We approach the problem of designing an automated trading strategy that can consistently profit by adapting to changing market conditions. This challenge can be framed as a Nonstationary Continuum-Armed Bandit (NCAB) problem. To solve the NCAB problem, we propose PRBO, a novel trading algorithm that uses Bayesian optimization and a ``bandit-over-bandit'' framework to dynamically adjust strategy parameters in response to market conditions. We use Bristol Stock Exchange (BSE) to simulate financial markets containing heterogeneous populations of automated trading agents and compare PRBO with PRSH, a reference trading strategy that adapts strategy parameters through stochastic hill-climbing. Results show that PRBO generates significantly more profit than PRSH, despite having fewer hyperparameters to tune. The code for PRBO and performing experiments is available online open-source (https://github.com/HarmoniaLeo/PRZI-Bayesian-Optimisation).
Changing conditions or environments can cause system dynamics to vary over time. To ensure optimal control performance, controllers should adapt to these changes. When the underlying cause and time of change is unknown, we need to rely on online data for this adaptation. In this paper, we will use time-varying Bayesian optimization (TVBO) to tune controllers online in changing environments using appropriate prior knowledge on the control objective and its changes. Two properties are characteristic of many online controller tuning problems: First, they exhibit incremental and lasting changes in the objective due to changes to the system dynamics, e.g., through wear and tear. Second, the optimization problem is convex in the tuning parameters. Current TVBO methods do not explicitly account for these properties, resulting in poor tuning performance and many unstable controllers through over-exploration of the parameter space. We propose a novel TVBO forgetting strategy using Uncertainty-Injection (UI), which incorporates the assumption of incremental and lasting changes. The control objective is modeled as a spatio-temporal Gaussian process (GP) with UI through a Wiener process in the temporal domain. Further, we explicitly model the convexity assumptions in the spatial dimension through GP models with linear inequality constraints. In numerical experiments, we show that our model outperforms the state-of-the-art method in TVBO, exhibiting reduced regret and fewer unstable parameter configurations.
Reinforcement learning (RL) offers the potential for training generally capable agents that can interact autonomously in the real world. However, one key limitation is the brittleness of RL algorithms to core hyperparameters and network architecture choice. Furthermore, non-stationarities such as evolving training data and increased agent complexity mean that different hyperparameters and architectures may be optimal at different points of training. This motivates AutoRL, a class of methods seeking to automate these design choices. One prominent class of AutoRL methods is Population-Based Training (PBT), which have led to impressive performance in several large scale settings. In this paper, we introduce two new innovations in PBT-style methods. First, we employ trust-region based Bayesian Optimization, enabling full coverage of the high-dimensional mixed hyperparameter search space. Second, we show that using a generational approach, we can also learn both architectures and hyperparameters jointly on-the-fly in a single training run. Leveraging the new highly parallelizable Brax physics engine, we show that these innovations lead to large performance gains, significantly outperforming the tuned baseline while learning entire configurations on the fly. Code is available at https://github.com/xingchenwan/bgpbt.
Bayesian optimization provides an effective method to optimize expensive-to-evaluate black box functions. It has been widely applied to problems in many fields, including notably in computer science, e.g. in machine learning to optimize hyperparameters of neural networks, and in engineering, e.g. in fluid dynamics to optimize control strategies that maximize drag reduction. This paper empirically studies and compares the performance and the robustness of common Bayesian optimization algorithms on a range of synthetic test functions to provide general guidance on the design of Bayesian optimization algorithms for specific problems. It investigates the choice of acquisition function, the effect of different numbers of training samples, the exact and Monte Carlo based calculation of acquisition functions, and both single-point and multi-point optimization. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of Bayesian optimization to specific challenges, and in general. To illustrate how these findings can be used to inform a Bayesian optimization setup tailored to a specific problem, two simulations in the area of computational fluid dynamics are optimized, giving evidence that suitable solutions can be found in a small number of evaluations of the objective function for complex, real problems. The results of our investigation can similarly be applied to other areas, such as machine learning and physical experiments, where objective functions are expensive to evaluate and their mathematical expressions are unknown.
