Bayesian optimization (BO) with Gaussian processes (GP) has become an indispensable algorithm for black box optimization problems. Not without a dash of irony, BO is often considered a black box itself, lacking ways to provide reasons as to why certain parameters are proposed to be evaluated. This is particularly relevant in human-in-the-loop applications of BO, such as in robotics. We address this issue by proposing ShapleyBO, a framework for interpreting BO's proposals by game-theoretic Shapley values.They quantify each parameter's contribution to BO's acquisition function. Exploiting the linearity of Shapley values, we are further able to identify how strongly each parameter drives BO's exploration and exploitation for additive acquisition functions like the confidence bound. We also show that ShapleyBO can disentangle the contributions to exploration into those that explore aleatoric and epistemic uncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human machine interface (HMI), allowing users to interfere with BO in case proposals do not align with human reasoning. We demonstrate this HMI's benefits for the use case of personalizing wearable robotic devices (assistive back exosuits) by human-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO can achieve lower regret than teams without.
We introduce a cooperative Bayesian optimization problem for optimizing black-box functions of two variables where two agents choose together at which points to query the function but have only control over one variable each. This setting is inspired by human-AI teamwork, where an AI-assistant helps its human user solve a problem, in this simplest case, collaborative optimization. We formulate the solution as sequential decision-making, where the agent we control models the user as a computationally rational agent with prior knowledge about the function. We show that strategic planning of the queries enables better identification of the global maximum of the function as long as the user avoids excessive exploration. This planning is made possible by using Bayes Adaptive Monte Carlo planning and by endowing the agent with a user model that accounts for conservative belief updates and exploratory sampling of the points to query.
The optimization of a black-box simulator over control parameters $\mathbf{x}$ arises in a myriad of scientific applications. In such applications, the simulator often takes the form $f(\mathbf{x},\boldsymbol{\theta})$, where $\boldsymbol{\theta}$ are parameters that are uncertain in practice. Robust optimization aims to optimize the objective $\mathbb{E}[f(\mathbf{x},\boldsymbol{\Theta})]$, where $\boldsymbol{\Theta} \sim \mathcal{P}$ is a random variable that models uncertainty on $\boldsymbol{\theta}$. For this, existing black-box methods typically employ a two-stage approach for selecting the next point $(\mathbf{x},\boldsymbol{\theta})$, where $\mathbf{x}$ and $\boldsymbol{\theta}$ are optimized separately via different acquisition functions. As such, these approaches do not employ a joint acquisition over $(\mathbf{x},\boldsymbol{\theta})$, and thus may fail to fully exploit control-to-noise interactions for effective robust optimization. To address this, we propose a new Bayesian optimization method called Targeted Variance Reduction (TVR). The TVR leverages a novel joint acquisition function over $(\mathbf{x},\boldsymbol{\theta})$, which targets variance reduction on the objective within the desired region of improvement. Under a Gaussian process surrogate on $f$, the TVR acquisition can be evaluated in closed form, and reveals an insightful exploration-exploitation-precision trade-off for robust black-box optimization. The TVR can further accommodate a broad class of non-Gaussian distributions on $\mathcal{P}$ via a careful integration of normalizing flows. We demonstrate the improved performance of TVR over the state-of-the-art in a suite of numerical experiments and an application to the robust design of automobile brake discs under operational uncertainty.
Bayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the exploitation-exploration dilemma. Thompson sampling (TS) is a preferred solution for BO to handle the exploitation-exploration trade-off. While it prioritizes exploration by generating and minimizing random sample paths from probabilistic models -- a fundamental ingredient of BO -- TS weakly manages exploitation by gathering information about the true objective function after it obtains new observations. In this work, we improve the exploitation of TS by incorporating the $\varepsilon$-greedy policy, a well-established selection strategy in reinforcement learning. We first delineate two extremes of TS, namely the generic TS and the sample-average TS. The former promotes exploration, while the latter favors exploitation. We then adopt the $\varepsilon$-greedy policy to randomly switch between these two extremes. Small and large values of $\varepsilon$ govern exploitation and exploration, respectively. By minimizing two benchmark functions and solving an inverse problem of a steel cantilever beam, we empirically show that $\varepsilon$-greedy TS equipped with an appropriate $\varepsilon$ is more robust than its two extremes, matching or outperforming the better of the generic TS and the sample-average TS.
