Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables stable single-player version of self-play training that helps the agent to escape local optima. The training on any problem instance can be accelerated by applying transfer learning from an agent trained on randomly generated problems. Our approach allows sampling high-quality solutions to the Ising problem with high probability and outperforms both baseline heuristics and a black-box hyperparameter optimization approach.
A traditional artificial neural network (ANN) is normally trained slowly by a gradient descent algorithm, such as the backpropagation algorithm, since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. Since a large number of hyperparameters of a deep neural network, such as a convolutional neural network, occupy much memory, a memory-inefficient deep learning model is not ideal for real-time Internet of Things (IoT) applications on various devices, such as mobile phones. Thus, it is necessary to develop fast and memory-efficient Artificial Intelligence of Things (AIoT) systems for real-time on-device applications. We created a novel wide and shallow 4-layer ANN called "Pairwise Neural Network" ("PairNet") with high-speed non-gradient-descent hyperparameter optimization. The PairNet is trained quickly with only one epoch since its hyperparameters are directly optimized one-time via simply solving a system of linear equations by using the multivariate least squares fitting method. In addition, an n-input space is partitioned into many n-input data subspaces, and a local PairNet is built in a local n-input subspace. This divide-and-conquer approach can train the local PairNet using specific local features to improve model performance. Simulation results indicate that the three PairNets with incremental learning have smaller average prediction mean squared errors, and achieve much higher speeds than traditional ANNs. An important future work is to develop better and faster non-gradient-descent hyperparameter optimization algorithms to generate effective, fast, and memory-efficient PairNets with incremental learning on optimal subspaces for real-time AIoT on-device applications.
Many of the recent triumphs in machine learning are dependent on well-tuned hyperparameters. This is particularly prominent in reinforcement learning (RL) where a small change in the configuration can lead to failure. Despite the importance of tuning hyperparameters, it remains expensive and is often done in a naive and laborious way. A recent solution to this problem is Population Based Training (PBT) which updates both weights and hyperparameters in a single training run of a population of agents. PBT has been shown to be particularly effective in RL, leading to widespread use in the field. However, PBT lacks theoretical guarantees since it relies on random heuristics to explore the hyperparameter space. This inefficiency means it typically requires vast computational resources, which is prohibitive for many small and medium sized labs. In this work, we introduce the first provably efficient PBT-style algorithm, Population-Based Bandits (PB2). PB2 uses a probabilistic model to guide the search in an efficient way, making it possible to discover high performing hyperparameter configurations with far fewer agents than typically required by PBT. We show in a series of RL experiments that PB2 is able to achieve high performance with a modest computational budget.
Algorithm selection (AS) deals with selecting an algorithm from a fixed set of candidate algorithms most suitable for a specific instance of an algorithmic problem, e.g., choosing solvers for SAT problems. Benchmark suites for AS usually comprise candidate sets consisting of at most tens of algorithms, whereas in combined algorithm selection and hyperparameter optimization problems the number of candidates becomes intractable, impeding to learn effective meta-models and thus requiring costly online performance evaluations. Therefore, here we propose the setting of extreme algorithm selection (XAS) where we consider fixed sets of thousands of candidate algorithms, facilitating meta learning. We assess the applicability of state-of-the-art AS techniques to the XAS setting and propose approaches leveraging a dyadic feature representation in which both problem instances and algorithms are described. We find the latter to improve significantly over the current state of the art in various metrics.
Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To highly speed up training, we created a novel shallow 4-layer ANN called "Pairwise Neural Network" ("PairNet") with high-speed hyperparameter optimization. In addition, a value of each input is partitioned into multiple intervals, and then an n-dimensional space is partitioned into M n-dimensional subspaces. M local PairNets are built in M partitioned local n-dimensional subspaces. A local PairNet is trained very quickly with only one epoch since its hyperparameters are directly optimized one-time via simply solving a system of linear equations by using the multivariate least squares fitting method. Simulation results for three regression problems indicated that the PairNet achieved much higher speeds and lower average testing mean squared errors (MSEs) for the three cases, and lower average training MSEs for two cases than the traditional ANNs. A significant future work is to develop better and faster optimization algorithms based on intelligent methods and parallel computing methods to optimize both partitioned subspaces and hyperparameters to build the fast and effective PairNets for applications in big data mining and real-time machine learning.
