Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification

Blanchard, Antoine; Sapsis, Themistoklis P.

doi:10.1137/20m1347486

Cited by 27 publications

(29 citation statements)

References 45 publications

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“…Motivated by the recent findings in [34][35][36], we introduce a novel UCB-type objective for online decision-making in multi-armed and contextual bandit problems that can overcome the aforementioned shortcomings. This is achieved by introducing an importance weight to effectively promote the exploration of 'heavy-tailed' (i.e.…”

Section: (B) Our Contributions (I) Primary Contributionmentioning

confidence: 99%

Output-weighted sampling for multi-armed bandits with extreme payoffs

et al. 2022

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We present a new type of acquisition function for online decision-making in multi-armed and contextual bandit problems with extreme payoffs. Specifically, we model the payoff function as a Gaussian process and formulate a novel type of upper confidence bound acquisition function that guides exploration towards the bandits that are deemed most relevant according to the variability of the observed rewards. This is achieved by computing a tractable likelihood ratio that quantifies the importance of the output relative to the inputs and essentially acts as an attention mechanism that promotes exploration of extreme rewards. Our formulation is supported by asymptotic zero-regret guarantees, and its performance is demonstrated across several synthetic benchmarks, as well as two realistic examples involving noisy sensor network data. Finally, we provide a JAX library for efficient bandit optimization using Gaussian processes.

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Section: (B) Our Contributions (I) Primary Contributionmentioning

confidence: 99%

Output-weighted sampling for multi-armed bandits with extreme payoffs

et al. 2022

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“…The acquisition function is the key component of the sequential search algorithm, as it guides algorithm 1 in exploring the input/parameter space and determines points at which the objective function is to be queried. Because of the lack of a closed analytical form of DNOs, we only consider two acquisition functions used previously with GPs on several test cases in [16]. The two functions we are interested in are the commonly used uncertainty sampling and the output-weighted uncertainty sampling proposed by [16].…”

Section: Data Selection: Acquisition Functionsmentioning

confidence: 99%

“…Appropriately defined acquisition functions for uncovering extreme behavior are just as critical as the chosen surrogate model. Recently, [16], in concert with several other works [17], [18], and [5], introduced a class of probabilistic acquisition functions specifically designed for discovering extreme events. By combining statistics of the input space along with statistics deduced from the surrogate model, the method can account for both the importance of the output relative to the input.…”

Section: Introductionmentioning

confidence: 99%

Discovering and forecasting extreme events via active learning in neural operators

Pickering¹,

Guth²,

Karniadakis³

et al. 2022

Preprint

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Extreme events in society and nature, such as pandemic spikes or rogue waves, can have catastrophic consequences. Characterizing extremes is difficult as they occur rarely, arise from seemingly benign conditions, and belong to complex and often unknown infinite-dimensional systems. Such challenges render attempts at characterizing them as moot. We address each of these difficulties by combining novel training schemes in Bayesian experimental design (BED) with an ensemble of deep neural operators (DNOs). This model-agnostic framework pairs a BED scheme that actively selects data for quantifying extreme events with an ensemble of DNOs that approximate infinite-dimensional nonlinear operators. We find that not only does this framework clearly beat Gaussian processes (GPs) but that 1) shallow ensembles of just two members perform best; 2) extremes are uncovered regardless of the state of initial data (i.e. with or without extremes); 3) our method eliminates "double-descent" phenomena; 4) the use of batches of suboptimal acquisition points compared to step-by-step global optima does not hinder BED performance; and 5) Monte Carlo acquisition outperforms standard minimizers in high-dimensions. Together these conclusions form the foundation of an AI-assisted experimental infrastructure that can efficiently infer and pinpoint critical situations across many domains, from physical to societal systems.

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“…Similar optimization criterion is also used in Refs. [2,3] for the purpose of computing the extreme-event probability.…”

Section: Derivation Of the Simplified Acquisition G(x)mentioning

confidence: 99%

Discussion: “Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions” (Pandita, P., Bilionis, I., and Panchal, J., 2019, ASME J. Mech. Des., 141(10), p. 101404)

Gong

Pan

2021

Journal of Mechanical Design

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The authors of the discussed paper simplified the information-based acquisition on estimating statistical expectation and developed analytical computation for each involved quantity under uniform input distribution. In this discussion, we show that (1) the last three terms of the acquisition always add up to zero, leaving a concise form with a much more intuitive interpretation of the acquisition; (2) the analytical computation of the acquisition can be generalized to arbitrary input distribution, greatly broadening the application of the developed framework.

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Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification

Cited by 27 publications

References 45 publications

Output-weighted sampling for multi-armed bandits with extreme payoffs

Output-weighted sampling for multi-armed bandits with extreme payoffs

Discovering and forecasting extreme events via active learning in neural operators

Discussion: “Bayesian Optimal Design of Experiments for Inferring the Statistical Expectation of Expensive Black-Box Functions” (Pandita, P., Bilionis, I., and Panchal, J., 2019, ASME J. Mech. Des., 141(10), p. 101404)

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