Spiking Neural Networks (SNN). SNNs are based on a more biologically inspired approach than usual artificial neural networks. Such models are characterized by complex dynamics between neurons and spikes. These are very sensitive to the hyperparameters, making their optimization challenging. To tackle hyperparameter optimization of SNNs, we initially extended the signal loss issue of SNNs to what we call silent networks. These networks fail to emit enough spikes at their outputs due to mistuned hyperparameters or architecture. Generally, search spaces are heavily restrained, sometimes even discretized, to prevent the sampling of such networks. By defining an early stopping criterion detecting silent networks and by designing specific constraints, we were able to instantiate larger and more flexible search spaces. We applied a constrained Bayesian optimization technique, which was asynchronously parallelized, as the evaluation time of a SNN is highly stochastic. Large-scale experiments were carried-out on a multi-GPU Petascale architecture. By leveraging silent networks, results show an acceleration of the search, while maintaining good performances of both the optimization algorithm and the best solution obtained. We were able to apply our methodology to two popular training algorithms, known as spike timing dependent plasticity and surrogate gradient. Early detection allowed us to prevent worthless and costly computation, directing the search toward promising hyperparameter combinations. Our methodology could be applied to multi-objective problems, where the spiking activity is often minimized to reduce the energy consumption. In this scenario, it becomes essential to find the delicate frontier between low-spiking and silent networks. Finally, our approach may have implications for neural architecture search, particularly in defining suitable spiking architectures.
Experimental (design) optimization is a key driver in designing and discovering new products and processes. Bayesian Optimization (BO) is an effective tool for optimizing expensive and black-box experimental design processes. While Bayesian optimization is a principled data-driven approach to experimental optimization, it learns everything from scratch and could greatly benefit from the expertise of its human (domain) experts who often reason about systems at different abstraction levels using physical properties that are not necessarily directly measured (or measurable). In this paper, we propose a human-AI collaborative Bayesian framework to incorporate expert preferences about unmeasured abstract properties into the surrogate modeling to further boost the performance of BO. We provide an efficient strategy that can also handle any incorrect/misleading expert bias in preferential judgments. We discuss the convergence behavior of our proposed framework. Our experimental results involving synthetic functions and real-world datasets show the superiority of our method against the baselines.
Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We investigate replacing this de facto stopping rule with criteria based on the probability that a point satisfies a given set of conditions. We focus on the prototypical example of an $(\epsilon, \delta)$-criterion: stop when a solution has been found whose value is within $\epsilon > 0$ of the optimum with probability at least $1 - \delta$ under the model. For Gaussian process priors, we show that Bayesian optimization satisfies this criterion under mild technical assumptions. Further, we give a practical algorithm for evaluating Monte Carlo stopping rules in a manner that is both sample efficient and robust to estimation error. These findings are accompanied by empirical results which demonstrate the strengths and weaknesses of the proposed approach.
Laser-directed-energy deposition (DED) offers advantages in additive manufacturing (AM) for creating intricate geometries and material grading. Yet, challenges like material inconsistency and part variability remain, mainly due to its layer-wise fabrication. A key issue is heat accumulation during DED, which affects the material microstructure and properties. While closed-loop control methods for heat management are common in DED research, few integrate real-time monitoring, physics-based modeling, and control in a unified framework. Our work presents a digital twin (DT) framework for real-time predictive control of DED process parameters to meet specific design objectives. We develop a surrogate model using Long Short-Term Memory (LSTM)-based machine learning with Bayesian Inference to predict temperatures in DED parts. This model predicts future temperature states in real time. We also introduce Bayesian Optimization (BO) for Time Series Process Optimization (BOTSPO), based on traditional BO but featuring a unique time series process profile generator with reduced dimensions. BOTSPO dynamically optimizes processes, identifying optimal laser power profiles to attain desired mechanical properties. The established process trajectory guides online optimizations, aiming to enhance performance. This paper outlines the digital twin framework's components, promoting its integration into a comprehensive system for AM.
