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.

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 unlabeled 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 zeroth-order informed fine-tuning paradigm for DM. The zeroth-order gradient estimator enables the computation graph rearrangement within the recursive diffusive chain, making the RLR's gradient estimator an unbiased one with the lower variance than other methods. We provide theoretical guarantees for the performance of the RLR. Extensive experiments are conducted on image and video generation tasks 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.

Reliable responses from large language models (LLMs) require adherence to user instructions and retrieved information. While alignment techniques help LLMs align with human intentions and values, improving context-faithfulness through alignment remains underexplored. To address this, we propose $\textbf{Context-DPO}$, the first alignment method specifically designed to enhance LLMs' context-faithfulness. We introduce $\textbf{ConFiQA}$, a benchmark that simulates Retrieval-Augmented Generation (RAG) scenarios with knowledge conflicts to evaluate context-faithfulness. By leveraging faithful and stubborn responses to questions with provided context from ConFiQA, our Context-DPO aligns LLMs through direct preference optimization. Extensive experiments demonstrate that our Context-DPO significantly improves context-faithfulness, achieving 35% to 280% improvements on popular open-source models. Further analysis demonstrates that Context-DPO preserves LLMs' generative capabilities while providing interpretable insights into context utilization. Our code and data are released at https://github.com/byronBBL/Context-DPO

This article addresses the challenge of parameter calibration in stochastic models where the likelihood function is not analytically available. We propose a gradient-based simulated parameter estimation framework, leveraging a multi-time scale algorithm that tackles the issue of ratio bias in both maximum likelihood estimation and posterior density estimation problems. Additionally, we introduce a nested simulation optimization structure, providing theoretical analyses including strong convergence, asymptotic normality, convergence rate, and budget allocation strategies for the proposed algorithm. The framework is further extended to neural network training, offering a novel perspective on stochastic approximation in machine learning. Numerical experiments show that our algorithm can improve the estimation accuracy and save computational costs.

We study the dynamic pricing and replenishment problems under inconsistent papers to INFORMS journals by means decision frequencies. Different from the traditional demand assumption, the of a style file template, which includes discreteness of demand and the parameter within the Poisson distribution as a function the journal title. However, use of a template of price introduce complexity into analyzing the problem property. We demonstrate does not certify that the paper the concavity of the single-period profit function with respect to product price and has been accepted for publication in the inventory within their respective domains. The demand model is enhanced by integrating named journal. INFORMS journal templates a decision tree-based machine learning approach, trained on comprehensive are for the exclusive purpose of market data. Employing a two-timescale stochastic approximation scheme, we address submitting to an INFORMS journal and the discrepancies in decision frequencies between pricing and replenishment, ensuring are not intended to be a true representation convergence to local optimum. We further refine our methodology by incorporating of the article's final published form.