MATSim (Multi-Agent Transport Simulation Toolkit) is an open source large-scale agent-based transportation planning project applied to various areas like road transport, public transport, freight transport, regional evacuation, etc. BEAM (Behavior, Energy, Autonomy, and Mobility) framework extends MATSim to enable powerful and scalable analysis of urban transportation systems. The agents from the BEAM simulation exhibit 'mode choice' behavior based on multinomial logit model. In our study, we consider eight mode choices viz. bike, car, walk, ride hail, driving to transit, walking to transit, ride hail to transit, and ride hail pooling. The 'alternative specific constants' for each mode choice are critical hyperparameters in a configuration file related to a particular scenario under experimentation. We use the 'Urbansim-10k' BEAM scenario (with 10,000 population size) for all our experiments. Since these hyperparameters affect the simulation in complex ways, manual calibration methods are time consuming. We present a parallel Bayesian optimization method with early stopping rule to achieve fast convergence for the given multi-in-multi-out problem to its optimal configurations. Our model is based on an open source HpBandSter package. This approach combines hierarchy of several 1D Kernel Density Estimators (KDE) with a cheap evaluator (Hyperband, a single multidimensional KDE). Our model has also incorporated extrapolation based early stopping rule. With our model, we could achieve a 25% L1 norm for a large-scale BEAM simulation in fully autonomous manner. To the best of our knowledge, our work is the first of its kind applied to large-scale multi-agent transportation simulations. This work can be useful for surrogate modeling of scenarios with very large populations.
Neural Processes (NPs) are a popular class of approaches for meta-learning. Similar to Gaussian Processes (GPs), NPs define distributions over functions and can estimate uncertainty in their predictions. However, unlike GPs, NPs and their variants suffer from underfitting and often have intractable likelihoods, which limit their applications in sequential decision making. We propose Transformer Neural Processes (TNPs), a new member of the NP family that casts uncertainty-aware meta learning as a sequence modeling problem. We learn TNPs via an autoregressive likelihood-based objective and instantiate it with a novel transformer-based architecture. The model architecture respects the inductive biases inherent to the problem structure, such as invariance to the observed data points and equivariance to the unobserved points. We further investigate knobs within the TNP framework that tradeoff expressivity of the decoding distribution with extra computation. Empirically, we show that TNPs achieve state-of-the-art performance on various benchmark problems, outperforming all previous NP variants on meta regression, image completion, contextual multi-armed bandits, and Bayesian optimization.
Neural networks' lack of robustness against attacks raises concerns in security-sensitive settings such as autonomous vehicles. While many countermeasures may look promising, only a few withstand rigorous evaluation. Defenses using random transformations (RT) have shown impressive results, particularly BaRT (Raff et al., 2019) on ImageNet. However, this type of defense has not been rigorously evaluated, leaving its robustness properties poorly understood. Their stochastic properties make evaluation more challenging and render many proposed attacks on deterministic models inapplicable. First, we show that the BPDA attack (Athalye et al., 2018a) used in BaRT's evaluation is ineffective and likely overestimates its robustness. We then attempt to construct the strongest possible RT defense through the informed selection of transformations and Bayesian optimization for tuning their parameters. Furthermore, we create the strongest possible attack to evaluate our RT defense. Our new attack vastly outperforms the baseline, reducing the accuracy by 83% compared to the 19% reduction by the commonly used EoT attack ($4.3\times$ improvement). Our result indicates that the RT defense on the Imagenette dataset (a ten-class subset of ImageNet) is not robust against adversarial examples. Extending the study further, we use our new attack to adversarially train RT defense (called AdvRT), resulting in a large robustness gain. Code is available at https://github.com/wagner-group/demystify-random-transform.
