arXiv subjects

Yijie Peng

Publications and source records attributed to Yijie Peng.

At least 37 records · Page 2Linked to original sources

arXiv2025

Beyond likelihood ratio bias: Nested multi-time-scale stochastic approximation for likelihood-free parameter estimation

We study parameter inference in simulation-based stochastic models where the analytical form of the likelihood is unknown. The main difficulty is that score evaluation as a ratio of noisy Monte Carlo estimators induces bias and instability, which we overcome with a ratio-free nested multi-time-scale (NMTS) stochastic approximation (SA) method that simultaneously tracks the score and drives the parameter update. We provide a comprehensive theoretical analysis of the proposed NMTS algorithm for solving likelihood-free inference problems, including strong convergence, asymptotic normality, and convergence rates. We show that our algorithm can eliminate the original asymptotic bias $O\big(\sqrt{\frac{1}{N}}\big)$ and accelerate the convergence rate from $O\big(β_k+\sqrt{\frac{1}{N}}\big)$ to $O\big(\frac{β_k}{α_k}+\sqrt{\frac{α_k}{N}}\big)$, where $N$ is the fixed batch size, $α_k$ and $β_k$ are decreasing step sizes with $α_k$, $β_k$, $β_k/α_k\rightarrow 0$. With proper choice of $α_k$ and $β_k$, our convergence rates can match the optimal rate in the multi-time-scale SA literature. Numerical experiments demonstrate that our algorithm can improve the estimation accuracy by one to two orders of magnitude at the same computational cost, making it efficient for parameter estimation in stochastic systems.

stat.ML↗

arXiv2025

InterCorpRel-LLM: Enhancing Financial Relational Understanding with Graph-Language Models

Identifying inter-firm relationships such as supply and competitive ties is critical for financial analysis and corporate governance, yet remains challenging due to the scale, sparsity, and contextual dependence of corporate data. Graph-based methods capture structure but miss semantic depth, while large language models (LLMs) excel at text but remain limited in their ability to represent relational dependencies. To address this, we propose InterCorpRel-LLM, a cross-modal framework that integrates GNNs with LLMs, supported by a proprietary dataset derived from FactSet supply chain records and three tailored training tasks: company graph matching, industry classification, and supply relation prediction. This design enables effective joint modeling of structure and semantics. Experiments show that InterCorpRel-LLM substantially outperforms strong baselines, including GPT-5, on a supply relation identification task, achieving an F-score of 0.8543 vs. 0.2287 with only a 7B-parameter backbone and lightweight training. The model also generalizes to zero-shot competitor identification, underscoring its ability to capture nuanced inter-firm dynamics. Our framework thus provides analysts and strategists with a robust tool for mapping and reasoning about complex corporate networks, enhancing decision-making and risk management in dynamic markets.

cs.LG↗

arXiv2025

Stochastic Approximation Methods for Distortion Risk Measure Optimization

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the Distortion-Measure (DM) form and Quantile-Function (QF) form. The DM-form employs a three-timescale algorithm to track quantiles, compute their gradients, and update decision variables, utilizing the Generalized Likelihood Ratio and kernel-based density estimation. The QF-form provides a simpler two-timescale approach that avoids the need for complex quantile gradient estimation. A hybrid form integrates both approaches, applying the DM-form for robust performance around distortion function jumps and the QF-form for efficiency in smooth regions. Proofs of strong convergence and convergence rates for the proposed algorithms are provided. In particular, the DM-form achieves an optimal rate of $O(k^{-4/7})$, while the QF-form attains a faster rate of $O(k^{-2/3})$. Numerical experiments confirm their effectiveness and demonstrate substantial improvements over baselines in robust portfolio selection tasks. The method's scalability is further illustrated through integration into deep reinforcement learning. Specifically, a DRM-based Proximal Policy Optimization algorithm is developed and applied to multi-echelon dynamic inventory management, showcasing its practical applicability.

cs.LG↗

arXiv2025

Closing the Loop: Coordinating Inventory and Recommendation via Deep Reinforcement Learning on Multiple Timescales

Effective cross-functional coordination is essential for enhancing firm-wide profitability, particularly in the face of growing organizational complexity and scale. Recent advances in artificial intelligence, especially in reinforcement learning (RL), offer promising avenues to address this fundamental challenge. This paper proposes a unified multi-agent RL framework tailored for joint optimization across distinct functional modules, exemplified via coordinating inventory replenishment and personalized product recommendation. We first develop an integrated theoretical model to capture the intricate interplay between these functions and derive analytical benchmarks that characterize optimal coordination. The analysis reveals synchronized adjustment patterns across products and over time, highlighting the importance of coordinated decision-making. Leveraging these insights, we design a novel multi-timescale multi-agent RL architecture that decomposes policy components according to departmental functions and assigns distinct learning speeds based on task complexity and responsiveness. Our model-free multi-agent design improves scalability and deployment flexibility, while multi-timescale updates enhance convergence stability and adaptability across heterogeneous decisions. We further establish the asymptotic convergence of the proposed algorithm. Extensive simulation experiments demonstrate that the proposed approach significantly improves profitability relative to siloed decision-making frameworks, while the behaviors of the trained RL agents align closely with the managerial insights from our theoretical model. Taken together, this work provides a scalable, interpretable RL-based solution to enable effective cross-functional coordination in complex business settings.

