Divide and Learn: A Divide and Conquer Approach for Predict Optimize Authors Ali Ugur Guler, 1 Emir Demirovic, 2 Jeffrey Chan, 3 James Bailey, 1 Christopher Leckie, 1 Peter J. Stuckey, 4 1 University of Melbourne, 2 Delft University of Technology, 3 RMIT University, 4 Monash University aguler@student.unimelb.edu.au, Abstract The predict optimize problem combines machine learning of problem coefficients with a combinatorial optimization problem that uses the predicted coefficients. While this problem can be solved in two separate stages, it is better to directly minimize the optimization loss. However, this requires differentiating through a discrete, non-differentiable combinatorial function. Most existing approaches use some form of surrogate gradient. Demirovic et al showed how to directly express the loss of the optimization problem in terms of the predicted coefficients as a piece-wise linear function. However, their approach is restricted to optimization problems with a dynamic programming formulation. In this work we propose a novel divide and conquer algorithm to tackle optimization problems without this restriction and predict its coefficients using the optimization loss. We also introduce a greedy version of this approach, which achieves similar results with less computation. We compare our approach with other approaches to the predict optimize problem and show we can successfully tackle some hard combinatorial problems better than other predict optimize methods. Introduction Machine Learning ( ML) has gained substantial attention in the last decade, and has proven to be useful in a wide range of industries. ML models usually focus on making accurate predictions by minimizing errors, such as mean squared error ( MSE). These predictions can then be used as coefficients in other decision making processes, such as a combinatorial optimization problem.

This paper presents the cognitive module of the cognitive architecture for artificial intelligence (CAAI) in cyber-physical production systems (CPPS). The goal of this architecture is to reduce the implementation effort of artificial intelligence (AI) algorithms in CPPS. Declarative user goals and the provided algorithm-knowledge base allow the dynamic pipeline orchestration and configuration. A big data platform (BDP) instantiates the pipelines and monitors the CPPS performance for further evaluation through the cognitive module. Thus, the cognitive module is able to select feasible and robust configurations for process pipelines in varying use cases. Furthermore, it automatically adapts the models and algorithms based on model quality and resource consumption. The cognitive module also instantiates additional pipelines to test algorithms from different classes. CAAI relies on well-defined interfaces to enable the integration of additional modules and reduce implementation effort. Finally, an implementation based on Docker, Kubernetes, and Kafka for the virtualization and orchestration of the individual modules and as messaging-technology for module communication is used to evaluate a real-world use case.

We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic $k$-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input--output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on two synthetic datasets and one dataset comprising dose statistics of radiation therapy treatment plans show that our mixture-of-experts method outperforms a Gaussian process benchmark model both in terms of validation metrics and visual inspection.

Full truckload transportation (FTL) in the form of freight containers represents one of the most important transportation modes in international trade. Due to large volume and scale, in FTL, delivery time is often less critical but cost and service quality are crucial. Therefore, efficiently solving large scale multiple shift FTL problems is becoming more and more important and requires further research. In one of our earlier studies, a set covering model and a three-stage solution method were developed for a multi-shift FTL problem. This paper extends the previous work and presents a significantly more efficient approach by hybridising pricing and cutting strategies with metaheuristics (a variable neighbourhood search and a genetic algorithm). The metaheuristics were adopted to find promising columns (vehicle routes) guided by pricing and cuts are dynamically generated to eliminate infeasible flow assignments caused by incompatible commodities. Computational experiments on real-life and artificial benchmark FTL problems showed superior performance both in terms of computational time and solution quality, when compared with previous MIP based three-stage methods and two existing metaheuristics. The proposed cutting and heuristic pricing approach can efficiently solve large scale real-life FTL problems.