Bayesian optimization (BO) has become a popular strategy for global optimization of many expensive real-world functions. Contrary to a common belief that BO is suited to optimizing black-box functions, it actually requires domain knowledge on characteristics of those functions to deploy BO successfully. Such domain knowledge often manifests in Gaussian process priors that specify initial beliefs on functions. However, even with expert knowledge, it is not an easy task to select a prior. This is especially true for hyperparameter tuning problems on complex machine learning models, where landscapes of tuning objectives are often difficult to comprehend. We seek an alternative practice for setting these functional priors. In particular, we consider the scenario where we have data from similar functions that allow us to pre-train a tighter distribution a priori. To verify our approach in realistic model training setups, we collected a large multi-task hyperparameter tuning dataset by training tens of thousands of configurations of near-state-of-the-art models on popular image and text datasets, as well as a protein sequence dataset. Our results show that on average, our method is able to locate good hyperparameters at least 3 times more efficiently than the best competing methods.
Tree ensembles can be well-suited for black-box optimization tasks such as algorithm tuning and neural architecture search, as they achieve good predictive performance with little or no manual tuning, naturally handle discrete feature spaces, and are relatively insensitive to outliers in the training data. Two well-known challenges in using tree ensembles for black-box optimization are (i) effectively quantifying model uncertainty for exploration and (ii) optimizing over the piece-wise constant acquisition function. To address both points simultaneously, we propose using the kernel interpretation of tree ensembles as a Gaussian Process prior to obtain model variance estimates, and we develop a compatible optimization formulation for the acquisition function. The latter further allows us to seamlessly integrate known constraints to improve sampling efficiency by considering domain-knowledge in engineering settings and modeling search space symmetries, e.g., hierarchical relationships in neural architecture search. Our framework performs as well as state-of-the-art methods for unconstrained black-box optimization over continuous/discrete features and outperforms competing methods for problems combining mixed-variable feature spaces and known input constraints.
Unsupervised and semi-supervised ML methods such as variational autoencoders (VAE) have become widely adopted across multiple areas of physics, chemistry, and materials sciences due to their capability in disentangling representations and ability to find latent manifolds for classification and regression of complex experimental data. Like other ML problems, VAEs require hyperparameter tuning, e.g., balancing the Kullback Leibler (KL) and reconstruction terms. However, the training process and resulting manifold topology and connectivity depend not only on hyperparameters, but also their evolution during training. Because of the inefficiency of exhaustive search in a high-dimensional hyperparameter space for the expensive to train models, here we explored a latent Bayesian optimization (zBO) approach for the hyperparameter trajectory optimization for the unsupervised and semi-supervised ML and demonstrate for joint-VAE with rotational invariances. We demonstrate an application of this method for finding joint discrete and continuous rotationally invariant representations for MNIST and experimental data of a plasmonic nanoparticles material system. The performance of the proposed approach has been discussed extensively, where it allows for any high dimensional hyperparameter tuning or trajectory optimization of other ML models.
The acquisition function, a critical component in Bayesian optimization (BO), can often be written as the expectation of a utility function under a surrogate model. However, to ensure that acquisition functions are tractable to optimize, restrictions must be placed on the surrogate model and utility function. To extend BO to a broader class of models and utilities, we propose likelihood-free BO (LFBO), an approach based on likelihood-free inference. LFBO directly models the acquisition function without having to separately perform inference with a probabilistic surrogate model. We show that computing the acquisition function in LFBO can be reduced to optimizing a weighted classification problem, where the weights correspond to the utility being chosen. By choosing the utility function for expected improvement (EI), LFBO outperforms various state-of-the-art black-box optimization methods on several real-world optimization problems. LFBO can also effectively leverage composite structures of the objective function, which further improves its regret by several orders of magnitude.
