Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization -- an algorithmic scheme that encourages exploration -- and is closely related to soft policy iteration and trust region policy optimization. Despite the empirical success, the theoretical underpinnings for NPG methods remain limited even for the tabular setting. This paper develops $\textit{non-asymptotic}$ convergence guarantees for entropy-regularized NPG methods under softmax parameterization, focusing on discounted Markov decision processes (MDPs). Assuming access to exact policy evaluation, we demonstrate that the algorithm converges linearly -- or even quadratically once it enters a local region around the optimal policy -- when computing optimal value functions of the regularized MDP. Moreover, the algorithm is provably stable vis-\`a-vis inexactness of policy evaluation. Our convergence results accommodate a wide range of learning rates, and shed light upon the role of entropy regularization in enabling fast convergence.

Out-of-Distribution (OOD) generalization problem is a problem of seeking the predictor function whose performance in the worst environments is optimal. This paper makes two contributions to OOD problem. We first use the basic results of probability to prove Maximal Invariant Predictor(MIP) condition, a theoretical result that can be used to identify the OOD optimal solution. We then use our MIP to derive Inter-environmental Gradient Alignment (IGA) algorithm that can be used to help seek the OOD optimal predictor. Previous studies that have investigated the theoretical aspect of the OOD problem use strong structural assumptions such as causal DAG. However, in cases involving image datasets, for example, the identification of hidden structural relations is itself a difficult problem. Our theoretical results are different from those of many previous studies in that it can be applied to cases in which the underlying structure of dataset is difficult to analyze. We present an extensive comparison of previous theoretical approaches to the OOD problems based on the assumptions they make. We also present an extension of the Colored-MNIST that can more accurately represent the pathological OOD situation than the original version, and demonstrate the superiority of IGA over previous methods on both the original and the extended version of Colored-MNIST.

This article proposes an efficient heuristic in accelerating the column generation by parallel resolution of pricing problems for aircrafts in the tail assignment problem (TAP). The approach is able to achieve considerable improvement in resolution time for real life test instances from two major Indian air carriers. The different restrictions on individual aircraft for maintenance routing as per aviation regulatory bodies are considered in this paper. We also present a variable fixing heuristic to improve the integrality of the solution. The hybridization of constraint programming and column generation was substantial in accelerating the resolution process.

Newly, the rates of energy and material consumption to augment industrial pro-duction are substantially high, thus the environmentally sustainable industrial de-velopment has emerged as the main issue of either developed or developing coun-tries. A novel approach to supply chain management is proposed to maintain economic growth along with environmentally friendly concerns for the design of the supply chain network. In this paper, a new green supply chain design approach has been suggested to maintain the financial virtue accompanying the environ-mental factors that required to be mitigated the negative effect of rapid industrial development on the environment. This approach has been suggested a multi-objective mathematical model minimizing the total costs and CO2 emissions for establishing an environmentally sustainable closed-loop supply chain. Two opti-mization methods are used namely Epsilon Constraint Method, and Genetic Al-gorithm Optimization Method. The results of the two mentioned methods have been compared and illustrated their effectiveness. The outcome of the analysis is approved to verify the accuracy of the proposed model to deal with financial and environmental issues concurrently.

Graph convolutional networks (GCNs) have achieved promising performance on various graph-based tasks. However they suffer from over-smoothing when stacking more layers. In this paper, we present a quantitative study on this observation and develop novel insights towards the deeper GCN. First, we interpret the current graph convolutional operations from an optimization perspective and argue that over-smoothing is mainly caused by the naive first-order approximation of the solution to the optimization problem. Subsequently, we introduce two metrics to measure the over-smoothing on node-level tasks. Specifically, we calculate the fraction of the pairwise distance between connected and disconnected nodes to the overall distance respectively. Based on our theoretical and empirical analysis, we establish a universal theoretical framework of GCN from an optimization perspective and derive a novel convolutional kernel named GCN+ which has lower parameter amount while relieving the over-smoothing inherently. Extensive experiments on real-world datasets demonstrate the superior performance of GCN+ over state-of-the-art baseline methods on the node classification tasks.