cs.AI↗

arXiv2025

RiskPO: Risk-based Policy Optimization via Verifiable Reward for LLM Post-Training

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from entropy collapse and limited reasoning gains. We argue that these issues stem from overemphasizing high-probability output sequences while neglecting rare but informative reasoning paths. To address these challenges, we propose Risk-based Policy Optimization (RiskPO), which substitutes classical mean-based objectives with principled risk measures. Specifically, we introduce a Mixed Value-at-Risk objective that integrates weighted attention over multiple regions of the reward distribution, thereby amplifying gradient signals on challenging instances and preventing overconfident convergence. We further design a bundling scheme that aggregates multiple questions into bundles, thus enriching the feedback signal and yielding more stable and informative training dynamics. Theoretically, we prove that the risk-averse update alleviates entropy collapse and promotes exploration. Numerically, RiskPO achieves consistent and significant improvements in mathematical reasoning, multi-modal reasoning, and code generation benchmarks, surpassing GRPO and its variants on both Pass@1 and Pass@k metrics. Our results demonstrate that risk-based optimization provides a rigorous and effective paradigm for enhancing LLM reasoning capabilities.

cs.LG↗

arXiv2025

Half-order Fine-Tuning for Diffusion Model: A Recursive Likelihood Ratio Optimizer

The probabilistic diffusion model (DM), generating content by inferencing through a recursive chain structure, has emerged as a powerful framework for visual generation. After pre-training on enormous data, the model needs to be properly aligned to meet requirements for downstream applications. How to efficiently align the foundation DM is a crucial task. Contemporary methods are either based on Reinforcement Learning (RL) or truncated Backpropagation (BP). However, RL and truncated BP suffer from low sample efficiency and biased gradient estimation, respectively, resulting in limited improvement or, even worse, complete training failure. To overcome the challenges, we propose the Recursive Likelihood Ratio (RLR) optimizer, a Half-Order (HO) fine-tuning paradigm for DM. The HO gradient estimator enables the computation graph rearrangement within the recursive diffusive chain, making the RLR's gradient estimator an unbiased one with lower variance than other methods. We theoretically investigate the bias, variance, and convergence of our method. Extensive experiments are conducted on image and video generation to validate the superiority of the RLR. Furthermore, we propose a novel prompt technique that is natural for the RLR to achieve a synergistic effect.

cs.CV↗

arXiv2025

CoNNect: Connectivity-Based Regularization for Structural Pruning

Pruning encompasses a range of techniques aimed at increasing the sparsity of neural networks (NNs). These techniques can generally be framed as minimizing a loss function subject to an $L_0$ norm constraint. This paper introduces CoNNect, a novel differentiable regularizer for sparse NN training that ensures connectivity between input and output layers. We prove that CoNNect approximates $L_0$ regularization, guaranteeing maximally connected network structures while avoiding issues like layer collapse. Moreover, CoNNect is easily integrated with established structural pruning strategies. Numerical experiments demonstrate that CoNNect can improve classical pruning strategies and enhance state-of-the-art one-shot pruners, such as DepGraph and LLM-pruner.

cs.LG↗

arXiv2025

Forward Learning with Differential Privacy

Differential privacy (DP) in deep learning is a critical concern as it ensures the confidentiality of training data while maintaining model utility. Existing DP training algorithms provide privacy guarantees by clipping and then injecting external noise into sample gradients computed by the backpropagation algorithm. Different from backpropagation, forward-learning algorithms based on perturbation inherently add noise during the forward pass and utilize randomness to estimate the gradients. Although these algorithms are non-privatized, the introduction of noise during the forward pass indirectly provides internal randomness protection to the model parameters and their gradients, suggesting the potential for naturally providing differential privacy. In this paper, we propose a \blue{privatized} forward-learning algorithm, Differential Private Unified Likelihood Ratio (DP-ULR), and demonstrate its differential privacy guarantees. DP-ULR features a novel batch sampling operation with rejection, of which we provide theoretical analysis in conjunction with classic differential privacy mechanisms. DP-ULR is also underpinned by a theoretically guided privacy controller that dynamically adjusts noise levels to manage privacy costs in each training step. Our experiments indicate that DP-ULR achieves competitive performance compared to traditional differential privacy training algorithms based on backpropagation, maintaining nearly the same privacy loss limits.

