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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.08678 |
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| _version_ | 1866916668856336384 |
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| author | Ding, Zihan Jin, Kexin Latz, Jonas Liu, Chenguang |
| author_facet | Ding, Zihan Jin, Kexin Latz, Jonas Liu, Chenguang |
| contents | Deep neural networks and other modern machine learning models are often susceptible to adversarial attacks. Indeed, an adversary may often be able to change a model's prediction through a small, directed perturbation of the model's input - an issue in safety-critical applications. Adversarially robust machine learning is usually based on a minmax optimisation problem that minimises the machine learning loss under maximisation-based adversarial attacks.
In this work, we study adversaries that determine their attack using a Bayesian statistical approach rather than maximisation. The resulting Bayesian adversarial robustness problem is a relaxation of the usual minmax problem. To solve this problem, we propose Abram - a continuous-time particle system that shall approximate the gradient flow corresponding to the underlying learning problem. We show that Abram approximates a McKean-Vlasov process and justify the use of Abram by giving assumptions under which the McKean-Vlasov process finds the minimiser of the Bayesian adversarial robustness problem. We discuss two ways to discretise Abram and show its suitability in benchmark adversarial deep learning experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to beat a Bayesian adversary Ding, Zihan Jin, Kexin Latz, Jonas Liu, Chenguang Machine Learning Optimization and Control Computation 90C15, 65C35, 68T07 Deep neural networks and other modern machine learning models are often susceptible to adversarial attacks. Indeed, an adversary may often be able to change a model's prediction through a small, directed perturbation of the model's input - an issue in safety-critical applications. Adversarially robust machine learning is usually based on a minmax optimisation problem that minimises the machine learning loss under maximisation-based adversarial attacks. In this work, we study adversaries that determine their attack using a Bayesian statistical approach rather than maximisation. The resulting Bayesian adversarial robustness problem is a relaxation of the usual minmax problem. To solve this problem, we propose Abram - a continuous-time particle system that shall approximate the gradient flow corresponding to the underlying learning problem. We show that Abram approximates a McKean-Vlasov process and justify the use of Abram by giving assumptions under which the McKean-Vlasov process finds the minimiser of the Bayesian adversarial robustness problem. We discuss two ways to discretise Abram and show its suitability in benchmark adversarial deep learning experiments. |
| title | How to beat a Bayesian adversary |
| topic | Machine Learning Optimization and Control Computation 90C15, 65C35, 68T07 |
| url | https://arxiv.org/abs/2407.08678 |