With the rise in engineered biomolecular devices, there is an increased need for tailor-made biological sequences. Often, many similar biological sequences need to be made for a specific application meaning numerous, sometimes prohibitively expensive, lab experiments are necessary for their optimization. This paper presents a transfer learning design of experiments workflow to make this development feasible. By combining a transfer learning surrogate model with Bayesian optimization, we show how the total number of experiments can be reduced by sharing information between optimization tasks. We demonstrate the reduction in the number of experiments using data from the development of DNA competitors for use in an amplification-based diagnostic assay. We use cross-validation to compare the predictive accuracy of different transfer learning models, and then compare the performance of the models for both single objective and penalized optimization tasks.
Reinforcement learning (RL) has revolutionized decision-making across a wide range of domains over the past few decades. Yet, deploying RL policies in real-world scenarios presents the crucial challenge of ensuring safety. Traditional safe RL approaches have predominantly focused on incorporating predefined safety constraints into the policy learning process. However, this reliance on predefined safety constraints poses limitations in dynamic and unpredictable real-world settings where such constraints may not be available or sufficiently adaptable. Bridging this gap, we propose a novel approach that concurrently learns a safe RL control policy and identifies the unknown safety constraint parameters of a given environment. Initializing with a parametric signal temporal logic (pSTL) safety specification and a small initial labeled dataset, we frame the problem as a bilevel optimization task, intricately integrating constrained policy optimization, using a Lagrangian-variant of the twin delayed deep deterministic policy gradient (TD3) algorithm, with Bayesian optimization for optimizing parameters for the given pSTL safety specification. Through experimentation in comprehensive case studies, we validate the efficacy of this approach across varying forms of environmental constraints, consistently yielding safe RL policies with high returns. Furthermore, our findings indicate successful learning of STL safety constraint parameters, exhibiting a high degree of conformity with true environmental safety constraints. The performance of our model closely mirrors that of an ideal scenario that possesses complete prior knowledge of safety constraints, demonstrating its proficiency in accurately identifying environmental safety constraints and learning safe policies that adhere to those constraints.
We consider a sequential decision making task, where the goal is to optimize an unknown function without evaluating parameters that violate an a~priori unknown (safety) constraint. A common approach is to place a Gaussian process prior on the unknown functions and allow evaluations only in regions that are safe with high probability. Most current methods rely on a discretization of the domain and cannot be directly extended to the continuous case. Moreover, the way in which they exploit regularity assumptions about the constraint introduces an additional critical hyperparameter. In this paper, we propose an information-theoretic safe exploration criterion that directly exploits the GP posterior to identify the most informative safe parameters to evaluate. The combination of this exploration criterion with a well known Bayesian optimization acquisition function yields a novel safe Bayesian optimization selection criterion. Our approach is naturally applicable to continuous domains and does not require additional explicit hyperparameters. We theoretically analyze the method and show that we do not violate the safety constraint with high probability and that we learn about the value of the safe optimum up to arbitrary precision. Empirical evaluations demonstrate improved data-efficiency and scalability.
Sequential learning methods, such as active learning and Bayesian optimization, aim to select the most informative data for task learning. In many applications, however, data selection is constrained by unknown safety conditions, motivating the development of safe learning approaches. A promising line of safe learning methods uses Gaussian processes to model safety conditions, restricting data selection to areas with high safety confidence. However, these methods are limited to local exploration around an initial seed dataset, as safety confidence centers around observed data points. As a consequence, task exploration is slowed down and safe regions disconnected from the initial seed dataset remain unexplored. In this paper, we propose safe transfer sequential learning to accelerate task learning and to expand the explorable safe region. By leveraging abundant offline data from a related source task, our approach guides exploration in the target task more effectively. We also provide a theoretical analysis to explain why single-task method cannot cope with disconnected regions. Finally, we introduce a computationally efficient approximation of our method that reduces runtime through pre-computations. Our experiments demonstrate that this approach, compared to state-of-the-art methods, learns tasks with lower data consumption and enhances global exploration across multiple disjoint safe regions, while maintaining comparable computational efficiency.