cs.LG↗

arXiv2025

A New Stochastic Approximation Method for Gradient-based Simulated Parameter Estimation

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation framework, which employs a multi-time scale stochastic approximation algorithm. This approach effectively addresses the ratio bias that arises in both maximum likelihood estimation and posterior density estimation problems. The proposed algorithm enhances estimation accuracy and significantly reduces computational costs, as demonstrated through extensive numerical experiments. Our work extends the GSPE framework to handle complex models such as hidden Markov models and variational inference-based problems, offering a robust solution for parameter estimation in challenging stochastic environments.

stat.ML↗

arXiv2025

FLOPS: Forward Learning with OPtimal Sampling

Given the limitations of backpropagation, perturbation-based gradient computation methods have recently gained focus for learning with only forward passes, also referred to as queries. Conventional forward learning consumes enormous queries on each data point for accurate gradient estimation through Monte Carlo sampling, which hinders the scalability of those algorithms. However, not all data points deserve equal queries for gradient estimation. In this paper, we study the problem of improving the forward learning efficiency from a novel perspective: how to reduce the gradient estimation variance with minimum cost? For this, we propose to allocate the optimal number of queries over each data in one batch during training to achieve a good balance between estimation accuracy and computational efficiency. Specifically, with a simplified proxy objective and a reparameterization technique, we derive a novel plug-and-play query allocator with minimal parameters. Theoretical results are carried out to verify its optimality. We conduct extensive experiments for fine-tuning Vision Transformers on various datasets and further deploy the allocator to two black-box applications: prompt tuning and multimodal alignment for foundation models. All findings demonstrate that our proposed allocator significantly enhances the scalability of forward-learning algorithms, paving the way for real-world applications.

cs.LG↗

arXiv2024

Series Expansion of Probability of Correct Selection for Improved Finite Budget Allocation in Ranking and Selection

This paper addresses the challenge of improving finite sample performance in Ranking and Selection by developing a Bahadur-Rao type expansion for the Probability of Correct Selection (PCS). While traditional large deviations approximations captures PCS behavior in the asymptotic regime, they can lack precision in finite sample settings. Our approach enhances PCS approximation under limited simulation budgets, providing more accurate characterization of optimal sampling ratios and optimality conditions dependent of budgets. Algorithmically, we propose a novel finite budget allocation (FCBA) policy, which sequentially estimates the optimality conditions and accordingly balances the sampling ratios. We illustrate numerically on toy examples that our FCBA policy achieves superior PCS performance compared to tested traditional methods. As an extension, we note that the non-monotonic PCS behavior described in the literature for low-confidence scenarios can be attributed to the negligence of simultaneous incorrect binary comparisons in PCS approximations. We provide a refined expansion and a tailored allocation strategy to handle low-confidence scenarios, addressing the non-monotonicity issue.

stat.ML↗

arXiv2024

Dual-Agent Deep Reinforcement Learning for Dynamic Pricing and Replenishment

We study the dynamic pricing and replenishment problems under inconsistent decision frequencies. Different from the traditional demand assumption, the discreteness of demand and the parameter within the Poisson distribution as a function of price introduce complexity into analyzing the problem property. We demonstrate the concavity of the single-period profit function with respect to product price and inventory within their respective domains. The demand model is enhanced by integrating a decision tree-based machine learning approach, trained on comprehensive market data. Employing a two-timescale stochastic approximation scheme, we address the discrepancies in decision frequencies between pricing and replenishment, ensuring convergence to local optimum. We further refine our methodology by incorporating deep reinforcement learning (DRL) techniques and propose a fast-slow dual-agent DRL algorithm. In this approach, two agents handle pricing and inventory and are updated on different scales. Numerical results from both single and multiple products scenarios validate the effectiveness of our methods.

cs.LG↗

arXiv2024

Forward Learning for Gradient-based Black-box Saliency Map Generation

Gradient-based saliency maps are widely used to explain deep neural network decisions. However, as models become deeper and more black-box, such as in closed-source APIs like ChatGPT, computing gradients become challenging, hindering conventional explanation methods. In this work, we introduce a novel unified framework for estimating gradients in black-box settings and generating saliency maps to interpret model decisions. We employ the likelihood ratio method to estimate output-to-input gradients and utilize them for saliency map generation. Additionally, we propose blockwise computation techniques to enhance estimation accuracy. Extensive experiments in black-box settings validate the effectiveness of our method, demonstrating accurate gradient estimation and explainability of generated saliency maps. Furthermore, we showcase the scalability of our approach by applying it to explain GPT-Vision, revealing the continued relevance of gradient-based explanation methods in the era of large, closed-source, and black-box models.

