICL, showing that the optimal linear self-attention (LSA) mechanism can implement one step of gradient descent for linear least-squares objectives when trained on random linear regression tasks. Building on this, we investigate ICL for nonlinear function classes. We first prove that LSA is inherently incapable of outperforming linear predictors on nonlinear tasks, underscoring why prior solutions cannot readily extend to these problems. To overcome this limitation, we analyze a Transformer block consisting of LSA and feed-forward layers inspired by the gated linear units (GLU), which is a standard component of modern Transformers. We show that this block achieves nonlinear ICL by implementing one step of gradient descent on a polynomial kernel regression loss. Furthermore, our analysis reveals that the expressivity of a single block is inherently limited by its dimensions. We then show that a deep Transformer can overcome this bottleneck by distributing the computation of richer kernel functions across multiple blocks, performing block-coordinate descent in a high-dimensional feature space that a single block cannot represent. Our findings highlight that the feed-forward layers provide a crucial and scalable mechanism by which Transformers can express nonlinear representations for ICL.

cs.LG↗

arXiv2025

Online Learning for Equilibrium Pricing in Markets under Incomplete Information

The computation of equilibrium prices at which the supply of goods matches their demand typically relies on complete information on agents' private attributes, e.g., suppliers' cost functions, which are often unavailable in practice. Motivated by this practical consideration, we consider the problem of learning equilibrium prices over a horizon of $T$ periods in the incomplete information setting wherein a market operator seeks to satisfy the customer demand for a commodity by purchasing it from competing suppliers with cost functions unknown to the operator. We first consider the setting when suppliers' cost functions are fixed and develop algorithms that, on three pertinent regret metrics, simultaneously achieve a regret of $O(1)$ when the customer demand is constant over time, and $O(\sqrt{T})$ when the demand varies over time. In the setting when the suppliers' cost functions vary over time, we demonstrate that, in general, no online algorithm can achieve sublinear regret on all three metrics. Thus, we consider an augmented setting wherein the operator has access to hints/contexts that reflect the variation in the cost functions and propose an algorithm with sublinear regret in this augmented setting. Finally, we present numerical experiments that validate our results and discuss various model extensions.

cs.GT↗

arXiv2025

Degenerate complex Monge-Ampère type equations on compact Hermitian manifolds and applications II

Let $(X,ω)$ be a compact Hermitian manifold of complex dimension $n$, equipped with a Hermitian metric $ω$. Let $β$ be a possibly non-closed smooth $(1,1)$-form on $X$ such that $\int_Xβ^n>0$. Assume that there is a bounded $β$-plurisubharmonic function $ρ$ on $X$ and $\underline{\mathrm{Vol}}(β) > 0$. In this paper, we establish solutions to the degenerate complex Monge-Ampère equations on $X$ within the Bott-Chern space of $β$ (as introduced by Boucksom-Guedj-Lu) and derive stability results for these solutions. As applications, we provide partial resolutions to the extended Tosatti-Weinkove conjecture and Demailly-P\u aun conjecture.

math.CV↗

arXiv2025

Reinforcement Fine-Tuning Powers Reasoning Capability of Multimodal Large Language Models

Standing in 2025, at a critical juncture in the pursuit of Artificial General Intelligence (AGI), reinforcement fine-tuning (RFT) has demonstrated significant potential in enhancing the reasoning capability of large language models (LLMs) and has led to the development of cutting-edge AI models such as OpenAI-o1 and DeepSeek-R1. Moreover, the efficient application of RFT to enhance the reasoning capability of multimodal large language models (MLLMs) has attracted widespread attention from the community. In this position paper, we argue that reinforcement fine-tuning powers the reasoning capability of multimodal large language models. To begin with, we provide a detailed introduction to the fundamental background knowledge that researchers interested in this field should be familiar with. Furthermore, we meticulously summarize the improvements of RFT in powering reasoning capability of MLLMs into five key points: diverse modalities, diverse tasks and domains, better training algorithms, abundant benchmarks and thriving engineering frameworks. Finally, we propose five promising directions for future research that the community might consider. We hope that this position paper will provide valuable insights to the community at this pivotal stage in the advancement toward AGI. Summary of works done on RFT for MLLMs is available at https://github.com/Sun-Haoyuan23/Awesome-RL-based-Reasoning-MLLMs.

