Decision trees offer the benefit of easy interpretation because they allow the classification of input data based on if--then rules. However, as decision trees are constructed by an algorithm that achieves clear classification with minimum necessary rules, the trees possess the drawback of extracting only minimum rules, even when various latent rules exist in data. Approaches that construct multiple trees using randomly selected feature subsets do exist. However, the number of trees that can be constructed remains at the same scale because the number of feature subsets is a combinatorial explosion. Additionally, when multiple trees are constructed, numerous rules are generated, of which several are untrustworthy and/or highly similar. Therefore, we propose "MAABO-MT" and "GS-MRM" algorithms that strategically construct trees with high estimation performance among all possible trees with small computational complexity and extract only reliable and non-similar rules, respectively. Experiments are conducted using several open datasets to analyze the effectiveness of the proposed method. The results confirm that MAABO-MT can discover reliable rules at a lower computational cost than other methods that rely on randomness. Furthermore, the proposed method is confirmed to provide deeper insights than single decision trees commonly used in previous studies. Therefore, MAABO-MT and GS-MRM can efficiently extract rules from combinatorially exploded decision trees.
We consider a gossip network, consisting of $n$ nodes, which tracks the information at a source. The source updates its information with a Poisson arrival process and also sends updates to the nodes in the network. The nodes themselves can exchange information among themselves to become as timely as possible. However, the network structure is sparse and irregular, i.e., not every node is connected to every other node in the network, rather, the order of connectivity is low, and varies across different nodes. This asymmetry of the network implies that the nodes in the network do not perform equally in terms of timelines. Due to the gossiping nature of the network, some nodes are able to track the source very timely, whereas, some nodes fall behind versions quite often. In this work, we investigate how the rate-constrained source should distribute its update rate across the network to maintain fairness regarding timeliness, i.e., the overall worst case performance of the network can be minimized. Due to the continuous search space for optimum rate allocation, we formulate this problem as a continuum-armed bandit problem and employ Gaussian process based Bayesian optimization to meet a trade-off between exploration and exploitation sequentially.
We study the problem of tuning the parameters of a room temperature controller to minimize its energy consumption, subject to the constraint that the daily cumulative thermal discomfort of the occupants is below a given threshold. We formulate it as an online constrained black-box optimization problem where, on each day, we observe some relevant environmental context and adaptively select the controller parameters. In this paper, we propose to use a data-driven Primal-Dual Contextual Bayesian Optimization (PDCBO) approach to solve this problem. In a simulation case study on a single room, we apply our algorithm to tune the parameters of a Proportional Integral (PI) heating controller and the pre-heating time. Our results show that PDCBO can save up to 4.7% energy consumption compared to other state-of-the-art Bayesian optimization-based methods while keeping the daily thermal discomfort below the given tolerable threshold on average. Additionally, PDCBO can automatically track time-varying tolerable thresholds while existing methods fail to do so. We then study an alternative constrained tuning problem where we aim to minimize the thermal discomfort with a given energy budget. With this formulation, PDCBO reduces the average discomfort by up to 63% compared to state-of-the-art safe optimization methods while keeping the average daily energy consumption below the required threshold.
We introduce a global, gradient-free surrogate optimization strategy for expensive black-box functions inspired by the Fokker-Planck and Langevin equations. These can be written as an optimization problem where the objective is the target function to maximize minus the logarithm of the current density of evaluated samples. This objective balances exploitation of the target objective with exploration of low-density regions. The method, Deterministic Langevin Optimization (DLO), relies on a Normalizing Flow density estimate to perform active learning and select proposal points for evaluation. This strategy differs qualitatively from the widely-used acquisition functions employed by Bayesian Optimization methods, and can accommodate a range of surrogate choices. We demonstrate superior or competitive progress toward objective optima on standard synthetic test functions, as well as on non-convex and multi-modal posteriors of moderate dimension. On real-world objectives, such as scientific and neural network hyperparameter optimization, DLO is competitive with state-of-the-art baselines.
