Adversarial Robustness Guarantees for Gaussian Processes
- URL: http://arxiv.org/abs/2104.03180v1
- Date: Wed, 7 Apr 2021 15:14:56 GMT
- Title: Adversarial Robustness Guarantees for Gaussian Processes
- Authors: Andrea Patane, Arno Blaas, Luca Laurenti, Luca Cardelli, Stephen
Roberts, Marta Kwiatkowska
- Abstract summary: Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications.
We present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations.
We develop a branch-and-bound scheme to refine the bounds and show, for any $epsilon > 0$, that our algorithm is guaranteed to converge to values $epsilon$-close to the actual values in finitely many iterations.
- Score: 22.403365399119107
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Gaussian processes (GPs) enable principled computation of model uncertainty,
making them attractive for safety-critical applications. Such scenarios demand
that GP decisions are not only accurate, but also robust to perturbations. In
this paper we present a framework to analyse adversarial robustness of GPs,
defined as invariance of the model's decision to bounded perturbations. Given a
compact subset of the input space $T\subseteq \mathbb{R}^d$, a point $x^*$ and
a GP, we provide provable guarantees of adversarial robustness of the GP by
computing lower and upper bounds on its prediction range in $T$. We develop a
branch-and-bound scheme to refine the bounds and show, for any $\epsilon > 0$,
that our algorithm is guaranteed to converge to values $\epsilon$-close to the
actual values in finitely many iterations. The algorithm is anytime and can
handle both regression and classification tasks, with analytical formulation
for most kernels used in practice. We evaluate our methods on a collection of
synthetic and standard benchmark datasets, including SPAM, MNIST and
FashionMNIST. We study the effect of approximate inference techniques on
robustness and demonstrate how our method can be used for interpretability. Our
empirical results suggest that the adversarial robustness of GPs increases with
accurate posterior estimation.
Related papers
- Regret Minimization and Statistical Inference in Online Decision Making with High-dimensional Covariates [7.21848268647674]
We integrate the $varepsilon$-greedy bandit algorithm for decision-making with a hard thresholding algorithm for estimating sparse bandit parameters.
Under a margin condition, our method achieves either $O(T1/2)$ regret or classical $O(T1/2)$-consistent inference.
arXiv Detail & Related papers (2024-11-10T01:47:11Z) - Robust Gaussian Processes via Relevance Pursuit [17.39376866275623]
We propose and study a GP model that achieves robustness against sparse outliers by inferring data-point-specific noise levels.
We show, surprisingly, that the model can be parameterized such that the associated log marginal likelihood is strongly concave in the data-point-specific noise variances.
arXiv Detail & Related papers (2024-10-31T17:59:56Z) - Towards Principled, Practical Policy Gradient for Bandits and Tabular MDPs [9.58750210024265]
We consider (stochastic) softmax policy gradient (PG) methods for bandits and Markov decision processes (MDPs)
We show that the proposed algorithm offers similar theoretical guarantees as the state-of-the art results, but does not require the knowledge of oracle-like quantities.
For the multi-armed bandit setting, our techniques result in a theoretically-principled PG algorithm that does not require explicit exploration, the knowledge of the reward gap, the reward distributions, or the noise.
arXiv Detail & Related papers (2024-05-21T18:12:39Z) - Neural Operator Variational Inference based on Regularized Stein
Discrepancy for Deep Gaussian Processes [23.87733307119697]
We introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes.
NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior.
We demonstrate that the bias introduced by our method can be controlled by multiplying the divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm.
arXiv Detail & Related papers (2023-09-22T06:56:35Z) - Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time
Guarantees [56.848265937921354]
Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy.
Many algorithms for IRL have an inherently nested structure.
We develop a novel single-loop algorithm for IRL that does not compromise reward estimation accuracy.
arXiv Detail & Related papers (2022-10-04T17:13:45Z) - Robust and Adaptive Temporal-Difference Learning Using An Ensemble of
Gaussian Processes [70.80716221080118]
The paper takes a generative perspective on policy evaluation via temporal-difference (TD) learning.
The OS-GPTD approach is developed to estimate the value function for a given policy by observing a sequence of state-reward pairs.
To alleviate the limited expressiveness associated with a single fixed kernel, a weighted ensemble (E) of GP priors is employed to yield an alternative scheme.
arXiv Detail & Related papers (2021-12-01T23:15:09Z) - Misspecified Gaussian Process Bandit Optimization [59.30399661155574]
Kernelized bandit algorithms have shown strong empirical and theoretical performance for this problem.
We introduce a emphmisspecified kernelized bandit setting where the unknown function can be $epsilon$--uniformly approximated by a function with a bounded norm in some Reproducing Kernel Hilbert Space (RKHS)
We show that our algorithm achieves optimal dependence on $epsilon$ with no prior knowledge of misspecification.
arXiv Detail & Related papers (2021-11-09T09:00:02Z) - A general sample complexity analysis of vanilla policy gradient [101.16957584135767]
Policy gradient (PG) is one of the most popular reinforcement learning (RL) problems.
"vanilla" theoretical understanding of PG trajectory is one of the most popular methods for solving RL problems.
arXiv Detail & Related papers (2021-07-23T19:38:17Z) - Large-Scale Methods for Distributionally Robust Optimization [53.98643772533416]
We prove that our algorithms require a number of evaluations gradient independent of training set size and number of parameters.
Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9--36 times more efficient than full-batch methods.
arXiv Detail & Related papers (2020-10-12T17:41:44Z) - Uncertainty quantification using martingales for misspecified Gaussian
processes [52.22233158357913]
We address uncertainty quantification for Gaussian processes (GPs) under misspecified priors.
We construct a confidence sequence (CS) for the unknown function using martingale techniques.
Our CS is statistically valid and empirically outperforms standard GP methods.
arXiv Detail & Related papers (2020-06-12T17:58:59Z)
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.