cs.CL↗

arXiv2024

Weak convergence of complex Monge-Ampère operators on compact Hermitian manifolds

Let $(X,ω)$ be a compact Hermitian manifold and let $\{β\}\in H^{1,1}(X,\mathbb R)$ be a real $(1,1)$-class with a smooth representative $β$, such that $\int_Xβ^n>0$. Assume that there is a bounded $β$-plurisubharmonic function $ρ$ on $X$. First, we provide a criterion for the weak convergence of non-pluripolar complex Monge-Ampère measures associated to a sequence of $β$-plurisubharmonic functions. Second, this criterion is utilized to solve a degenerate complex Monge-Ampère equation with an $L^1$-density. Finally, an $L^\infty$-estimate of the solution to the complex Monge-Ampère equation for a finite positive Radon measure is given.

math.CV↗

arXiv2024

Generalizing Alignment Paradigm of Text-to-Image Generation with Preferences through $f$-divergence Minimization

Direct Preference Optimization (DPO) has recently expanded its successful application from aligning large language models (LLMs) to aligning text-to-image models with human preferences, which has generated considerable interest within the community. However, we have observed that these approaches rely solely on minimizing the reverse Kullback-Leibler divergence during alignment process between the fine-tuned model and the reference model, neglecting the incorporation of other divergence constraints. In this study, we focus on extending reverse Kullback-Leibler divergence in the alignment paradigm of text-to-image models to $f$-divergence, which aims to garner better alignment performance as well as good generation diversity. We provide the generalized formula of the alignment paradigm under the $f$-divergence condition and thoroughly analyze the impact of different divergence constraints on alignment process from the perspective of gradient fields. We conduct comprehensive evaluation on image-text alignment performance, human value alignment performance and generation diversity performance under different divergence constraints, and the results indicate that alignment based on Jensen-Shannon divergence achieves the best trade-off among them. The option of divergence employed for aligning text-to-image models significantly impacts the trade-off between alignment performance (especially human value alignment) and generation diversity, which highlights the necessity of selecting an appropriate divergence for practical applications.

cs.CV↗

arXiv2024

A Method on Searching Better Activation Functions

The success of artificial neural networks (ANNs) hinges greatly on the judicious selection of an activation function, introducing non-linearity into network and enabling them to model sophisticated relationships in data. However, the search of activation functions has largely relied on empirical knowledge in the past, lacking theoretical guidance, which has hindered the identification of more effective activation functions. In this work, we offer a proper solution to such issue. Firstly, we theoretically demonstrate the existence of the worst activation function with boundary conditions (WAFBC) from the perspective of information entropy. Furthermore, inspired by the Taylor expansion form of information entropy functional, we propose the Entropy-based Activation Function Optimization (EAFO) methodology. EAFO methodology presents a novel perspective for designing static activation functions in deep neural networks and the potential of dynamically optimizing activation during iterative training. Utilizing EAFO methodology, we derive a novel activation function from ReLU, known as Correction Regularized ReLU (CRReLU). Experiments conducted with vision transformer and its variants on CIFAR-10, CIFAR-100 and ImageNet-1K datasets demonstrate the superiority of CRReLU over existing corrections of ReLU. Extensive empirical studies on task of large language model (LLM) fine-tuning, CRReLU exhibits superior performance compared to GELU, suggesting its broader potential for practical applications.

