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Recent years have seen a rise in interest in terms of using machine learning, particularly reinforcement learning (RL), for production scheduling problems of varying degrees of complexity. The general approach is to break down the scheduling problem into a Markov Decision Process (MDP), whereupon a simulation implementing the MDP is used to train an RL agent. Since existing studies rely on (sometimes) complex simulations for which the code is unavailable, the experiments presented are hard, or, in the case of stochastic environments, impossible to reproduce accurately. Furthermore, there is a vast array of RL designs to choose from. To make RL methods widely applicable in production scheduling and work out their strength for the industry, the standardisation of model descriptions - both production setup and RL design - and validation scheme are a prerequisite. Our contribution is threefold: First, we standardize the description of production setups used in RL studies based on established nomenclature. Secondly, we classify RL design choices from existing publications. Lastly, we propose recommendations for a validation scheme focusing on reproducibility and sufficient benchmarking.

We propose a new unified framework for describing and designing gradient-based convex optimization methods from a numerical analysis perspective. There the key is the new concept of weak discrete gradients (weak DGs), which is a generalization of DGs standard in numerical analysis. Via weak DG, we consider abstract optimization methods, and prove unified convergence rate estimates that hold independent of the choice of weak DGs except for some constants in the final estimate. With some choices of weak DGs, we can reproduce many popular existing methods, such as the steepest descent and Nesterov's accelerated gradient method, and also some recent variants from numerical analysis community. By considering new weak DGs, we can easily explore new theoretically-guaranteed optimization methods; we show some examples. We believe this work is the first attempt to fully integrate research branches in optimization and numerical analysis areas, so far independently developed.

Deep learning has contributed greatly to many successes in artificial intelligence in recent years. Today, it is possible to train models that have thousands of layers and hundreds of billions of parameters. Large-scale deep models have achieved great success, but the enormous computational complexity and gigantic storage requirements make it extremely difficult to implement them in real-time applications. On the other hand, the size of the dataset is still a real problem in many domains. Data are often missing, too expensive, or impossible to obtain for other reasons. Ensemble learning is partially a solution to the problem of small datasets and overfitting. However, ensemble learning in its basic version is associated with a linear increase in computational complexity. We analyzed the impact of the ensemble decision-fusion mechanism and checked various methods of sharing the decisions including voting algorithms. We used the modified knowledge distillation framework as a decision-fusion mechanism which allows in addition compressing of the entire ensemble model into a weight space of a single model. We showed that knowledge distillation can aggregate knowledge from multiple teachers in only one student model and, with the same computational complexity, obtain a better-performing model compared to a model trained in the standard manner. We have developed our own method for mimicking the responses of all teachers at the same time, simultaneously. We tested these solutions on several benchmark datasets. In the end, we presented a wide application use of the efficient multi-teacher knowledge distillation framework. In the first example, we used knowledge distillation to develop models that could automate corrosion detection on aircraft fuselage. The second example describes detection of smoke on observation cameras in order to counteract wildfires in forests.

Large and performant neural networks are often overparameterized and can be drastically reduced in size and complexity thanks to pruning. Pruning is a group of methods, which seeks to remove redundant or unnecessary weights or groups of weights in a network. These techniques allow the creation of lightweight networks, which are particularly critical in embedded or mobile applications. In this paper, we devise an alternative pruning method that allows extracting effective subnetworks from larger untrained ones. Our method is stochastic and extracts subnetworks by exploring different topologies which are sampled using Gumbel Softmax. The latter is also used to train probability distributions which measure the relevance of weights in the sampled topologies. The resulting subnetworks are further enhanced using a highly efficient rescaling mechanism that reduces training time and improves performance. Extensive experiments conducted on CIFAR show the outperformance of our subnetwork extraction method against the related work.

