With the rising complexity of numerous novel applications that serve our modern society comes the strong need to design efficient computing platforms. Designing efficient hardware is, however, a complex multi-objective problem that deals with multiple parameters and their interactions. Given that there are a large number of parameters and objectives involved in hardware design, synthesizing all possible combinations is not a feasible method to find the optimal solution. One promising approach to tackle this problem is statistical modeling of a desired hardware performance. Here, we propose a model-based active learning approach to solve this problem. Our proposed method uses Bayesian models to characterize various aspects of hardware performance. We also use transfer learning and Gaussian regression bootstrapping techniques in conjunction with active learning to create more accurate models. Our proposed statistical modeling method provides hardware models that are sufficiently accurate to perform design space exploration as well as performance prediction simultaneously. We use our proposed method to perform design space exploration and performance prediction for various hardware setups, such as micro-architecture design and OpenCL kernels for FPGA targets. Our experiments show that the number of samples required to create performance models significantly reduces while maintaining the predictive power of our proposed statistical models. For instance, in our performance prediction setting, the proposed method needs 65% fewer samples to create the model, and in the design space exploration setting, our proposed method can find the best parameter settings by exploring less than 50 samples.
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A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~$\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing $\mathtt{iLQR}$-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.
We propose a method for estimation and inference for bounds for heterogeneous causal effect parameters in general sample selection models where the treatment can affect whether an outcome is observed and no exclusion restrictions are available. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. It allows for conducting valid statistical inference on the unidentified conditional effects. We use a flexible debiased/double machine learning approach that can accommodate non-linear functional forms and high-dimensional confounders. Easily verifiable high-level conditions for estimation, misspecification robust confidence intervals, and uniform confidence bands are provided as well. Re-analyzing data from a large scale field experiment on Facebook, we find significant depolarization effects of counter-attitudinal news subscription nudges. The effect bounds are highly heterogeneous and suggest strong depolarization effects for moderates, conservatives, and younger users.
The pervasive uncertainty and dynamic nature of real-world environments present significant challenges for the widespread implementation of machine-driven Intelligent Decision-Making (IDM) systems. Consequently, IDM should possess the ability to continuously acquire new skills and effectively generalize across a broad range of applications. The advancement of Artificial General Intelligence (AGI) that transcends task and application boundaries is critical for enhancing IDM. Recent studies have extensively investigated the Transformer neural architecture as a foundational model for various tasks, including computer vision, natural language processing, and reinforcement learning. We propose that a Foundation Decision Model (FDM) can be developed by formulating diverse decision-making tasks as sequence decoding tasks using the Transformer architecture, offering a promising solution for expanding IDM applications in complex real-world situations. In this paper, we discuss the efficiency and generalization improvements offered by a foundation decision model for IDM and explore its potential applications in multi-agent game AI, production scheduling, and robotics tasks. Lastly, we present a case study demonstrating our FDM implementation, DigitalBrain (DB1) with 1.3 billion parameters, achieving human-level performance in 870 tasks, such as text generation, image captioning, video game playing, robotic control, and traveling salesman problems. As a foundation decision model, DB1 represents an initial step toward more autonomous and efficient real-world IDM applications.
The paper combines research approaches that traditionally have been disjoint: 1) model checking as used in formal verification of programs, and 2) auto-tuning as often used in high-performance computing. Auto-tuning frameworks optimize parallel programs by finding the optimal values of the performance-critical parameters -- so-called tuning parameters -- for a particular high-performance architecture and input data size. As there are many parameters influencing program's performance, finding the optimal parameter configuration is a hardly manageable task even for experts. Auto-tuning automates this process, but it is often time-consuming. We apply model checking for accelerating auto-tuning by using a counterexample constructed during the verification of the optimality property of the program. We describe in detail an implementation of our approach for programs written in OpenCL -- the standard for programming modern high-performance architectures -- using the model representation language Promela and the popular SPIN verification tool, and we report experimental results for an application use case.