Convolutional neural network (CNN) is one of the most frequently used deep learning techniques. Various forms of models have been proposed and im-proved for learning at CNN. When learning with CNN, it is necessary to determine the optimal hyperparameters. However, the number of hyperparameters is so large that it is difficult to do it manually, so much research has been done on automation. A method that uses metaheuristic algorithms is attracting attention in research on hyperparameter optimization. Metaheuristic algorithms are naturally inspired and include evolution strategies, genetic algorithms, antcolony optimization and particle swarm optimization. In particular, particle swarm optimization converges faster than genetic algorithms, and various models have been proposed. In this paper, we pro-pose CNN hyperparameter optimization with linearly decreasing weight particle swarm optimization (LDWPSO). In the experiment, the MNIST data set and CIFAR-10 data set, which are often used as benchmark data sets, are used. By opti-mizing CNN hyperparameters with LDWPSO, learning the MNIST and CIFAR-10 datasets, we compare the accuracy with a standard CNN based on LeNet-5. As a result, when using the MNIST dataset, the baseline CNN is 94.02% at the 5th epoch, compared to 98.95% for LDWPSO CNN, which improves accuracy. When using the CIFAR-10 dataset, the Baseline CNN is 28.07% at the 10th epoch, compared to 69.37% for the LDWPSO CNN, which greatly improves accuracy. This paper is presented at the 36th Annual Conference of the Japanese Society for Artificial In-telligence. The final version is available at the following URL: https://doi.org/10.11517/pjsai.JSAI2022.0_2S4IS2b03
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample efficiency, Bayesian Optimization over a Gaussian Processes modeling of the parameter space has become the method of choice. Unfortunately, this approach suffers from a cubic compute complexity due to underlying Cholesky factorization, which makes it very hard to be scaled beyond a small number of sampling steps. In this paper, we present a novel, highly accurate approximation of the underlying Gaussian Process. Reducing its computational complexity from cubic to quadratic allows an efficient strong scaling of Bayesian Optimization while outperforming the previous approach regarding optimization accuracy. The first experiments show speedups of a factor of 162 in single node and further speed up by a factor of 5 in a parallel environment.
Bayesian optimization is normally performed within fixed variable bounds. In cases like hyperparameter tuning for machine learning algorithms, setting the variable bounds is not trivial. It is hard to guarantee that any fixed bounds will include the true global optimum. We propose a Bayesian optimization approach that only needs to specify an initial search space that does not necessarily include the global optimum, and expands the search space when necessary. However, over-exploration may occur during the search space expansion. Our method can adaptively balance exploration and exploitation in an expanding space. Results on a range of synthetic test functions and an MLP hyperparameter optimization task show that the proposed method out-performs or at least as good as the current state-of-the-art methods.
Both feature selection and hyperparameter tuning are key tasks in machine learning. Hyperparameter tuning is often useful to increase model performance, while feature selection is undertaken to attain sparse models. Sparsity may yield better model interpretability and lower cost of data acquisition, data handling and model inference. While sparsity may have a beneficial or detrimental effect on predictive performance, a small drop in performance may be acceptable in return for a substantial gain in sparseness. We therefore treat feature selection as a multi-objective optimization task. We perform hyperparameter tuning and feature selection simultaneously because the choice of features of a model may influence what hyperparameters perform well. We present, benchmark, and compare two different approaches for multi-objective joint hyperparameter optimization and feature selection: The first uses multi-objective model-based optimization. The second is an evolutionary NSGA-II-based wrapper approach to feature selection which incorporates specialized sampling, mutation and recombination operators. Both methods make use of parameterized filter ensembles. While model-based optimization needs fewer objective evaluations to achieve good performance, it incurs computational overhead compared to the NSGA-II, so the preferred choice depends on the cost of evaluating a model on given data.
Deep learning models are full of hyperparameters, which are set manually before the learning process can start. To find the best configuration for these hyperparameters in such a high dimensional space, with time-consuming and expensive model training / validation, is not a trivial challenge. Bayesian optimization is a powerful tool for the joint optimization of hyperparameters, efficiently trading off exploration and exploitation of the hyperparameter space. In this paper, we discuss Bayesian hyperparameter optimization, including hyperparameter optimization, Bayesian optimization, and Gaussian processes. We also review BoTorch, GPyTorch and Ax, the new open-source frameworks that we use for Bayesian optimization, Gaussian process inference and adaptive experimentation, respectively. For experimentation, we apply Bayesian hyperparameter optimization, for optimizing group weights, to weighted group pooling, which couples unsupervised tiered graph autoencoders learning and supervised graph prediction learning for molecular graphs. We find that Ax, BoTorch and GPyTorch together provide a simple-to-use but powerful framework for Bayesian hyperparameter optimization, using Ax's high-level API that constructs and runs a full optimization loop and returns the best hyperparameter configuration.
