Before starting this tutorial we suggest you to read documentation#getstarted which will provide an example of data communication between your client code and Indie Solver. You should have a registered account to communicate with the solver. If you are a student or a researcher, don't forget to contact us at contact@indiesolver.com after registering your account to upgrade it to the standard subscription plan which is free for academic researchers. It will allow you to deal with more challenging optimization problems. The source code of this tutorial is available for download and includes two Python files: Rosenbrock10D.py and IndieSolver.py. The former is specific to this tutorial while the latter is our thin wrapper code to communicate with Indie Solver.

AI has long been used to optimize large-scale system. On the other hand, intelligent optimization algorithms are also the basic tools for analysing microeconomic environment. Essentially, blockchain and microeconomics are both large-scale distributed systems, and there are inherent connections found between them. In principle, a blockchain system (including various nodes such as full node, mining node, and lightweight node) and a micro economic system (including a social system, which consists of producers, consumers, and markets) have many similarities: different interconnected subsystems, decentralized computations, and so on. The broad concern of microeconomics is to allocate scarce resources among various uses with the goal of maximizing users' utility and producers' profit.

Policy optimization is an effective reinforcement learning approach to solve continuous control tasks. Recent achievements have shown that alternating on-line and off-line optimization is a successful choice for efficient trajectory reuse. However, deciding when to stop optimizing and collect new trajectories is non-trivial as it requires to account for the variance of the objective function estimate. In this paper, we propose a novel model-free policy search algorithm, POIS, applicable in both control-based and parameter-based settings. We first derive a high-confidence bound for importance sampling estimation and then we define a surrogate objective function which is optimized off-line using a batch of trajectories. Finally, the algorithm is tested on a selection of continuous control tasks, with both linear and deep policies, and compared with the state-of-the-art policy optimization methods.

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the "single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes. We propose a new approach for capturing this decision-making process through counterfactual reasoning in pairwise comparisons. Our approach is model-free and does not require iterating through the state space. We demonstrate that this approach accurately learns multifaceted heuristics on a synthetic and real world data sets. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of schedule optimization. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates optimal solutions up to 9.5 times faster than a state-of-the-art optimization algorithm.

Black box discrete optimization (BBDO) appears in wide range of engineering tasks. Evolutionary or other BBDO approaches have been applied, aiming at automating necessary tuning of system parameters, such as hyper parameter tuning of machine learning based systems when being installed for a specific task. However, automation is often jeopardized by the need of strategy parameter tuning for BBDO algorithms. An expert with the domain knowledge must undergo time-consuming strategy parameter tuning. This paper proposes a parameterless BBDO algorithm based on information geometric optimization, a recent framework for black box optimization using stochastic natural gradient. Inspired by some theoretical implications, we develop an adaptation mechanism for strategy parameters of the stochastic natural gradient method for discrete search domains. The proposed algorithm is evaluated on commonly used test problems. It is further extended to two examples of simultaneous optimization of the hyper parameters and the connection weights of deep learning models, leading to a faster optimization than the existing approaches without any effort of parameter tuning.

We consider a multitask learning problem, in which several predictors are learned jointly. Prior research has shown that learning the relations between tasks, and between the input features, together with the predictor, can lead to better generalization and interpretability, which proved to be useful for applications in many domains. In this paper, we consider a formulation of multitask learning that learns the relationships both between tasks and between features, represented through a task covariance and a feature covariance matrix, respectively. First, we demonstrate that existing methods proposed for this problem present an issue that may lead to ill-posed optimization. We then propose an alternative formulation, as well as an efficient algorithm to optimize it. Using ideas from optimization and graph theory, we propose an efficient coordinate-wise minimization algorithm that has a closed form solution for each block subproblem. Our experiments show that the proposed optimization method is orders of magnitude faster than its competitors. We also provide a nonlinear extension that is able to achieve better generalization than existing methods.