The large volume and complexity of medical imaging datasets are bottlenecks for storage, transmission, and processing. To tackle these challenges, the application of low-rank matrix approximation (LRMA) and its derivative, local LRMA (LLRMA) has demonstrated potential. A detailed analysis of the literature identifies LRMA and LLRMA methods applied to various imaging modalities, and the challenges and limitations associated with existing LRMA and LLRMA methods are addressed. We note a significant shift towards a preference for LLRMA in the medical imaging field since 2015, demonstrating its potential and effectiveness in capturing complex structures in medical data compared to LRMA. Acknowledging the limitations of shallow similarity methods used with LLRMA, we suggest advanced semantic image segmentation for similarity measure, explaining in detail how it can be used to measure similar patches and its feasibility. We note that LRMA and LLRMA are mainly applied to unstructured medical data, and we propose extending their application to different medical data types, including structured and semi-structured. This paper also discusses how LRMA and LLRMA can be applied to regular data with missing entries and the impact of inaccuracies in predicting missing values and their effects. We discuss the impact of patch size and propose the use of random search (RS) to determine the optimal patch size. To enhance feasibility, a hybrid approach using Bayesian optimization and RS is proposed, which could improve the application of LRMA and LLRMA in medical imaging.
Physics informed neural networks (PINNs) have recently been proposed as surrogate models for solving process optimization problems. However, in an active learning setting collecting enough data for reliably training PINNs poses a challenge. This study proposes a broadly applicable method for incorporating physics information into existing machine learning (ML) models of any type. The proposed method - referred to as PI-CoF for Physics-Informed Correction Factors - introduces additive or multiplicative correction factors for pointwise inference, which are identified by solving a regularized unconstrained optimization problem for reconciliation of physics information and ML model predictions. When ML models are used in an optimization context, using the proposed approach translates into a bilevel optimization problem, where the reconciliation problem is solved as an inner problem each time before evaluating the objective and constraint functions of the outer problem. The utility of the proposed approach is demonstrated through a numerical example, emphasizing constraint satisfaction in a safe Bayesian optimization (BO) setting. Furthermore, a simulation study is carried out by using PI-CoF for the real-time optimization of a fuel cell system. The results show reduced fuel consumption and better reference tracking performance when using the proposed PI-CoF approach in comparison to a constrained BO algorithm not using physics information.
Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often non-differentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time-consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest towards active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge on the system in form of partially known physics laws and often varies exploration policies during the experiment. Here, we explore interactive workflows building on multi-fidelity BO (MFBO), starting with classical (data-driven) MFBO, then structured (physics-driven) sMFBO, and extending it to allow human in the loop interactive iMFBO workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly non-smooth multi-fidelity simulation data generated from an Ising model, considering spin-spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and on-the-fly human decisions for improved exploration, current challenges, and potential opportunities for algorithm development with combining data, physics and real time human decisions.
Given a Hyperparameter Optimization(HPO) problem, how to design an algorithm to find optimal configurations efficiently? Bayesian Optimization(BO) and the multi-fidelity BO methods employ surrogate models to sample configurations based on history evaluations. More recent studies obtain better performance by integrating BO with HyperBand(HB), which accelerates evaluation by early stopping mechanism. However, these methods ignore the advantage of a suitable evaluation scheme over the default HyperBand, and the capability of BO is still constrained by skewed evaluation results. In this paper, we propose FlexHB, a new method pushing multi-fidelity BO to the limit as well as re-designing a framework for early stopping with Successive Halving(SH). Comprehensive study on FlexHB shows that (1) our fine-grained fidelity method considerably enhances the efficiency of searching optimal configurations, (2) our FlexBand framework (self-adaptive allocation of SH brackets, and global ranking of configurations in both current and past SH procedures) grants the algorithm with more flexibility and improves the anytime performance. Our method achieves superior efficiency and outperforms other methods on various HPO tasks. Empirical results demonstrate that FlexHB can achieve up to 6.9X and 11.1X speedups over the state-of-the-art MFES-HB and BOHB respectively.