In this paper, we compare the three most popular algorithms for hyperparameter optimization (Grid Search, Random Search, and Genetic Algorithm) and attempt to use them for neural architecture search (NAS). We use these algorithms for building a convolutional neural network (search architecture). Experimental results on CIFAR-10 dataset further demonstrate the performance difference between compared algorithms. The comparison results are based on the execution time of the above algorithms and accuracy of the proposed models.
When faced with a specific optimization problem, choosing which algorithm to use is always a tough task. Not only is there a vast variety of algorithms to select from, but these algorithms often are controlled by many hyperparameters, which need to be tuned in order to achieve the best performance possible. Usually, this problem is separated into two parts: algorithm selection and algorithm configuration. With the significant advances made in Machine Learning, however, these problems can be integrated into a combined algorithm selection and hyperparameter optimization task, commonly known as the CASH problem. In this work we compare sequential and integrated algorithm selection and configuration approaches for the case of selecting and tuning the best out of 4608 variants of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) tested on the Black Box Optimization Benchmark (BBOB) suite. We first show that the ranking of the modular CMA-ES variants depends to a large extent on the quality of the hyperparameters. This implies that even a sequential approach based on complete enumeration of the algorithm space will likely result in sub-optimal solutions. In fact, we show that the integrated approach manages to provide competitive results at a much smaller computational cost. We also compare two different mixed-integer algorithm configuration techniques, called irace and Mixed-Integer Parallel Efficient Global Optimization (MIP-EGO). While we show that the two methods differ significantly in their treatment of the exploration-exploitation balance, their overall performances are very similar.
Electromyogram (EMG) classification is a key technique in EMG-based control systems. The existing EMG classification methods do not consider the characteristics of EMG features that the distribution has skewness and kurtosis, causing drawbacks such as the requirement of hyperparameter tuning. In this paper, we propose a neural network based on the Johnson $S_\mathrm{U}$ translation system that is capable of representing distributions with skewness and kurtosis. The Johnson system is a normalizing translation that transforms non-normal data to a normal distribution, thereby enabling the representation of a wide range of distributions. In this study, a discriminative model based on the multivariate Johnson $S_\mathrm{U}$ translation system is transformed into a linear combination of coefficients and input vectors using log-linearization. This is then incorporated into a neural network structure, thereby allowing the calculation of the posterior probability of the input vectors for each class and the determination of model parameters as weight coefficients of the network. The uniqueness of convergence of the network learning is theoretically guaranteed. In the experiments, the suitability of the proposed network for distributions including skewness and kurtosis is evaluated using artificially generated data. Its applicability for real biological data is also evaluated via an EMG classification experiment. The results show that the proposed network achieves high classification performance without the need for hyperparameter optimization.
One of the major challenges in multivariate analysis is the estimation of population covariance matrix from sample covariance matrix (SCM). Most recent covariance matrix estimators use either shrinkage transformations or asymptotic results from Random Matrix Theory (RMT). Shrinkage techniques help in pulling extreme correlation values towards certain target values whereas tools from RMT help in removing noisy eigenvalues of SCM. Both of these techniques use different approaches to achieve a similar goal which is to remove noisy correlations and add structure to SCM to overcome the bias-variance trade-off. In this paper, we first critically evaluate the pros and cons of these two techniques and then propose an improved estimator which exploits the advantages of both by taking an optimally weighted convex combination of covariance matrices estimated by an improved shrinkage transformation and a RMT based filter. It is a generalized estimator which can adapt to changing sampling noise conditions in various datasets by performing hyperparameter optimization. We show the effectiveness of this estimator on the problem of designing a financial portfolio with minimum risk. We have chosen this problem because the complex properties of stock market data provide extreme conditions to test the robustness of a covariance estimator. Using data from four of the world's largest stock exchanges, we show that our proposed estimator outperforms existing estimators in minimizing the out-of-sample risk of the portfolio and hence predicts population statistics more precisely. Since covariance analysis is a crucial statistical tool, this estimator can be used in a wide range of machine learning, signal processing and high dimensional pattern recognition applications.
How can we make software analytics simpler and faster? One method is to match the complexity of analysis to the intrinsic complexity of the data being explored. For example, hyperparameter optimizers find the control settings for data miners that improve the predictions generated via software analytics. Sometimes, very fast hyperparameter optimization can be achieved by "DODGE-ing"; i.e. simply steering way from settings that lead to similar conclusions. But when is it wise to use that simple approach and when must we use more complex (and much slower) optimizers?} To answer this, we applied hyperparameter optimization to 120 SE data sets that explored bad smell detection, predicting Github issue close time, bug report analysis, defect prediction, and dozens of other non-SE problems. We find that the simple DODGE works best for data sets with low "intrinsic dimensionality" (u ~ 3) and very poorly for higher-dimensional data (u > 8). Nearly all the SE data seen here was intrinsically low-dimensional, indicating that DODGE is applicable for many SE analytics tasks.