This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic expansion with the local coordinates in the transition-layer region, we prove the existence and uniqueness of a smooth solution with a sharp transition layer for a three-dimensional partial differential equation. Moreover, with the help of asymptotic expansion, a simplified model is derived for the corresponding inverse source problem, which is close to the original inverse problem over the entire region except for a narrow transition layer. We show that such simplification does not reduce the accuracy of the inversion results when the measurement data contain noise. Based on this simpler inversion model, an asymptotic-expansion regularization algorithm is proposed for efficiently solving the inverse source problem in the three-dimensional case. A model problem shows the feasibility of the proposed numerical approach.

Designing and analyzing model-based RL (MBRL) algorithms with guaranteed monotonic improvement has been challenging, mainly due to the interdependence between policy optimization and model learning. Existing discrepancy bounds generally ignore the impacts of model shifts, and their corresponding algorithms are prone to degrade performance by drastic model updating. In this work, we first propose a novel and general theoretical scheme for a non-decreasing performance guarantee of MBRL. Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. These discoveries encourage us to formulate a constrained lower-bound optimization problem to permit the monotonicity of MBRL. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns. Motivated by these analyses, we design a simple but effective algorithm CMLO (Constrained Model-shift Lower-bound Optimization), by introducing an event-triggered mechanism that flexibly determines when to update the model. Experiments show that CMLO surpasses other state-of-the-art methods and produces a boost when various policy optimization methods are employed.

Coded distributed computing (CDC) introduced by Li \emph{et al.} can greatly reduce the communication load for MapReduce computing systems. In the general cascaded CDC with $K$ workers, $N$ input files and $Q$ Reduce functions, each input file will be mapped by $r$ workers and each Reduce function will be computed by $s$ workers such that coding techniques can be applied to achieve the maximum multicast gain. The main drawback of most existing CDC schemes is that they require the original data to be split into a large number of input files that grows exponentially with $K$, which can significantly increase the coding complexity and degrade system performance. In this paper, we first use a classic combinatorial structure $t$-design, for any integer $t\geq 2$, to develop a low-complexity and asymptotically optimal CDC with $r=s$. The main advantages of our scheme via $t$-design are two-fold: 1) having much smaller $N$ and $Q$ than the existing schemes under the same parameters $K$, $r$ and $s$; and 2) achieving smaller communication loads compared with the state-of-the-art schemes. Remarkably, unlike the previous schemes that realize on large operation fields, our scheme operates on the minimum binary field $\mathbb{F}_2$. Furthermore, we show that our construction method can incorporate the other combinatorial structures that have a similar property to $t$-design. For instance, we use $t$-GDD to obtain another asymptotically optimal CDC scheme over $\mathbb{F}_2$ that has different parameters from $t$-design. Finally, we show that our construction method can also be used to construct CDC schemes with $r\neq s$ that have small file number and Reduce function number.

Mobile parcel lockers have been recently proposed by logistics operators as a technology that could help reduce traffic congestion and operational costs in urban freight distribution. Given their ability to relocate throughout their area of deployment, they hold the potential to improve customer accessibility and convenience. In this study, we formulate the Mobile Parcel Locker Problem (MPLP) , a special case of the Location-Routing Problem (LRP) which determines the optimal stopover location for MPLs throughout the day and plans corresponding delivery routes. A Hybrid Q Learning Network based Method (HQM) is developed to resolve the computational complexity of the resulting large problem instances while escaping local optima. In addition, the HQM is integrated with global and local search mechanisms to resolve the dilemma of exploration and exploitation faced by classic reinforcement learning methods. We examine the performance of HQM under different problem sizes (up to 200 nodes) and benchmarked it against the exact approach and Genetic Algorithm (GA). Our results indicate that HQM achieves better optimisation performance with shorter computation time than the exact approach solved by the Gurobi solver in large problem instances. Additionally, the average reward obtained by HQM is 1.96 times greater than GA, which demonstrates that HQM has a better optimisation ability. Further, we identify critical factors that contribute to fleet size requirements, travel distances, and service delays. Our findings outline that the efficiency of MPLs is mainly contingent on the length of time windows and the deployment of MPL stopovers. Finally, we highlight managerial implications based on parametric analysis to provide guidance for logistics operators in the context of efficient last-mile distribution operations.

Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.

This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.