The performance of spectral clustering heavily relies on the quality of affinity matrix. A variety of affinity-matrix-construction (AMC) methods have been proposed but they have hyperparameters to determine beforehand, which requires strong experience and leads to difficulty in real applications, especially when the inter-cluster similarity is high and/or the dataset is large. In addition, we often need to choose different AMC methods for different datasets, which still depends on experience. To solve these two challenging problems, in this paper, we present a simple yet effective method for automated spectral clustering. First, we propose to find the most reliable affinity matrix via grid search or Bayesian optimization among a set of candidates given by different AMC methods with different hyperparameters, where the reliability is quantified by the \textit{relative-eigen-gap} of graph Laplacian introduced in this paper. Second, we propose a fast and accurate AMC method based on least squares representation and thresholding and prove its effectiveness theoretically. Finally, we provide a large-scale extension for the automated spectral clustering method, of which the time complexity is linear with the number of data points. Extensive experiments of natural image clustering show that our method is more versatile, accurate, and efficient than baseline methods.
Bayesian Optimization is a sample-efficient black-box optimization procedure that is typically applied to problems with a small number of independent objectives. However, in practice we often wish to optimize objectives defined over many correlated outcomes (or "tasks"). For example, scientists may want to optimize the coverage of a cell tower network across a dense grid of locations. Similarly, engineers may seek to balance the performance of a robot across dozens of different environments via constrained or robust optimization. However, the Gaussian Process (GP) models typically used as probabilistic surrogates for multi-task Bayesian Optimization scale poorly with the number of outcomes, greatly limiting applicability. We devise an efficient technique for exact multi-task GP sampling that combines exploiting Kronecker structure in the covariance matrices with Matheron's identity, allowing us to perform Bayesian Optimization using exact multi-task GP models with tens of thousands of correlated outputs. In doing so, we achieve substantial improvements in sample efficiency compared to existing approaches that only model aggregate functions of the outcomes. We demonstrate how this unlocks a new class of applications for Bayesian Optimization across a range of tasks in science and engineering, including optimizing interference patterns of an optical interferometer with more than 65,000 outputs.
Reinforcement learning (RL) aims to find an optimal policy by interaction with an environment. Consequently, learning complex behavior requires a vast number of samples, which can be prohibitive in practice. Nevertheless, instead of systematically reasoning and actively choosing informative samples, policy gradients for local search are often obtained from random perturbations. These random samples yield high variance estimates and hence are sub-optimal in terms of sample complexity. Actively selecting informative samples is at the core of Bayesian optimization, which constructs a probabilistic surrogate of the objective from past samples to reason about informative subsequent ones. In this paper, we propose to join both worlds. We develop an algorithm utilizing a probabilistic model of the objective function and its gradient. Based on the model, the algorithm decides where to query a noisy zeroth-order oracle to improve the gradient estimates. The resulting algorithm is a novel type of policy search method, which we compare to existing black-box algorithms. The comparison reveals improved sample complexity and reduced variance in extensive empirical evaluations on synthetic objectives. Further, we highlight the benefits of active sampling on popular RL benchmarks.
This paper addresses the problem of policy selection in domains with abundant logged data, but with a restricted interaction budget. Solving this problem would enable safe evaluation and deployment of offline reinforcement learning policies in industry, robotics, and recommendation domains among others. Several off-policy evaluation (OPE) techniques have been proposed to assess the value of policies using only logged data. However, there is still a big gap between the evaluation by OPE and the full online evaluation. Yet, large amounts of online interactions are often not possible in practice. To overcome this problem, we introduce active offline policy selection - a novel sequential decision approach that combines logged data with online interaction to identify the best policy. We use OPE estimates to warm start the online evaluation. Then, in order to utilize the limited environment interactions wisely we decide which policy to evaluate next based on a Bayesian optimization method with a kernel that represents policy similarity. We use multiple benchmarks, including real-world robotics, with a large number of candidate policies to show that the proposed approach improves upon state-of-the-art OPE estimates and pure online policy evaluation.
