Eliminating Ratio Bias for Gradient-based Simulated Parameter Estimation

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.

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.

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.

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.

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.

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.

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.

Sample-Efficient Clustering and Conquer Procedures for Parallel Large-Scale Ranking and Selection

We propose novel "clustering and conquer" procedures for the parallel large-scale ranking and selection (R&S) problem, which leverage correlation information for clustering to break the bottleneck of sample efficiency. In parallel computing environments, correlation-based clustering can achieve an $\mathcal{O}(p)$ sample complexity reduction rate, which is the optimal reduction rate theoretically attainable. Our proposed framework is versatile, allowing for seamless integration of various prevalent R&S methods under both fixed-budget and fixed-precision paradigms. It can achieve improvements without the necessity of highly accurate correlation estimation and precise clustering. In large-scale AI applications such as neural architecture search, a screening-free version of our procedure surprisingly surpasses fully-sequential benchmarks in terms of sample efficiency. This suggests that leveraging valuable structural information, such as correlation, is a viable path to bypassing the traditional need for screening via pairwise comparison--a step previously deemed essential for high sample efficiency but problematic for parallelization. Additionally, we propose a parallel few-shot clustering algorithm tailored for large-scale problems.

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.

Training Neural Networks without Backpropagation: A Deeper Dive into the Likelihood Ratio Method

Backpropagation (BP) is the most important gradient estimation method for training neural networks in deep learning. However, the literature shows that neural networks trained by BP are vulnerable to adversarial attacks. We develop the likelihood ratio (LR) method, a new gradient estimation method, for training a broad range of neural network architectures, including convolutional neural networks, recurrent neural networks, graph neural networks, and spiking neural networks, without recursive gradient computation. We propose three methods to efficiently reduce the variance of the gradient estimation in the neural network training process. Our experiments yield numerical results for training different neural networks on several datasets. All results demonstrate that the LR method is effective for training various neural networks and significantly improves the robustness of the neural networks under adversarial attacks relative to the BP method.