Yes, both hyperparameter tuning and architecture selection are optimization problems. Whether these are actually less difficult than NN training is debatable -- I think there are as around many papers on new architectures than there are on optimization techniques. Certainly, they are easier in the sense that a human can manually tune parameters and select an architecture which works reasonably well, but not select NN weights. Optimizing deep graphical models such as deep boltzmann machines is probably a more difficult optimization problem than training a neural network, depending on whether you consider DBMs a type of neural network.

A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically acquired modality. Inferring data pdf is of prime importance, allowing to analyze various model hypotheses and perform smart decision making. However, most density estimation techniques are limited in their representation expressiveness to specific kernel type or predetermined distribution family, and have other restrictions. For example, kernel density estimation (KDE) methods require meticulous parameter search and are extremely slow at querying new points. In this paper we present a novel non-parametric density estimation approach, DeepPDF, that uses a neural network to approximate a target pdf given samples from thereof. Such a representation provides high inference accuracy for a wide range of target pdfs using a relatively simple network structure, making our method highly statistically robust. This is done via a new stochastic optimization algorithm, \emph{Probabilistic Surface Optimization} (PSO), that turns to advantage the stochastic nature of sample points in order to force network output to be identical to the output of a target pdf. Once trained, query point evaluation can be efficiently done in DeepPDF by a simple network forward pass, with linear complexity in the number of query points. Moreover, the PSO algorithm is capable of inferring the frequency of data samples and may also be used in other statistical tasks such as conditional estimation and distribution transformation. We compare the derived approach with KDE methods showing its superior performance and accuracy.

Recent breakthroughs in Deep Learning (DL) applications have made DL models a key component in almost every modern computing system. The increased popularity of DL applications deployed on a wide-spectrum of platforms have resulted in a plethora of design challenges related to the constraints introduced by the hardware itself. What is the latency or energy cost for an inference made by a Deep Neural Network (DNN)? Is it possible to predict this latency or energy consumption before a model is trained? If yes, how can machine learners take advantage of these models to design the hardware-optimal DNN for deployment? From lengthening battery life of mobile devices to reducing the runtime requirements of DL models executing in the cloud, the answers to these questions have drawn significant attention. One cannot optimize what isn't properly modeled. Therefore, it is important to understand the hardware efficiency of DL models during serving for making an inference, before even training the model. This key observation has motivated the use of predictive models to capture the hardware performance or energy efficiency of DL applications. Furthermore, DL practitioners are challenged with the task of designing the DNN model, i.e., of tuning the hyper-parameters of the DNN architecture, while optimizing for both accuracy of the DL model and its hardware efficiency. Therefore, state-of-the-art methodologies have proposed hardware-aware hyper-parameter optimization techniques. In this paper, we provide a comprehensive assessment of state-of-the-art work and selected results on the hardware-aware modeling and optimization for DL applications. We also highlight several open questions that are poised to give rise to novel hardware-aware designs in the next few years, as DL applications continue to significantly impact associated hardware systems and platforms.

Creating impact in real-world settings requires artificial intelligence techniques to span the full pipeline from data, to predictive models, to decisions. These components are typically approached separately: a machine learning model is first trained via a measure of predictive accuracy, and then its predictions are used as input into an optimization algorithm which produces a decision. However, the loss function used to train the model may easily be misaligned with the end goal, which is to make the best decisions possible. Hand-tuning the loss function to align with optimization is a difficult and error-prone process (which is often skipped entirely). We focus on combinatorial optimization problems and introduce a general framework for decision-focused learning, where the machine learning model is directly trained in conjunction with the optimization algorithm to produce high-quality decisions. Technically, our contribution is a means of integrating discrete optimization problems into deep learning or other predictive models, which are typically trained via gradient descent. The main idea is to use a continuous relaxation of the discrete problem to propagate gradients through the optimization procedure. We instantiate this framework for two broad classes of combinatorial problems: linear programs and submodular maximization. Experimental results across a variety of domains show that decision-focused learning often leads to improved optimization performance compared to traditional methods. We find that standard measures of accuracy are not a reliable proxy for a predictive model's utility in optimization, and our method's ability to specify the true goal as the model's training objective yields substantial dividends across a range of decision problems.