With the surge in the number of hyperparameters and training times of modern machine learning models, hyperparameter tuning is becoming increasingly expensive. However, after assessing 40 tuning methods systematically, we find that each faces certain limitations. In particular, methods that speed up tuning via knowledge transfer typically require the final performance of hyperparameters and do not focus on low-fidelity information. As we demonstrate empirically, this common practice is suboptimal and can incur an unnecessary use of resources. It is more cost-efficient to instead leverage low-fidelity tuning observations to measure inter-task similarity and transfer knowledge from existing to new tasks accordingly. However, performing multi-fidelity tuning comes with its own challenges in the transfer setting: the noise in additional observations and the need for performance forecasting. Therefore, we propose and conduct a thorough analysis of a multi-task multi-fidelity Bayesian optimization framework, which leads to the best instantiation--amortized auto-tuning (AT2). We further present an offline-computed 27-task hyperparameter recommendation (HyperRec) database to serve the community. Extensive experiments on HyperRec and other real-world databases illustrate the effectiveness of our AT2 method.
Bayesian optimization (BO) is a popular method for optimizing expensive-to-evaluate black-box functions. BO budgets are typically given in iterations, which implicitly assumes each evaluation has the same cost. In fact, in many BO applications, evaluation costs vary significantly in different regions of the search space. In hyperparameter optimization, the time spent on neural network training increases with layer size; in clinical trials, the monetary cost of drug compounds vary; and in optimal control, control actions have differing complexities. Cost-constrained BO measures convergence with alternative cost metrics such as time, money, or energy, for which the sample efficiency of standard BO methods is ill-suited. For cost-constrained BO, cost efficiency is far more important than sample efficiency. In this paper, we formulate cost-constrained BO as a constrained Markov decision process (CMDP), and develop an efficient rollout approximation to the optimal CMDP policy that takes both the cost and future iterations into account. We validate our method on a collection of hyperparameter optimization problems as well as a sensor set selection application.
We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design optimization via lab experiments, discrete and continuous variables correspond to the presence/absence of primitive elements and their relative concentrations respectively. The key challenge is to accurately model the complex interactions between discrete and continuous variables. In this paper, we propose a novel approach referred as Hybrid Bayesian Optimization (HyBO) by utilizing diffusion kernels, which are naturally defined over continuous and discrete variables. We develop a principled approach for constructing diffusion kernels over hybrid spaces by utilizing the additive kernel formulation, which allows additive interactions of all orders in a tractable manner. We theoretically analyze the modeling strength of additive hybrid kernels and prove that it has the universal approximation property. Our experiments on synthetic and six diverse real-world benchmarks show that HyBO significantly outperforms the state-of-the-art methods.
In the field of machine learning (ML) for materials optimization, active learning algorithms, such as Bayesian Optimization (BO), have been leveraged for guiding autonomous and high-throughput experimentation systems. However, very few studies have evaluated the efficiency of BO as a general optimization algorithm across a broad range of experimental materials science domains. In this work, we evaluate the performance of BO algorithms with a collection of surrogate model and acquisition function pairs across five diverse experimental materials systems, namely carbon nanotube polymer blends, silver nanoparticles, lead-halide perovskites, as well as additively manufactured polymer structures and shapes. By defining acceleration and enhancement metrics for general materials optimization objectives, we find that for surrogate model selection, Gaussian Process (GP) with anisotropic kernels (automatic relevance detection, ARD) and Random Forests (RF) have comparable performance and both outperform the commonly used GP without ARD. We discuss the implicit distributional assumptions of RF and GP, and the benefits of using GP with anisotropic kernels in detail. We provide practical insights for experimentalists on surrogate model selection of BO during materials optimization campaigns.
The goal of Multi-task Bayesian Optimization (MBO) is to minimize the number of queries required to accurately optimize a target black-box function, given access to offline evaluations of other auxiliary functions. When offline datasets are large, the scalability of prior approaches comes at the expense of expressivity and inference quality. We propose JUMBO, an MBO algorithm that sidesteps these limitations by querying additional data based on a combination of acquisition signals derived from training two Gaussian Processes (GP): a cold-GP operating directly in the input domain and a warm-GP that operates in the feature space of a deep neural network pretrained using the offline data. Such a decomposition can dynamically control the reliability of information derived from the online and offline data and the use of pretrained neural networks permits scalability to large offline datasets. Theoretically, we derive regret bounds for JUMBO and show that it achieves no-regret under conditions analogous to GP-UCB (Srinivas et. al. 2010). Empirically, we demonstrate significant performance improvements over existing approaches on two real-world optimization problems: hyper-parameter optimization and automated circuit design.