Bayesian optimization (BO) is a typical approach to solve expensive optimization problems. In each iteration of BO, a Gaussian process(GP) model is trained using the previously evaluated solutions; then next candidate solutions for expensive evaluation are recommended by maximizing a cheaply-evaluated acquisition function on the trained surrogate model. The acquisition function plays a crucial role in the optimization process. However, each acquisition function has its own strengths and weaknesses, and no single acquisition function can consistently outperform the others on all kinds of problems. To better leverage the advantages of different acquisition functions, we propose a new method for batch BO. In each iteration, three acquisition functions are dynamically selected from a set based on their current and historical performance to form a multi-objective optimization problem (MOP). Using an evolutionary multi-objective algorithm to optimize such a MOP, a set of non-dominated solutions can be obtained. To select batch candidate solutions, we rank these non-dominated solutions into several layers according to their relative performance on the three acquisition functions. The empirical results show that the proposed method is competitive with the state-of-the-art methods on different problems.
Bayesian optimization (BO) is a widely-used sequential method for zeroth-order optimization of complex and expensive-to-compute black-box functions. The existing BO methods assume that the function evaluation (feedback) is available to the learner immediately or after a fixed delay. Such assumptions may not be practical in many real-life problems like online recommendations, clinical trials, and hyperparameter tuning where feedback is available after a random delay. To benefit from the experimental parallelization in these problems, the learner needs to start new function evaluations without waiting for delayed feedback. In this paper, we consider the BO under stochastic delayed feedback problem. We propose algorithms with sub-linear regret guarantees that efficiently address the dilemma of selecting new function queries while waiting for randomly delayed feedback. Building on our results, we also make novel contributions to batch BO and contextual Gaussian process bandits. Experiments on synthetic and real-life datasets verify the performance of our algorithms.
We focus on the problem of adversarial attacks against models on discrete sequential data in the black-box setting where the attacker aims to craft adversarial examples with limited query access to the victim model. Existing black-box attacks, mostly based on greedy algorithms, find adversarial examples using pre-computed key positions to perturb, which severely limits the search space and might result in suboptimal solutions. To this end, we propose a query-efficient black-box attack using Bayesian optimization, which dynamically computes important positions using an automatic relevance determination (ARD) categorical kernel. We introduce block decomposition and history subsampling techniques to improve the scalability of Bayesian optimization when an input sequence becomes long. Moreover, we develop a post-optimization algorithm that finds adversarial examples with smaller perturbation size. Experiments on natural language and protein classification tasks demonstrate that our method consistently achieves higher attack success rate with significant reduction in query count and modification rate compared to the previous state-of-the-art methods.
Bayesian Optimization (BO) has shown great promise for the global optimization of functions that are expensive to evaluate, but despite many successes, standard approaches can struggle in high dimensions. To improve the performance of BO, prior work suggested incorporating gradient information into a Gaussian process surrogate of the objective, giving rise to kernel matrices of size $nd \times nd$ for $n$ observations in $d$ dimensions. Na\"ively multiplying with (resp. inverting) these matrices requires $\mathcal{O}(n^2d^2)$ (resp. $\mathcal{O}(n^3d^3$)) operations, which becomes infeasible for moderate dimensions and sample sizes. Here, we observe that a wide range of kernels gives rise to structured matrices, enabling an exact $\mathcal{O}(n^2d)$ matrix-vector multiply for gradient observations and $\mathcal{O}(n^2d^2)$ for Hessian observations. Beyond canonical kernel classes, we derive a programmatic approach to leveraging this type of structure for transformations and combinations of the discussed kernel classes, which constitutes a structure-aware automatic differentiation algorithm. Our methods apply to virtually all canonical kernels and automatically extend to complex kernels, like the neural network, radial basis function network, and spectral mixture kernels without any additional derivations, enabling flexible, problem-dependent modeling while scaling first-order BO to high $d$.