While Convolutional Neural Networks (CNNs) have long been investigated and applied, as well as theorized, we aim to provide a slightly different perspective into their nature -- through the perspective of their Hessian maps. The reason is that the loss Hessian captures the pairwise interaction of parameters and therefore forms a natural ground to probe how the architectural aspects of CNN get manifested in its structure and properties. We develop a framework relying on Toeplitz representation of CNNs, and then utilize it to reveal the Hessian structure and, in particular, its rank. We prove tight upper bounds (with linear activations), which closely follow the empirical trend of the Hessian rank and hold in practice in more general settings. Overall, our work generalizes and establishes the key insight that, even in CNNs, the Hessian rank grows as the square root of the number of parameters.
Generalized linear mixed models (GLMMs) are widely used in research for their ability to model correlated outcomes with non-Gaussian conditional distributions. The proper selection of fixed and random effects is a critical part of the modeling process, where model misspecification may lead to significant bias. However, the joint selection of fixed and and random effects has historically been limited to lower dimensional GLMMs, largely due to the use of criterion-based model selection strategies. Here we present the R package glmmPen, one of the first that to select fixed and random effects in higher dimension using a penalized GLMM modeling framework. Model parameters are estimated using a Monte Carlo expectation conditional minimization (MCECM) algorithm, which leverages Stan and RcppArmadillo for increased computational efficiency. Our package supports multiple distributional families and penalty functions. In this manuscript we discuss the modeling procedure, estimation scheme, and software implementation through application to a pancreatic cancer subtyping study.
Nonlinear model predictive control (NMPC) solves a multivariate optimization problem to estimate the system's optimal control inputs in each control cycle. Such optimization is made more difficult by several factors, such as nonlinearities inherited in the system, highly coupled inputs, and various constraints related to the system's physical limitations. These factors make the optimization to be non-convex and hard to solve traditionally. Genetic algorithm (GA) is typically used extensively to tackle such optimization in several application domains because it does not involve differential calculation or gradient evaluation in its solution estimation. However, the size of the search space in which the GA searches for the optimal control inputs is crucial for the applicability of the GA with systems that require fast response. This paper proposes an approach to accelerate the genetic optimization of NMPC by learning optimal search space size. The proposed approach trains a multivariate regression model to adaptively predict the best smallest search space in every control cycle. The estimated best smallest size of search space is fed to the GA to allow for searching the optimal control inputs within this search space. The proposed approach not only reduces the GA's computational time but also improves the chance of obtaining the optimal control inputs in each cycle. The proposed approach was evaluated on two nonlinear systems and compared with two other genetic-based NMPC approaches implemented on the GPU of a Nvidia Jetson TX2 embedded platform in a processor-in-the-loop (PIL) fashion. The results show that the proposed approach provides a 39-53\% reduction in computational time. Additionally, it increases the convergence percentage to the optimal control inputs within the cycle's time by 48-56\%, resulting in a significant performance enhancement. The source code is available on GitHub.
An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. Firstly, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Secondly, we introduce an adaptation of the one-sided sign test that uses a modified \textit{p}-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
This paper serves as a survey of recent advances in large margin training and its theoretical foundations, mostly for (nonlinear) deep neural networks (DNNs) that are probably the most prominent machine learning models for large-scale data in the community over the past decade. We generalize the formulation of classification margins from classical research to latest DNNs, summarize theoretical connections between the margin, network generalization, and robustness, and introduce recent efforts in enlarging the margins for DNNs comprehensively. Since the viewpoint of different methods is discrepant, we categorize them into groups for ease of comparison and discussion in the paper. Hopefully, our discussions and overview inspire new research work in the community that aim to improve the performance of DNNs, and we also point to directions where the large margin principle can be verified to provide theoretical evidence why certain regularizations for DNNs function well in practice. We managed to shorten the paper such that the crucial spirit of large margin learning and related methods are better emphasized.
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