Generating droplets from a continuous stream of fluid requires precise tuning of a device to find optimized control parameter conditions. It is analytically intractable to compute the necessary control parameter values of a droplet-generating device that produces optimized droplets. Furthermore, as the length scale of the fluid flow changes, the formation physics and optimized conditions that induce flow decomposition into droplets also change. Hence, a single proportional integral derivative controller is too inflexible to optimize devices of different length scales or different control parameters, while classification machine learning techniques take days to train and require millions of droplet images. Therefore, the question is posed, can a single method be created that universally optimizes multiple length-scale droplets using only a few data points and is faster than previous approaches? In this paper, a Bayesian optimization and computer vision feedback loop is designed to quickly and reliably discover the control parameter values that generate optimized droplets within different length-scale devices. This method is demonstrated to converge on optimum parameter values using 60 images in only 2.3 hours, 30x faster than previous approaches. Model implementation is demonstrated for two different length-scale devices: a milliscale inkjet device and a microfluidics device.
The learning rate (LR) schedule is one of the most important hyper-parameters needing careful tuning in training DNNs. However, it is also one of the least automated parts of machine learning systems and usually costs significant manual effort and computing. Though there are pre-defined LR schedules and optimizers with adaptive LR, they introduce new hyperparameters that need to be tuned separately for different tasks/datasets. In this paper, we consider the question: Can we automatically tune the LR over the course of training without human involvement? We propose an efficient method, AutoLRS, which automatically optimizes the LR for each training stage by modeling training dynamics. AutoLRS aims to find an LR applied to every $\tau$ steps that minimizes the resulted validation loss. We solve this black-box optimization on the fly by Bayesian optimization (BO). However, collecting training instances for BO requires a system to evaluate each LR queried by BO's acquisition function for $\tau$ steps, which is prohibitively expensive in practice. Instead, we apply each candidate LR for only $\tau'\ll\tau$ steps and train an exponential model to predict the validation loss after $\tau$ steps. This mutual-training process between BO and the loss-prediction model allows us to limit the training steps invested in the BO search. We demonstrate the advantages and the generality of AutoLRS through extensive experiments of training DNNs for tasks from diverse domains using different optimizers. The LR schedules auto-generated by AutoLRS lead to a speedup of $1.22\times$, $1.43\times$, and $1.5\times$ when training ResNet-50, Transformer, and BERT, respectively, compared to the LR schedules in their original papers, and an average speedup of $1.31\times$ over state-of-the-art heavily-tuned LR schedules.
Optimizing multiple competing black-box objectives is a challenging problem in many fields, including science, engineering, and machine learning. Multi-objective Bayesian optimization (MOBO) is a sample-efficient approach for identifying the optimal trade-offs between the objectives. However, many existing methods perform poorly when the observations are corrupted by noise. We propose a novel acquisition function, NEHVI, that overcomes this important practical limitation by applying a Bayesian treatment to the popular expected hypervolume improvement (EHVI) criterion and integrating over this uncertainty in the Pareto frontier. We argue that, even in the noiseless setting, generating multiple candidates in parallel is an incarnation of EHVI with uncertainty in the Pareto frontier and therefore can be addressed using the same underlying technique. Through this lens, we derive a natural parallel variant, $q$NEHVI, that reduces computational complexity of parallel EHVI from exponential to polynomial with respect to the batch size. $q$NEHVI is one-step Bayes-optimal for hypervolume maximization in both noisy and noiseless environments, and we show that it can be optimized effectively with gradient-based methods via sample average approximation. Empirically, we demonstrate not only that $q$NEHVI is substantially more robust to observation noise than existing MOBO approaches, but also that it achieves state-of-the-art optimization performance and competitive wall-times in large-batch environments.