The ability to extract material parameters of perovskite from quantitative experimental analysis is essential for rational design of photovoltaic and optoelectronic applications. However, the difficulty of this analysis increases significantly with the complexity of the theoretical model and the number of material parameters for perovskite. Here we use Bayesian optimization to develop an analysis platform that can extract up to 8 fundamental material parameters of an organometallic perovskite semiconductor from a transient photoluminescence experiment, based on a complex full physics model that includes drift-diffusion of carriers and dynamic defect occupation. An example study of thermal degradation reveals that the carrier mobility and trap-assisted recombination coefficient are reduced noticeably, while the defect energy level remains nearly unchanged. The reduced carrier mobility can dominate the overall effect on thermal degradation of perovskite solar cells by reducing the fill factor, despite the opposite effect of the reduced trap-assisted recombination coefficient on increasing the fill factor. In future, this platform can be conveniently applied to other experiments or to combinations of experiments, accelerating materials discovery and optimization of semiconductor materials for photovoltaics and other applications.
Bayesian optimization is a widely used technique for optimizing black-box functions, with Expected Improvement (EI) being the most commonly utilized acquisition function in this domain. While EI is often viewed as distinct from other information-theoretic acquisition functions, such as entropy search (ES) and max-value entropy search (MES), our work reveals that EI can be considered a special case of MES when approached through variational inference (VI). In this context, we have developed the Variational Entropy Search (VES) methodology and the VES-Gamma algorithm, which adapts EI by incorporating principles from information-theoretic concepts. The efficacy of VES-Gamma is demonstrated across a variety of test functions and read datasets, highlighting its theoretical and practical utilities in Bayesian optimization scenarios.
Bayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in particular, the search space of the next query may depend on previous ones. Example challenges arise in the physical sciences in the form of local movement constraints, required monotonicity in certain variables, and transitions influencing the accuracy of measurements. Altogether, such transition constraints necessitate a form of planning. This work extends classical Bayesian optimization via the framework of Markov Decision Processes. We iteratively solve a tractable linearization of our utility function using reinforcement learning to obtain a policy that plans ahead for the entire horizon. This is a parallel to the optimization of an acquisition function in policy space. The resulting policy is potentially history-dependent and non-Markovian. We showcase applications in chemical reactor optimization, informative path planning, machine calibration, and other synthetic examples.
Adapting to a priori unknown noise level is a very important but challenging problem in sequential decision-making as efficient exploration typically requires knowledge of the noise level, which is often loosely specified. We report significant progress in addressing this issue for linear bandits in two respects. First, we propose a novel confidence set that is `semi-adaptive' to the unknown sub-Gaussian parameter $\sigma_*^2$ in the sense that the (normalized) confidence width scales with $\sqrt{d\sigma_*^2 + \sigma_0^2}$ where $d$ is the dimension and $\sigma_0^2$ is the specified sub-Gaussian parameter (known) that can be much larger than $\sigma_*^2$. This is a significant improvement over $\sqrt{d\sigma_0^2}$ of the standard confidence set of Abbasi-Yadkori et al. (2011), especially when $d$ is large or $\sigma_*^2=0$. We show that this leads to an improved regret bound in linear bandits. Second, for bounded rewards, we propose a novel variance-adaptive confidence set that has much improved numerical performance upon prior art. We then apply this confidence set to develop, as we claim, the first practical variance-adaptive linear bandit algorithm via an optimistic approach, which is enabled by our novel regret analysis technique. Both of our confidence sets rely critically on `regret equality' from online learning. Our empirical evaluation in diverse Bayesian optimization tasks shows that our proposed algorithms demonstrate better or comparable performance compared to existing methods.