cs.LG↗

arXiv2024

Improving Offline Reinforcement Learning with Inaccurate Simulators

Offline reinforcement learning (RL) provides a promising approach to avoid costly online interaction with the real environment. However, the performance of offline RL highly depends on the quality of the datasets, which may cause extrapolation error in the learning process. In many robotic applications, an inaccurate simulator is often available. However, the data directly collected from the inaccurate simulator cannot be directly used in offline RL due to the well-known exploration-exploitation dilemma and the dynamic gap between inaccurate simulation and the real environment. To address these issues, we propose a novel approach to combine the offline dataset and the inaccurate simulation data in a better manner. Specifically, we pre-train a generative adversarial network (GAN) model to fit the state distribution of the offline dataset. Given this, we collect data from the inaccurate simulator starting from the distribution provided by the generator and reweight the simulated data using the discriminator. Our experimental results in the D4RL benchmark and a real-world manipulation task confirm that our method can benefit more from both inaccurate simulator and limited offline datasets to achieve better performance than the state-of-the-art methods.

cs.RO↗

arXiv2024

A least-square method for non-asymptotic identification in linear switching control

The focus of this paper is on linear system identification in the setting where it is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We first consider the problem of identification from a given trajectory, which in this setting reduces to identifying the index of the true model with high probability. We characterize the finite-time sample complexity of this problem by leveraging recent advances in the non-asymptotic analysis of linear least-square methods in the literature. In comparison to the earlier results that assume no prior knowledge of the system, our approach takes advantage of the smaller hypothesis class and leads to the design of a learner with a dimension-free sample complexity bound. Next, we consider the switching control of linear systems, where there is a candidate controller for each of the candidate models and data is collected through interaction of the system with a collection of potentially destabilizing controllers. We develop a dimension-dependent criterion that can detect those destabilizing controllers in finite time. By leveraging these results, we propose a data-driven switching strategy that identifies the unknown parameters of the underlying system. We then provide a non-asymptotic analysis of its performance and discuss its implications on the classical method of estimator-based supervisory control.

math.OC↗

arXiv2024

A Unified Approach to Controlling Implicit Regularization via Mirror Descent

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how optimization algorithms impact generalization through their "preferred" solutions, a phenomenon commonly referred to as implicit regularization. In particular, it has been argued that gradient descent (GD) induces an implicit $\ell_2$-norm regularization in regression and classification problems. However, the implicit regularization of different algorithms are confined to either a specific geometry or a particular class of learning problems, indicating a gap in a general approach for controlling the implicit regularization. To address this, we present a unified approach using mirror descent (MD), a notable generalization of GD, to control implicit regularization in both regression and classification settings. More specifically, we show that MD with the general class of homogeneous potential functions converges in direction to a generalized maximum-margin solution for linear classification problems, thereby answering a long-standing question in the classification setting. Further, we show that MD can be implemented efficiently and enjoys fast convergence under suitable conditions. Through comprehensive experiments, we demonstrate that MD is a versatile method to produce learned models with different regularizers, which in turn have different generalization performances.

cs.LG↗

arXiv2023

Private Synthetic Data Meets Ensemble Learning

When machine learning models are trained on synthetic data and then deployed on real data, there is often a performance drop due to the distribution shift between synthetic and real data. In this paper, we introduce a new ensemble strategy for training downstream models, with the goal of enhancing their performance when used on real data. We generate multiple synthetic datasets by applying a differential privacy (DP) mechanism several times in parallel and then ensemble the downstream models trained on these datasets. While each synthetic dataset might deviate more from the real data distribution, they collectively increase sample diversity. This may enhance the robustness of downstream models against distribution shifts. Our extensive experiments reveal that while ensembling does not enhance downstream performance (compared with training a single model) for models trained on synthetic data generated by marginal-based or workload-based DP mechanisms, our proposed ensemble strategy does improve the performance for models trained using GAN-based DP mechanisms in terms of both accuracy and calibration of downstream models.