Radiotherapy inverse planning often requires planners to modify parameters in the treatment planning system's objective function to produce clinically acceptable plans. Due to the manual steps in this process, plan quality can vary depending on the planning time available and the planner's skills. This study investigates two hyperparameter-tuning methods for automated inverse planning. Because this framework does not train a model on previously-optimized plans, it can be readily adapted to practice pattern changes, and plan quality is not limited by that of a training cohort. We selected 10 patients who received lung SBRT using manually-generated clinical plans. We used random sampling (RS) and Bayesian optimization (BO) to tune parameters using linear-quadratic utility functions based on 11 clinical goals. Normalizing all plans to have PTV D95 equal to 48 Gy, we compared plan quality for the automatically-generated and manually-generated plans. We also investigated the impact of iteration count on the automatically-generated plans, comparing planning time and plan utility for RS and BO plans with and without stopping criteria. Without stopping criteria, the median planning time was 1.9 and 2.3 hours for RS and BO plans. The OAR doses in the RS and BO plans had a median percent difference (MPD) of 48.7% and 60.4% below clinical dose limits and an MPD of 2.8% and 3.3% below clinical plan doses. With stopping criteria, the utility decreased by an MPD of 5.3% and 3.9% for RS and BO plans, but the median planning time was reduced to 0.5 and 0.7 hours, and the OAR doses still had an MPD of 42.9% and 49.7% below clinical dose limits and an MPD of 0.3% and 1.8% below clinical plan doses. This study demonstrates that hyperparameter-tuning approaches to automated inverse planning can reduce active planning time with plan quality that is similar to or better than manually-generated plans.
Tensor computations overwhelm traditional general-purpose computing devices due to the large amounts of data and operations of the computations. They call for a holistic solution composed of both hardware acceleration and software mapping. Hardware/software (HW/SW) co-design optimizes the hardware and software in concert and produces high-quality solutions. There are two main challenges in the co-design flow. First, multiple methods exist to partition tensor computation and have different impacts on performance and energy efficiency. Besides, the hardware part must be implemented by the intrinsic functions of spatial accelerators. It is hard for programmers to identify and analyze the partitioning methods manually. Second, the overall design space composed of HW/SW partitioning, hardware optimization, and software optimization is huge. The design space needs to be efficiently explored. To this end, we propose an agile co-design approach HASCO that provides an efficient HW/SW solution to dense tensor computation. We use tensor syntax trees as the unified IR, based on which we develop a two-step approach to identify partitioning methods. For each method, HASCO explores the hardware and software design spaces. We propose different algorithms for the explorations, as they have distinct objectives and evaluation costs. Concretely, we develop a multi-objective Bayesian optimization algorithm to explore hardware optimization. For software optimization, we use heuristic and Q-learning algorithms. Experiments demonstrate that HASCO achieves a 1.25X to 1.44X latency reduction through HW/SW co-design compared with developing the hardware and software separately.
In this paper, we develop a ytopt autotuning framework that leverages Bayesian optimization to explore the parameter space search and compare four different supervised learning methods within Bayesian optimization and evaluate their effectiveness. We select six of the most complex PolyBench benchmarks and apply the newly developed LLVM Clang/Polly loop optimization pragmas to the benchmarks to optimize them. We then use the autotuning framework to optimize the pragma parameters to improve their performance. The experimental results show that our autotuning approach outperforms the other compiling methods to provide the smallest execution time for the benchmarks syr2k, 3mm, heat-3d, lu, and covariance with two large datasets in 200 code evaluations for effectively searching the parameter spaces with up to 170,368 different configurations. We find that the Floyd-Warshall benchmark did not benefit from autotuning because Polly uses heuristics to optimize the benchmark to make it run much slower. To cope with this issue, we provide some compiler option solutions to improve the performance. Then we present loop autotuning without a user's knowledge using a simple mctree autotuning framework to further improve the performance of the Floyd-Warshall benchmark. We also extend the ytopt autotuning framework to tune a deep learning application.
Bayesian optimization (BO) is a popular paradigm for global optimization of expensive black-box functions, but there are many domains where the function is not completely a black-box. The data may have some known structure (e.g. symmetries) and/or the data generation process may be a composite process that yields useful intermediate or auxiliary information in addition to the value of the optimization objective. However, surrogate models traditionally employed in BO, such as Gaussian Processes (GPs), scale poorly with dataset size and do not easily accommodate known structure. Instead, we use Bayesian neural networks, a class of scalable and flexible surrogate models with inductive biases, to extend BO to complex, structured problems with high dimensionality. We demonstrate BO on a number of realistic problems in physics and chemistry, including topology optimization of photonic crystal materials using convolutional neural networks, and chemical property optimization of molecules using graph neural networks. On these complex tasks, we show that neural networks often outperform GPs as surrogate models for BO in terms of both sampling efficiency and computational cost.