The growing ubiquity of machine learning (ML) has led it to enter various areas of computer science, including black-box optimization (BBO). Recent research is particularly concerned with Bayesian optimization (BO). BO-based algorithms are popular in the ML community, as they are used for hyperparameter optimization and more generally for algorithm configuration. However, their efficiency decreases as the dimensionality of the problem and the budget of evaluations increase. Meanwhile, derivative-free optimization methods have evolved independently in the optimization community. Therefore, we urge to understand whether cross-fertilization is possible between the two communities, ML and BBO, i.e., whether algorithms that are heavily used in ML also work well in BBO and vice versa. Comparative experiments often involve rather small benchmarks and show visible problems in the experimental setup, such as poor initialization of baselines, overfitting due to problem-specific setting of hyperparameters, and low statistical significance. With this paper, we update and extend a comparative study presented by Hutter et al. in 2013. We compare BBO tools for ML with more classical heuristics, first on the well-known BBOB benchmark suite from the COCO environment and then on Direct Policy Search for OpenAI Gym, a reinforcement learning benchmark. Our results confirm that BO-based optimizers perform well on both benchmarks when budgets are limited, albeit with a higher computational cost, while they are often outperformed by algorithms from other families when the evaluation budget becomes larger. We also show that some algorithms from the BBO community perform surprisingly well on ML tasks.
This paper studies the problem of distributed multi-agent Bayesian optimization with both coupled black-box constraints and known affine constraints. A primal-dual distributed algorithm is proposed that achieves similar regret/violation bounds as those in the single-agent case for the black-box objective and constraint functions. Additionally, the algorithm guarantees an $\mathcal{O}(N\sqrt{T})$ bound on the cumulative violation for the known affine constraints, where $N$ is the number of agents. Hence, it is ensured that the average of the samples satisfies the affine constraints up to the error $\mathcal{O}({N}/{\sqrt{T}})$. Furthermore, we characterize certain conditions under which our algorithm can bound a stronger metric of cumulative violation and provide best-iterate convergence without affine constraint. The method is then applied to both sampled instances from Gaussian processes and a real-world optimal power allocation problem for wireless communication; the results show that our method simultaneously provides close-to-optimal performance and maintains minor violations on average, corroborating our theoretical analysis.
3D reconstruction is a fundamental task in robotics that gained attention due to its major impact in a wide variety of practical settings, including agriculture, underwater, and urban environments. This task can be carried out via view planning (VP), which aims to optimally place a certain number of cameras in positions that maximize the visual information, improving the resulting 3D reconstruction. Nonetheless, in most real-world settings, existing environmental noise can significantly affect the performance of 3D reconstruction. To that end, this work advocates a novel geometric-based reconstruction quality function for VP, that accounts for the existing noise of the environment, without requiring its closed-form expression. With no analytic expression of the objective function, this work puts forth an adaptive Bayesian optimization algorithm for accurate 3D reconstruction in the presence of noise. Numerical tests on noisy agricultural environments showcase the merits of the proposed approach for 3D reconstruction with even a small number of available cameras.
Bayesian optimization (BO) is a popular black-box function optimization method, which makes sequential decisions based on a Bayesian model, typically a Gaussian process (GP), of the function. To ensure the quality of the model, transfer learning approaches have been developed to automatically design GP priors by learning from observations on "training" functions. These training functions are typically required to have the same domain as the "test" function (black-box function to be optimized). In this paper, we introduce MPHD, a model pre-training method on heterogeneous domains, which uses a neural net mapping from domain-specific contexts to specifications of hierarchical GPs. MPHD can be seamlessly integrated with BO to transfer knowledge across heterogeneous search spaces. Our theoretical and empirical results demonstrate the validity of MPHD and its superior performance on challenging black-box function optimization tasks.