cs.CV↗

arXiv2024

Approximated Likelihood Ratio: A Forward-Only and Parallel Framework for Boosting Neural Network Training

Efficient and biologically plausible alternatives to backpropagation in neural network training remain a challenge due to issues such as high computational complexity and additional assumptions about neural networks, which limit scalability to deeper networks. The likelihood ratio method offers a promising gradient estimation strategy but is constrained by significant memory consumption, especially when deploying multiple copies of data to reduce estimation variance. In this paper, we introduce an approximation technique for the likelihood ratio (LR) method to alleviate computational and memory demands in gradient estimation. By exploiting the natural parallelism during the backward pass using LR, we further provide a high-performance training strategy, which pipelines both the forward and backward pass, to make it more suitable for the computation on specialized hardware. Extensive experiments demonstrate the effectiveness of the approximation technique in neural network training. This work underscores the potential of the likelihood ratio method in achieving high-performance neural network training, suggesting avenues for further exploration.

cs.LG↗

arXiv2024

Deep Reinforcement Learning for Solving Management Problems: Towards A Large Management Mode

We introduce a deep reinforcement learning (DRL) approach for solving management problems including inventory management, dynamic pricing, and recommendation. This DRL approach has the potential to lead to a large management model based on certain transformer neural network structures, resulting in an artificial general intelligence paradigm for various management tasks. Traditional methods have limitations for solving complex real-world problems, and we demonstrate how DRL can surpass existing heuristic approaches for solving management tasks. We aim to solve the problems in a unified framework, considering the interconnections between different tasks. Central to our methodology is the development of a foundational decision model coordinating decisions across the different domains through generative decision-making. Our experimental results affirm the effectiveness of our DRL-based framework in complex and dynamic business environments. This work opens new pathways for the application of DRL in management problems, highlighting its potential to revolutionize traditional business management.

cs.AI↗

arXiv2024

RiskMiner: Discovering Formulaic Alphas via Risk Seeking Monte Carlo Tree Search

The formulaic alphas are mathematical formulas that transform raw stock data into indicated signals. In the industry, a collection of formulaic alphas is combined to enhance modeling accuracy. Existing alpha mining only employs the neural network agent, unable to utilize the structural information of the solution space. Moreover, they didn't consider the correlation between alphas in the collection, which limits the synergistic performance. To address these problems, we propose a novel alpha mining framework, which formulates the alpha mining problems as a reward-dense Markov Decision Process (MDP) and solves the MDP by the risk-seeking Monte Carlo Tree Search (MCTS). The MCTS-based agent fully exploits the structural information of discrete solution space and the risk-seeking policy explicitly optimizes the best-case performance rather than average outcomes. Comprehensive experiments are conducted to demonstrate the efficiency of our framework. Our method outperforms all state-of-the-art benchmarks on two real-world stock sets under various metrics. Backtest experiments show that our alphas achieve the most profitable results under a realistic trading setting.

q-fin.CP↗

arXiv2024

AlphaRank: An Artificial Intelligence Approach for Ranking and Selection Problems

We introduce AlphaRank, an artificial intelligence approach to address the fixed-budget ranking and selection (R&S) problems. We formulate the sequential sampling decision as a Markov decision process and propose a Monte Carlo simulation-based rollout policy that utilizes classic R&S procedures as base policies for efficiently learning the value function of stochastic dynamic programming. We accelerate online sample-allocation by using deep reinforcement learning to pre-train a neural network model offline based on a given prior. We also propose a parallelizable computing framework for large-scale problems, effectively combining "divide and conquer" and "recursion" for enhanced scalability and efficiency. Numerical experiments demonstrate that the performance of AlphaRank is significantly improved over the base policies, which could be attributed to AlphaRank's superior capability on the trade-off among mean, variance, and induced correlation overlooked by many existing policies.

cs.LG↗

arXiv2023

One Forward is Enough for Neural Network Training via Likelihood Ratio Method

While backpropagation (BP) is the mainstream approach for gradient computation in neural network training, its heavy reliance on the chain rule of differentiation constrains the designing flexibility of network architecture and training pipelines. We avoid the recursive computation in BP and develop a unified likelihood ratio (ULR) method for gradient estimation with just one forward propagation. Not only can ULR be extended to train a wide variety of neural network architectures, but the computation flow in BP can also be rearranged by ULR for better device adaptation. Moreover, we propose several variance reduction techniques to further accelerate the training process. Our experiments offer numerical results across diverse aspects, including various neural network training scenarios, computation flow rearrangement, and fine-tuning of pre-trained models. All findings demonstrate that ULR effectively enhances the flexibility of neural network training by permitting localized module training without compromising the global objective and significantly boosts the network robustness.

cs.LG↗