Automated Machine Learning (AutoML) refers to techniques for automatically discovering well-performing models for predictive modeling tasks with very little user involvement. TPOT is an open-source library for performing AutoML in Python. It makes use of the popular Scikit-Learn machine learning library for data transforms and machine learning algorithms and uses a Genetic Programming stochastic global search procedure to efficiently discover a top-performing model pipeline for a given dataset. In this tutorial, you will discover how to use TPOT for AutoML with Scikit-Learn machine learning algorithms in Python. TPOT for Automated Machine Learning in Python Photo by Gwen, some rights reserved.

We consider a distributed empirical risk minimization (ERM) optimization problem with communication efficiency and privacy requirements, motivated by the federated learning (FL) framework. Unique challenges to the traditional ERM problem in the context of FL include (i) need to provide privacy guarantees on clients' data, (ii) compress the communication between clients and the server, since clients might have low-bandwidth links, (iii) work with a dynamic client population at each round of communication between the server and the clients, as a small fraction of clients are sampled at each round. To address these challenges we develop (optimal) communication-efficient schemes for private mean estimation for several $\ell_p$ spaces, enabling efficient gradient aggregation for each iteration of the optimization solution of the ERM. We also provide lower and upper bounds for mean estimation with privacy and communication constraints for arbitrary $\ell_p$ spaces. To get the overall communication, privacy, and optimization performance operation point, we combine this with privacy amplification opportunities inherent to this setup. Our solution takes advantage of the inherent privacy amplification provided by client sampling and data sampling at each client (through Stochastic Gradient Descent) as well as the recently developed privacy framework using anonymization, which effectively presents to the server responses that are randomly shuffled with respect to the clients. Putting these together, we demonstrate that one can get the same privacy, optimization-performance operating point developed in recent methods that use full-precision communication, but at a much lower communication cost, i.e., effectively getting communication efficiency for "free".

Constraint Programming (CP) is a well-established area in AI as a programming paradigm for modelling and solving discrete optimization problems, and it has been been successfully applied to tackle the on-line job dispatching problem in HPC systems including those running modern applications. The limitations of the available CP-based job dispatchers may hinder their practical use in today's systems that are becoming larger in size and more demanding in resource allocation. In an attempt to bring basic AI research closer to a deployed application, we present a new CP-based on-line job dispatcher for modern HPC systems and applications. Unlike its predecessors, our new dispatcher tackles the entire problem in CP and its model size is independent of the system size. Experimental results based on a simulation study show that with our approach dispatching performance increases significantly in a large system and in a system where allocation is nontrivial.

Proximal Policy Optimization (PPO) is a popular deep policy gradient algorithm. In standard implementations, PPO regularizes policy updates with clipped probability ratios, and parameterizes policies with either continuous Gaussian distributions or discrete Softmax distributions. These design choices are widely accepted, and motivated by empirical performance comparisons on MuJoCo and Atari benchmarks. We revisit these practices outside the regime of current benchmarks, and expose three failure modes of standard PPO. We explain why standard design choices are problematic in these cases, and show that alternative choices of surrogate objectives and policy parameterizations can prevent the failure modes. We hope that our work serves as a reminder that many algorithmic design choices in reinforcement learning are tied to specific simulation environments. We should not implicitly accept these choices as a standard part of a more general algorithm.

A vital problem in solving classification or regression problem is to apply feature engineering and variable selection on data before fed into models.One of a most popular feature engineering method is to discretisize continous variable with some cutting points,which is refered to as bining processing.Good cutting points are important for improving model's ability, because wonderful bining may ignore some noisy variance in continous variable range and keep useful leveled information with good ordered encodings.However, to our best knowledge a majority of cutting point selection is done via researchers domain knownledge or some naive methods like equal-width cutting or equal-frequency cutting.In this paper we propose an end-to-end supervised cutting point selection method based on group and fused lasso along with the automatically variable selection effect.We name our method \textbf{ABM}(automatic bining machine). We firstly cut each variable range into fine grid bins and train model with our group and group fused lasso regularization on each successive bins.It is a method that integrates feature engineering,variable selection and model training simultanously.And one more inspiring thing is that the method is flexible such that it can be taken into a bunch of loss function based model including deep neural networks.We have also implemented the method in R and open the source code to other researchers.A Python version will also meet the community in days.