Machine learning (ML) methods offer a wide range of configurable hyperparameters that have a significant influence on their performance. While accuracy is a commonly used performance objective, in many settings, it is not sufficient. Optimizing the ML models with respect to multiple objectives such as accuracy, confidence, fairness, calibration, privacy, latency, and memory consumption is becoming crucial. To that end, hyperparameter optimization, the approach to systematically optimize the hyperparameters, which is already challenging for a single objective, is even more challenging for multiple objectives. In addition, the differences in objective scales, the failures, and the presence of outlier values in objectives make the problem even harder. We propose a multi-objective Bayesian optimization (MoBO) algorithm that addresses these problems through uniform objective normalization and randomized weights in scalarization. We increase the efficiency of our approach by imposing constraints on the objective to avoid exploring unnecessary configurations (e.g., insufficient accuracy). Finally, we leverage an approach to parallelize the MoBO which results in a 5x speed-up when using 16x more workers.
In this paper, we propose a method to automatically and efficiently tune high-dimensional vectors of controller parameters. The proposed method first learns a mapping from the high-dimensional controller parameter space to a lower dimensional space using a machine learning-based algorithm. This mapping is then utilized in an actor-critic framework using Bayesian optimization (BO). The proposed approach is applicable to complex systems (such as quadruped robots). In addition, the proposed approach also enables efficient generalization to different control tasks while also reducing the number of evaluations required while tuning the controller parameters. We evaluate our method on a legged locomotion application. We show the efficacy of the algorithm in tuning the high-dimensional controller parameters and also reducing the number of evaluations required for the tuning. Moreover, it is shown that the method is successful in generalizing to new tasks and is also transferable to other robot dynamics.
Virtual screening of large compound libraries to identify potential hit candidates is one of the earliest steps in drug discovery. As the size of commercially available compound collections grows exponentially to the scale of billions, brute-force virtual screening using traditional tools such as docking becomes infeasible in terms of time and computational resources. Active learning and Bayesian optimization has recently been proven as effective methods of narrowing down the search space. An essential component in those methods is a surrogate machine learning model that is trained with a small subset of the library to predict the desired properties of compounds. Accurate model can achieve high sample efficiency by finding the most promising compounds with only a fraction of the whole library being virtually screened. In this study, we examined the performance of pretrained transformer-based language model and graph neural network in Bayesian optimization active learning framework. The best pretrained models identifies 58.97% of the top-50000 by docking score after screening only 0.6% of an ultra-large library containing 99.5 million compounds, improving 8% over previous state-of-the-art baseline. Through extensive benchmarks, we show that the superior performance of pretrained models persists in both structure-based and ligand-based drug discovery. Such model can serve as a boost to the accuracy and sample efficiency of active learning based molecule virtual screening.
We examine a stochastic formulation for data-driven optimization wherein the decision-maker is not privy to the true distribution, but has knowledge that it lies in some hypothesis set and possesses a historical data set, from which information about it can be gleaned. We define a prescriptive solution as a decision rule mapping such a data set to decisions. As there does not exist prescriptive solutions that are generalizable over the entire hypothesis set, we define out-of-sample optimality as a local average over a neighbourhood of hypotheses, and averaged over the sampling distribution. We prove sufficient conditions for local out-of-sample optimality, which reduces to functions of the sufficient statistic of the hypothesis family. We present an optimization problem that would solve for such an out-of-sample optimal solution, and does so efficiently by a combination of sampling and bisection search algorithms. Finally, we illustrate our model on the newsvendor model, and find strong performance when compared against alternatives in the literature. There are potential implications of our research on end-to-end learning and Bayesian optimization.
Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their quality and capacity to preserve structural and contextual information remains a challenge. In this paper, we address this need by proposing a method to measure the \textit{representation capacity} of embeddings. The motivation behind this work stems from the importance of understanding the strengths and limitations of embeddings, enabling researchers and practitioners to make informed decisions in selecting appropriate embedding models for their specific applications. By combining extrinsic evaluation methods, such as classification and clustering, with t-SNE-based neighborhood analysis, such as neighborhood agreement and trustworthiness, we provide a comprehensive assessment of the representation capacity. Additionally, the use of optimization techniques (bayesian optimization) for weight optimization (for classification, clustering, neighborhood agreement, and trustworthiness) ensures an objective and data-driven approach in selecting the optimal combination of metrics. The proposed method not only contributes to advancing the field of embedding evaluation but also empowers researchers and practitioners with a quantitative measure to assess the effectiveness of embeddings in capturing structural and contextual information. For the evaluation, we use $3$ real-world biological sequence (proteins and nucleotide) datasets and performed representation capacity analysis of $4$ embedding methods from the literature, namely Spike2Vec, Spaced $k$-mers, PWM2Vec, and AutoEncoder.
This paper proposes a novel fuzzy cascaded Proportional-Derivative (PD) controller for under-actuated single-link flexible joint manipulators. The original flexible joint system is considered as two coupled $2^{nd}$-order sub-systems. The proposed controller is composed of two cascaded PD controllers and two fuzzy logic regulators (FLRs). The first (virtual) PD controller is used to generate desired control input that stabilizes the first $2^{nd}$-order sub-system. Solving the equation by considering the coupling terms as design variables, the reference signal is generated for the second sub-system. Then through simple compensation design, together with the second PD controller, the cascaded PD controller is derived. In order to further improve the performance, two FLRs are implemented that adaptively tune the parameters of PD controllers. Under natural assumptions, the cascaded fuzzy PD controller is proved to possess locally asymptotic stability. All the offline tuning processes are completed data-efficiently by Bayesian Optimization. The results in simulation illustrate the stability and validity of our proposed method. Besides, the idea of cascaded PD controller presented here may be extended as a novel control method for other under-actuated systems, and the stability analysis renders a new perspective towards the stability proof of all other fuzzy-enhanced PID controllers.
Apache TVM (Tensor Virtual Machine), an open source machine learning compiler framework designed to optimize computations across various hardware platforms, provides an opportunity to improve the performance of dense matrix factorizations such as LU (Lower Upper) decomposition and Cholesky decomposition on GPUs and AI (Artificial Intelligence) accelerators. In this paper, we propose a new TVM autotuning framework using Bayesian Optimization and use the TVM tensor expression language to implement linear algebra kernels such as LU, Cholesky, and 3mm. We use these scientific computation kernels to evaluate the effectiveness of our methods on a GPU cluster, called Swing, at Argonne National Laboratory. We compare the proposed autotuning framework with the TVM autotuning framework AutoTVM with four tuners and find that our framework outperforms AutoTVM in most cases.
Optimizing the configuration and placement of sensors is crucial for reliable fall detection, indoor localization, and activity recognition in assisted living spaces. We propose a novel, sample-efficient approach to find a high-quality sensor placement in an arbitrary indoor space based on grey-box Bayesian optimization and simulation-based evaluation. Our key technical contribution lies in capturing domain-specific knowledge about the spatial distribution of activities and incorporating it into the iterative selection of query points in Bayesian optimization. Considering two simulated indoor environments and a real-world dataset containing human activities and sensor triggers, we show that our proposed method performs better compared to state-of-the-art black-box optimization techniques in identifying high-quality sensor placements, leading to accurate activity recognition in terms of F1-score, while also requiring a significantly lower (51.3% on average) number of expensive function queries.