Bounded Max-Sum (BMS) is a message-passing algorithm that provides approximation solution to a specific form of de-centralized coordination problems, namely Distributed Constrained Optimization Problems (DCOPs). In particular, BMS algorithm is able to solve problems of this type having large search space at the expense of low computational cost. Notably, the traditional DCOP formulation does not consider those constraints that must be satisfied(also known as hard constraints), rather it concentrates only on soft constraints. Hence, although the presence of both types of constraints are observed in a number of real-world applications, the BMS algorithm does not actively capitalize on the hard constraints. To address this issue, we tailor BMS in such a way that can deal with DCOPs having both type constraints. In so doing, our approach improves the solution quality of the algorithm. The empirical results exhibit a marked improvement in the quality of the solutions of large DCOPs.

Multi-objective optimization of the textile manufacturing process is an increasing challenge because of the growing complexity involved in the development of the textile industry. The use of intelligent techniques has been often discussed in this domain, although a significant improvement from certain successful applications has been reported, the traditional methods failed to work with high-as well as human intervention. Upon which, this paper proposed a multi-agent reinforcement learning (MARL) framework to transform the optimization process into a stochastic game and introduced the deep Q-networks algorithm to train the multiple agents. A utilitarian selection mechanism was employed in the stochastic game, which (-greedy policy) in each state to avoid the interruption of multiple equilibria and achieve the correlated equilibrium optimal solutions of the optimizing process. The case study result reflects that the proposed MARL system is possible to achieve the optimal solutions for the textile ozonation process and it performs better than the traditional approaches.

Training a fair machine learning model is essential to prevent demographic disparity. Existing techniques for improving model fairness require broad changes in either data preprocessing or model training, rendering themselves difficult-to-adopt for potentially already complex machine learning systems. We address this problem via the lens of bilevel optimization. While keeping the standard training algorithm as an inner optimizer, we incorporate an outer optimizer so as to equip the inner problem with an additional functionality: Adaptively selecting minibatch sizes for the purpose of improving model fairness. Our batch selection algorithm, which we call FairBatch, implements this optimization and supports prominent fairness measures: equal opportunity, equalized odds, and demographic parity. FairBatch comes with a significant implementation benefit -- it does not require any modification to data preprocessing or model training. For instance, a single-line change of PyTorch code for replacing batch selection part of model training suffices to employ FairBatch. Our experiments conducted both on synthetic and benchmark real data demonstrate that FairBatch can provide such functionalities while achieving comparable (or even greater) performances against the state of the arts. Furthermore, FairBatch can readily improve fairness of any pre-trained model simply via fine-tuning. It is also compatible with existing batch selection techniques intended for different purposes, such as faster convergence, thus gracefully achieving multiple purposes.

Federated learning is a useful framework for centralized learning from distributed data under practical considerations of heterogeneity, asynchrony, and privacy. Federated architectures are frequently deployed in deep learning settings, which generally give rise to non-convex optimization problems. Nevertheless, most existing analysis are either limited to convex loss functions, or only establish first-order stationarity, despite the fact that saddle-points, which are first-order stationary, are known to pose bottlenecks in deep learning. We draw on recent results on the second-order optimality of stochastic gradient algorithms in centralized and decentralized settings, and establish second-order guarantees for a class of federated learning algorithms.

During the training phase of machine learning (ML) models, it is usually necessary to configure several hyperparameters. This process is computationally intensive and requires an extensive search to infer the best hyperparameter set for the given problem. The challenge is exacerbated by the fact that most ML models are complex internally, and training involves trial-and-error processes that could remarkably affect the predictive result. Moreover, each hyperparameter of an ML algorithm is potentially intertwined with the others, and changing it might result in unforeseeable impacts on the remaining hyperparameters. Evolutionary optimization is a promising method to try and address those issues. According to this method, performant models are stored, while the remainder are improved through crossover and mutation processes inspired by genetic algorithms. We present VisEvol, a visual analytics tool that supports interactive exploration of hyperparameters and intervention in this evolutionary procedure. In summary, our proposed tool helps the user to generate new models through evolution and eventually explore powerful hyperparameter combinations in diverse regions of the extensive hyperparameter space. The outcome is a voting ensemble (with equal rights) that boosts the final predictive performance. The utility and applicability of VisEvol are demonstrated with two use cases and interviews with ML experts who evaluated the effectiveness of the tool.

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of learning setups and DRO ambiguity sets. We investigate the asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.