Bayesian optimization (BO) has become popular for sequential optimization of black-box functions. When BO is used to optimize a target function, we often have access to previous evaluations of potentially related functions. This begs the question as to whether we can leverage these previous experiences to accelerate the current BO task through meta-learning (meta-BO), while ensuring robustness against potentially harmful dissimilar tasks that could sabotage the convergence of BO. This paper introduces two scalable and provably robust meta-BO algorithms: robust meta-Gaussian process-upper confidence bound (RM-GP-UCB) and RM-GP-Thompson sampling (RM-GP-TS). We prove that both algorithms are asymptotically no-regret even when some or all previous tasks are dissimilar to the current task, and show that RM-GP-UCB enjoys a better theoretical robustness than RM-GP-TS. We also exploit the theoretical guarantees to optimize the weights assigned to individual previous tasks through regret minimization via online learning, which diminishes the impact of dissimilar tasks and hence further enhances the robustness. Empirical evaluations show that (a) RM-GP-UCB performs effectively and consistently across various applications, and (b) RM-GP-TS, despite being less robust than RM-GP-UCB both in theory and in practice, performs competitively in some scenarios with less dissimilar tasks and is more computationally efficient.
Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces trust in HPO, and thus hinders its broad adoption. Here, we study the combination of HPO with interpretable machine learning (IML) methods such as partial dependence plots. These techniques are more and more used to explain the marginal effect of hyperparameters on the black-box cost function or to quantify the importance of hyperparameters. However, if such methods are naively applied to the experimental data of the HPO process in a post-hoc manner, the underlying sampling bias of the optimizer can distort interpretations. We propose a modified HPO method which efficiently balances the search for the global optimum w.r.t. predictive performance \emph{and} the reliable estimation of IML explanations of an underlying black-box function by coupling Bayesian optimization and Bayesian Algorithm Execution. On benchmark cases of both synthetic objectives and HPO of a neural network, we demonstrate that our method returns more reliable explanations of the underlying black-box without a loss of optimization performance.
Information-theoretic Bayesian optimization techniques have become popular for optimizing expensive-to-evaluate black-box functions due to their non-myopic qualities. Entropy Search and Predictive Entropy Search both consider the entropy over the optimum in the input space, while the recent Max-value Entropy Search considers the entropy over the optimal value in the output space. We propose Joint Entropy Search (JES), a novel information-theoretic acquisition function that considers an entirely new quantity, namely the entropy over the joint optimal probability density over both input and output space. To incorporate this information, we consider the reduction in entropy from conditioning on fantasized optimal input/output pairs. The resulting approach primarily relies on standard GP machinery and removes complex approximations typically associated with information-theoretic methods. With minimal computational overhead, JES shows superior decision-making, and yields state-of-the-art performance for information-theoretic approaches across a wide suite of tasks. As a light-weight approach with superior results, JES provides a new go-to acquisition function for Bayesian optimization.
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive distributions no longer necessarily interpolates the observed values when they are outside ranges of interest, but are simply constrained to remain outside. This method called relaxed Gaussian process (reGP) interpolation provides better predictive distributions in ranges of interest, especially in cases where a stationarity assumption for the GP model is not appropriate. It can be viewed as a goal-oriented method and becomes particularly interesting in Bayesian optimization, for example, for the minimization of an objective function, where good predictive distributions for low function values are important. When the expected improvement criterion and reGP are used for sequentially choosing evaluation points, the convergence of the resulting optimization algorithm is theoretically guaranteed (provided that the function to be optimized lies in the reproducing kernel Hilbert space attached to the known covariance of the underlying Gaussian process). Experiments indicate that using reGP instead of stationary GP models in Bayesian optimization is beneficial.
This paper presents a new type of hybrid model for Bayesian optimization (BO) adept at managing mixed variables, encompassing both quantitative (continuous and integer) and qualitative (categorical) types. Our proposed new hybrid models (named hybridM) merge the Monte Carlo Tree Search structure (MCTS) for categorical variables with Gaussian Processes (GP) for continuous ones. hybridM leverages the upper confidence bound tree search (UCTS) for MCTS strategy, showcasing the tree architecture's integration into Bayesian optimization. Our innovations, including dynamic online kernel selection in the surrogate modeling phase and a unique UCTS search strategy, position our hybrid models as an advancement in mixed-variable surrogate models. Numerical experiments underscore the superiority of hybrid models, highlighting their potential in Bayesian optimization.