Given the urgent need of simplifying the end-of-line tuning of complex vehicle dynamics controllers, the Twin-in-the-Loop Control (TiL-C) approach was recently proposed in the automotive field. In TiL-C, a digital twin is run on-board to compute a nominal control action in run-time and an additional block C_delta is used to compensate for the mismatch between the simulator and the real vehicle. As the digital twin is assumed to be the best replica available of the real plant, the key issue in TiL-C becomes the tuning of the compensator, which must be performed relying on data only. In this paper, we investigate the use of different black-box optimization techniques for the calibration of C_delta. More specifically, we compare the originally proposed Bayesian Optimization (BO) approach with the recently developed Set Membership Global Optimization (SMGO) and Virtual Reference Feedback Tuning (VRFT), a one-shot direct data-driven design method. The analysis will be carried out within a professional multibody simulation environment on a novel TiL-C application case study -- the yaw-rate tracking problem -- so as to further prove the TiL-C effctiveness on a challenging problem. Simulations will show that the VRFT approach is capable of providing a well tuned controller after a single iteration, while 10 to 15 iterations are necessary for refining it with global optimizers. Also, SMGO is shown to significantly reduce the computational effort required by BO.
For a wide range of applications the structure of systems like Neural Networks or complex simulations, is unknown and approximation is costly or even impossible. Black-box optimization seeks to find optimal (hyper-) parameters for these systems such that a pre-defined objective function is minimized. Polynomial-Model-Based Optimization (PMBO) is a novel blackbox optimizer that finds the minimum by fitting a polynomial surrogate to the objective function. Motivated by Bayesian optimization the model is iteratively updated according to the acquisition function Expected Improvement, thus balancing the exploitation and exploration rate and providing an uncertainty estimate of the model. PMBO is benchmarked against other state-of-the-art algorithms for a given set of artificial, analytical functions. PMBO competes successfully with those algorithms and even outperforms all of them in some cases. As the results suggest, we believe PMBO is the pivotal choice for solving blackbox optimization tasks occurring in a wide range of disciplines.
In this paper, we consider improving the efficiency of information-based autonomous robot exploration in unknown and complex environments. We first utilize Gaussian process (GP) regression to learn a surrogate model to infer the confidence-rich mutual information (CRMI) of querying control actions, then adopt an objective function consisting of predicted CRMI values and prediction uncertainties to conduct Bayesian optimization (BO), i.e., GP-based BO (GPBO). The trade-off between the best action with the highest CRMI value (exploitation) and the action with high prediction variance (exploration) can be realized. To further improve the efficiency of GPBO, we propose a novel lightweight information gain inference method based on Bayesian kernel inference and optimization (BKIO), achieving an approximate logarithmic complexity without the need for training. BKIO can also infer the CRMI and generate the best action using BO with bounded cumulative regret, which ensures its comparable accuracy to GPBO with much higher efficiency. Extensive numerical and real-world experiments show the desired efficiency of our proposed methods without losing exploration performance in different unstructured, cluttered environments. We also provide our open-source implementation code at https://github.com/Shepherd-Gregory/BKIO-Exploration.
Recent research indicates that the performance of machine learning models can be improved by aligning the geometry of the latent space with the underlying data structure. Rather than relying solely on Euclidean space, researchers have proposed using hyperbolic and spherical spaces with constant curvature, or combinations thereof, to better model the latent space and enhance model performance. However, little attention has been given to the problem of automatically identifying the optimal latent geometry for the downstream task. We mathematically define this novel formulation and coin it as neural latent geometry search (NLGS). More specifically, we introduce an initial attempt to search for a latent geometry composed of a product of constant curvature model spaces with a small number of query evaluations, under some simplifying assumptions. To accomplish this, we propose a novel notion of distance between candidate latent geometries based on the Gromov-Hausdorff distance from metric geometry. In order to compute the Gromov-Hausdorff distance, we introduce a mapping function that enables the comparison of different manifolds by embedding them in a common high-dimensional ambient space. We then design a graph search space based on the notion of smoothness between latent geometries and employ the calculated distances as an additional inductive bias. Finally, we use Bayesian optimization to search for the optimal latent geometry in a query-efficient manner. This is a general method which can be applied to search for the optimal latent geometry for a variety of models and downstream tasks. We perform experiments on synthetic and real-world datasets to identify the optimal latent geometry for multiple machine learning problems.