Machine learning algorithms are very sensitive to the hyperparameters, and their evaluations are generally expensive. Users desperately need intelligent methods to quickly optimize hyperparameter settings according to known evaluation information, and thus reduce computational cost and promote optimization efficiency. Motivated by this, we propose ExperienceThinking algorithm to quickly find the best possible hyperparameter configuration of machine learning algorithms within a few configuration evaluations. ExperienceThinking design two novel methods, which intelligently infer optimal configurations from two aspects: search space pruning and knowledge utilization respectively. Two methods complement each other and solve the constrained hyperparameter optimization problems effectively. To demonstrate the benefit of ExperienceThinking, we compare it with 3 classical hyperparameter optimization algorithms with a small number of configuration evaluations. The experimental results present that our proposed algorithm provides superior results and achieve better performance.
The leading approaches in language modeling are all obsessed with TV shows of my youth - namely Transformers and Sesame Street. Transformers this, Transformers that, and over here a bonfire worth of GPU-TPU-neuromorphic wafer scale silicon. We opt for the lazy path of old and proven techniques with a fancy crypto inspired acronym: the Single Headed Attention RNN (SHA-RNN). The author's lone goal is to show that the entire field might have evolved a different direction if we had instead been obsessed with a slightly different acronym and slightly different result. We take a previously strong language model based only on boring LSTMs and get it to within a stone's throw of a stone's throw of state-of-the-art byte level language model results on enwik8. This work has undergone no intensive hyperparameter optimization and lived entirely on a commodity desktop machine that made the author's small studio apartment far too warm in the midst of a San Franciscan summer. The final results are achievable in plus or minus 24 hours on a single GPU as the author is impatient. The attention mechanism is also readily extended to large contexts with minimal computation. Take that Sesame Street.
The aim of black-box optimization is to optimize an objective function within the constraints of a given evaluation budget. In this problem, it is generally assumed that the computational cost for evaluating a point is large; thus, it is important to search efficiently with as low budget as possible. Bayesian optimization is an efficient method for black-box optimization and provides exploration-exploitation trade-off by constructing a surrogate model that considers uncertainty of the objective function. However, because Bayesian optimization should construct the surrogate model for the entire search space, it does not exhibit good performance when points are not sampled sufficiently. In this study, we develop a heuristic method refining the search space for Bayesian optimization when the available evaluation budget is low. The proposed method refines a promising region by dividing the original region so that Bayesian optimization can be executed with the promising region as the initial search space. We confirm that Bayesian optimization with the proposed method outperforms Bayesian optimization alone and shows equal or better performance to two search-space division algorithms through experiments on the benchmark functions and the hyperparameter optimization of machine learning algorithms.
Recurrent neural networks (RNNs) have gained a great deal of attention in solving sequential learning problems. The learning of long-term dependencies, however, remains challenging due to the problem of a vanishing or exploding hidden states gradient. By exploring further the recently established connections between RNNs and dynamical systems we propose a novel RNN architecture, which we call a Hamiltonian recurrent neural network (Hamiltonian RNN), based on a symplectic discretization of an appropriately chosen Hamiltonian system. The key benefit of this approach is that the corresponding RNN inherits the favorable long time properties of the Hamiltonian system, which in turn allows us to control the hidden states gradient with a hyperparameter of the Hamiltonian RNN architecture. This enables us to handle sequential learning problems with arbitrary sequence lengths, since for a range of values of this hyperparameter the gradient neither vanishes nor explodes. Additionally, we provide a heuristic for the optimal choice of the hyperparameter, which we use in our numerical simulations to illustrate that the Hamiltonian RNN is able to outperform other state-of-the-art RNNs without the need of computationally intensive hyperparameter optimization.
We study the problem of using low computational cost to automate the choices of learners and hyperparameters for an ad-hoc training dataset and error metric, by conducting trials of different configurations on the given training data. We investigate the joint impact of multiple factors on both trial cost and model error, and propose several design guidelines. Following them, we build a fast and lightweight library FLAML which optimizes for low computational resource in finding accurate models. FLAML integrates several simple but effective search strategies into an adaptive system. It significantly outperforms top-ranked AutoML libraries on a large open source AutoML benchmark under equal, or sometimes orders of magnitude smaller budget constraints.