cs.CR↗

arXiv2022

Mirror Descent Maximizes Generalized Margin and Can Be Implemented Efficiently

Driven by the empirical success and wide use of deep neural networks, understanding the generalization performance of overparameterized models has become an increasingly popular question. To this end, there has been substantial effort to characterize the implicit bias of the optimization algorithms used, such as gradient descent (GD), and the structural properties of their preferred solutions. This paper answers an open question in this literature: For the classification setting, what solution does mirror descent (MD) converge to? Specifically, motivated by its efficient implementation, we consider the family of mirror descent algorithms with potential function chosen as the $p$-th power of the $\ell_p$-norm, which is an important generalization of GD. We call this algorithm $p$-$\textsf{GD}$. For this family, we characterize the solutions it obtains and show that it converges in direction to a generalized maximum-margin solution with respect to the $\ell_p$-norm for linearly separable classification. While the MD update rule is in general expensive to compute and perhaps not suitable for deep learning, $p$-$\textsf{GD}$ is fully parallelizable in the same manner as SGD and can be used to train deep neural networks with virtually no additional computational overhead. Using comprehensive experiments with both linear and deep neural network models, we demonstrate that $p$-$\textsf{GD}$ can noticeably affect the structure and the generalization performance of the learned models.

cs.LG↗

arXiv2021

Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems

We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future $k$ time steps. We show that when the prediction window $k$ is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of $O(λ^k T)$, where $λ< 1$ is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. Under more assumptions on the terminal costs, we also show that predictive control obtains the first competitive bound for the control of linear time-varying systems: $1 + O(λ^k)$. Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory.

math.OC↗

arXiv2020

Distributed Submodular Maximization with Parallel Execution

The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy algorithm which guarantees approximation at least 1/2 of the optimal solution. This greedy algorithm can be implemented with a set of agents, each making a decision sequentially based on the choices of all prior agents. In this paper, we consider a generalization of the greedy algorithm in which agents can make decisions in parallel, rather than strictly in sequence. In particular, we are interested in partitioning the agents, where a set of agents in the partition all make a decision simultaneously based on the choices of prior agents, so that the algorithm terminates in limited iterations. We provide bounds on the performance of this parallelized version of the greedy algorithm and show that dividing the agents evenly among the sets in the partition yields an optimal structure. We additionally show that this optimal structure is still near-optimal when the objective function exhibits a certain monotone property. Lastly, we show that the same performance guarantees can be achieved in the parallelized greedy algorithm even when agents can only observe the decisions of a subset of prior agents.

cs.DC↗

arXiv2019

Analytic Continued Fractions for Regression: A Memetic Algorithm Approach

We present an approach for regression problems that employs analytic continued fractions as a novel representation. Comparative computational results using a memetic algorithm are reported in this work. Our experiments included fifteen other different machine learning approaches including five genetic programming methods for symbolic regression and ten machine learning methods. The comparison on training and test generalization was performed using 94 datasets of the Penn State Machine Learning Benchmark. The statistical tests showed that the generalization results using analytic continued fractions provides a powerful and interesting new alternative in the quest for compact and interpretable mathematical models for artificial intelligence.

cs.NE↗

arXiv2019

Beyond Online Balanced Descent: An Optimal Algorithm for Smoothed Online Optimization

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strongly convex and the movement costs are the squared $\ell_2$ norm. This lower bound shows that no algorithm can achieve a competitive ratio that is $o(m^{-1/2})$ as $m$ tends to zero. No existing algorithms have competitive ratios matching this bound, and we show that the state-of-the-art algorithm, Online Balanced Decent (OBD), has a competitive ratio that is $Ω(m^{-2/3})$. We additionally propose two new algorithms, Greedy OBD (G-OBD) and Regularized OBD (R-OBD) and prove that both algorithms have an $O(m^{-1/2})$ competitive ratio. The result for G-OBD holds when the hitting costs are quasiconvex and the movement costs are the squared $\ell_2$ norm, while the result for R-OBD holds when the hitting costs are $m$-strongly convex and the movement costs are Bregman Divergences. Further, we show that R-OBD simultaneously achieves constant, dimension-free competitive ratio and sublinear regret when hitting costs are strongly convex.

cs.LG↗