Model-based Causal Bayesian Optimization
- URL: http://arxiv.org/abs/2211.10257v1
- Date: Fri, 18 Nov 2022 14:28:21 GMT
- Title: Model-based Causal Bayesian Optimization
- Authors: Scott Sussex and Anastasiia Makarova and Andreas Krause
- Abstract summary: We propose model-based causal Bayesian optimization (MCBO)
MCBO learns a full system model instead of only modeling intervention-reward pairs.
Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form.
- Score: 78.120734120667
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: How should we intervene on an unknown structural causal model to maximize a
downstream variable of interest? This optimization of the output of a system of
interconnected variables, also known as causal Bayesian optimization (CBO), has
important applications in medicine, ecology, and manufacturing. Standard
Bayesian optimization algorithms fail to effectively leverage the underlying
causal structure. Existing CBO approaches assume noiseless measurements and do
not come with guarantees. We propose model-based causal Bayesian optimization
(MCBO), an algorithm that learns a full system model instead of only modeling
intervention-reward pairs. MCBO propagates epistemic uncertainty about the
causal mechanisms through the graph and trades off exploration and exploitation
via the optimism principle. We bound its cumulative regret, and obtain the
first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization,
our acquisition function cannot be evaluated in closed form, so we show how the
reparameterization trick can be used to apply gradient-based optimizers.
Empirically we find that MCBO compares favorably with existing state-of-the-art
approaches.
Related papers
- Robust Bayesian Optimization via Localized Online Conformal Prediction [37.549297668783254]
We introduce localized online conformal prediction-based Bayesian optimization (LOCBO)
LOCBO calibrates the GP model through localized online conformal prediction (CP)
We provide theoretical performance guarantees for LOCBO's iterates that hold for the unobserved objective function.
arXiv Detail & Related papers (2024-11-26T12:45:54Z) - Poisson Process for Bayesian Optimization [126.51200593377739]
We propose a ranking-based surrogate model based on the Poisson process and introduce an efficient BO framework, namely Poisson Process Bayesian Optimization (PoPBO)
Compared to the classic GP-BO method, our PoPBO has lower costs and better robustness to noise, which is verified by abundant experiments.
arXiv Detail & Related papers (2024-02-05T02:54:50Z) - Model-based Causal Bayesian Optimization [74.78486244786083]
We introduce the first algorithm for Causal Bayesian Optimization with Multiplicative Weights (CBO-MW)
We derive regret bounds for CBO-MW that naturally depend on graph-related quantities.
Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system.
arXiv Detail & Related papers (2023-07-31T13:02:36Z) - When to Update Your Model: Constrained Model-based Reinforcement
Learning [50.74369835934703]
We propose a novel and general theoretical scheme for a non-decreasing performance guarantee of model-based RL (MBRL)
Our follow-up derived bounds reveal the relationship between model shifts and performance improvement.
A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns.
arXiv Detail & Related papers (2022-10-15T17:57:43Z) - Generalizing Bayesian Optimization with Decision-theoretic Entropies [102.82152945324381]
We consider a generalization of Shannon entropy from work in statistical decision theory.
We first show that special cases of this entropy lead to popular acquisition functions used in BO procedures.
We then show how alternative choices for the loss yield a flexible family of acquisition functions.
arXiv Detail & Related papers (2022-10-04T04:43:58Z) - A General Recipe for Likelihood-free Bayesian Optimization [115.82591413062546]
We propose likelihood-free BO (LFBO) to extend BO to a broader class of models and utilities.
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.
arXiv Detail & Related papers (2022-06-27T03:55:27Z) - Accounting for Gaussian Process Imprecision in Bayesian Optimization [0.0]
We study the effect of the Gaussian processes' prior specifications on classical BO's convergence.
We introduce PROBO as a generalization of BO that aims at rendering the method more robust towards prior mean parameter misspecification.
We test our approach against classical BO on a real-world problem from material science and observe PROBO to converge faster.
arXiv Detail & Related papers (2021-11-16T08:45:39Z) - How Bayesian Should Bayesian Optimisation Be? [0.024790788944106048]
We investigate whether a fully-Bayesian treatment of the Gaussian process hyperparameters in BO (FBBO) leads to improved optimisation performance.
We compare FBBO using three approximate inference schemes to the maximum likelihood approach, using the Expected Improvement (EI) and Upper Confidence Bound (UCB) acquisition functions.
We find that FBBO using EI with an ARD kernel leads to the best performance in the noise-free setting, with much less difference between combinations of BO components when the noise is increased.
arXiv Detail & Related papers (2021-05-03T14:28:11Z) - Causal Bayesian Optimization [8.958125394444679]
We study the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed.
Our approach combines ideas from causal inference, uncertainty quantification and sequential decision making.
We show how knowing the causal graph significantly improves the ability to reason about optimal decision making strategies.
arXiv Detail & Related papers (2020-05-24T13:20:50Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.