Integrated Offline and Online Learning to Solve a Large Class of Scheduling Problems

In this paper, we develop a unified machine learning (ML) approach to predict high-quality solutions for single-machine scheduling problems with a non-decreasing min-sum objective function with or without release times. Our ML approach is novel in three major aspects. First, our approach is developed for the entire class of the aforementioned problems. To achieve this, we exploit the fact that the entire class of the problems considered can be formulated as a time-indexed formulation in a unified manner. We develop a deep neural network (DNN) which uses the cost parameters in the time-indexed formulation as the inputs to effectively predict a continuous solution to this formulation, based on which a feasible discrete solution is easily constructed. The second novel aspect of our approach lies in how the DNN model is trained. In view of the NP-hard nature of the problems, labels (i.e., optimal solutions) are hard to generate for training. To overcome this difficulty, we generate and utilize a set of special instances, for which optimal solutions can be found with little computational effort, to train the ML model offline. The third novel idea we employ in our approach is that we develop an online single-instance learning approach to fine tune the parameters in the DNN for a given online instance, with the goal of generating an improved solution for the given instance. To this end, we develop a feasibility surrogate that approximates the objective value of a given instance as a continuous function of the outputs of the DNN, which then enables us to derive gradients and update the learnable parameters in the DNN. Numerical results show that our approach can efficiently generate high-quality solutions for a variety of single-machine scheduling min-sum problems with up to 1000 jobs.

A Parameter-Efficient Quantum Anomaly Detection Method on a Superconducting Quantum Processor

Quantum machine learning has gained attention for its potential to address computational challenges. However, whether those algorithms can effectively solve practical problems and outperform their classical counterparts, especially on current quantum hardware, remains a critical question. In this work, we propose a novel quantum machine learning method, called Quantum Support Vector Data Description (QSVDD), for practical anomaly detection, which aims to achieve both parameter efficiency and superior accuracy compared to classical models. Emulation results indicate that QSVDD demonstrates favourable recognition capabilities compared to classical baselines, achieving an average accuracy of over 90% on benchmarks with significantly fewer trainable parameters. Theoretical analysis confirms that QSVDD has a comparable expressivity to classical counterparts while requiring only a fraction of the parameters. Furthermore, we demonstrate the first implementation of a quantum machine learning method for anomaly detection on a superconducting quantum processor. Specifically, we achieve an accuracy of over 80% with only 16 parameters on the device, providing initial evidence of QSVDD's practical viability in the noisy intermediate-scale quantum era and highlighting its significant reduction in parameter requirements.

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.

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.

Quantile-Based Deep Reinforcement Learning using Two-Timescale Policy Gradient Algorithms

Classical reinforcement learning (RL) aims to optimize the expected cumulative reward. In this work, we consider the RL setting where the goal is to optimize the quantile of the cumulative reward. We parameterize the policy controlling actions by neural networks, and propose a novel policy gradient algorithm called Quantile-Based Policy Optimization (QPO) and its variant Quantile-Based Proximal Policy Optimization (QPPO) for solving deep RL problems with quantile objectives. QPO uses two coupled iterations running at different timescales for simultaneously updating quantiles and policy parameters, whereas QPPO is an off-policy version of QPO that allows multiple updates of parameters during one simulation episode, leading to improved algorithm efficiency. Our numerical results indicate that the proposed algorithms outperform the existing baseline algorithms under the quantile criterion.

A Novel Noise Injection-based Training Scheme for Better Model Robustness

Noise injection-based method has been shown to be able to improve the robustness of artificial neural networks in previous work. In this work, we propose a novel noise injection-based training scheme for better model robustness. Specifically, we first develop a likelihood ratio method to estimate the gradient with respect to both synaptic weights and noise levels for stochastic gradient descent training. Then, we design an approximation for the vanilla noise injection-based training method to reduce memory and improve computational efficiency. Next, we apply our proposed scheme to spiking neural networks and evaluate the performance of classification accuracy and robustness on MNIST and Fashion-MNIST datasets. Experiment results show that our proposed method achieves a much better performance on adversarial robustness and slightly better performance on original accuracy, compared with the conventional gradient-based training method.

Quantile-Based Policy Optimization for Reinforcement Learning

Classical reinforcement learning (RL) aims to optimize the expected cumulative rewards. In this work, we consider the RL setting where the goal is to optimize the quantile of the cumulative rewards. We parameterize the policy controlling actions by neural networks and propose a novel policy gradient algorithm called Quantile-Based Policy Optimization (QPO) and its variant Quantile-Based Proximal Policy Optimization (QPPO) to solve deep RL problems with quantile objectives. QPO uses two coupled iterations running at different time scales for simultaneously estimating quantiles and policy parameters and is shown to converge to the global optimal policy under certain conditions. Our numerical results demonstrate that the proposed algorithms outperform the existing baseline algorithms under the quantile criterion.