This paper introduces a probabilistic framework to estimate parameters of an acquisition function given observed human behavior that can be modeled as a collection of sample paths from a Bayesian optimization procedure. The methodology involves defining a likelihood on observed human behavior from an optimization task, where the likelihood is parameterized by a Bayesian optimization subroutine governed by an unknown acquisition function. This structure enables us to make inference on a subject's acquisition function while allowing their behavior to deviate around the solution to the Bayesian optimization subroutine. To test our methods, we designed a sequential optimization task which forced subjects to balance exploration and exploitation in search of an invisible target location. Applying our proposed methods to the resulting data, we find that many subjects tend to exhibit exploration preferences beyond that of standard acquisition functions to capture. Guided by the model discrepancies, we augment the candidate acquisition functions to yield a superior fit to the human behavior in this task.
In many real-world problems, we want to infer some property of an expensive black-box function $f$, given a budget of $T$ function evaluations. One example is budget constrained global optimization of $f$, for which Bayesian optimization is a popular method. Other properties of interest include local optima, level sets, integrals, or graph-structured information induced by $f$. Often, we can find an algorithm $\mathcal{A}$ to compute the desired property, but it may require far more than $T$ queries to execute. Given such an $\mathcal{A}$, and a prior distribution over $f$, we refer to the problem of inferring the output of $\mathcal{A}$ using $T$ evaluations as Bayesian Algorithm Execution (BAX). To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. Applying this to Dijkstra's algorithm, for instance, we infer shortest paths in synthetic and real-world graphs with black-box edge costs. Using evolution strategies, we yield variants of Bayesian optimization that target local, rather than global, optima. On these problems, InfoBAX uses up to 500 times fewer queries to $f$ than required by the original algorithm. Our method is closely connected to other Bayesian optimal experimental design procedures such as entropy search methods and optimal sensor placement using Gaussian processes.
Bayesian optimization (BO) is a widely popular approach for the hyperparameter optimization (HPO) in machine learning. At its core, BO iteratively evaluates promising configurations until a user-defined budget, such as wall-clock time or number of iterations, is exhausted. While the final performance after tuning heavily depends on the provided budget, it is hard to pre-specify an optimal value in advance. In this work, we propose an effective and intuitive termination criterion for BO that automatically stops the procedure if it is sufficiently close to the global optimum. Our key insight is that the discrepancy between the true objective (predictive performance on test data) and the computable target (validation performance) suggests stopping once the suboptimality in optimizing the target is dominated by the statistical estimation error. Across an extensive range of real-world HPO problems and baselines, we show that our termination criterion achieves a better trade-off between the test performance and optimization time. Additionally, we find that overfitting may occur in the context of HPO, which is arguably an overlooked problem in the literature, and show how our termination criterion helps to mitigate this phenomenon on both small and large datasets.
We propose a novel surrogate-assisted Evolutionary Algorithm for solving expensive combinatorial optimization problems. We integrate a surrogate model, which is used for fitness value estimation, into a state-of-the-art P3-like variant of the Gene-Pool Optimal Mixing Algorithm (GOMEA) and adapt the resulting algorithm for solving non-binary combinatorial problems. We test the proposed algorithm on an ensemble learning problem. Ensembling several models is a common Machine Learning technique to achieve better performance. We consider ensembles of several models trained on disjoint subsets of a dataset. Finding the best dataset partitioning is naturally a combinatorial non-binary optimization problem. Fitness function evaluations can be extremely expensive if complex models, such as Deep Neural Networks, are used as learners in an ensemble. Therefore, the number of fitness function evaluations is typically limited, necessitating expensive optimization techniques. In our experiments we use five classification datasets from the OpenML-CC18 benchmark and Support-vector Machines as learners in an ensemble. The proposed algorithm demonstrates better performance than alternative approaches, including Bayesian optimization algorithms. It manages to find better solutions using just several thousand fitness function evaluations for an ensemble learning problem with up to 500 variables.