**Universal Multi-Party Poisoning Attacks**

*Saeed Mahloujifar and Mahammad Mahmoody and Ameer Mohammed*

**Abstract: **In this work, we demonstrate universal multi-party poisoning attacks that adapt and apply to any multi-party learning process with arbitrary interaction pattern between the parties. More generally, we introduce and study $(k,p)$-poisoning attacks in which an adversary controls $k\in[m]$ of the parties, and for each corrupted party $P_i$, the adversary submits some poisoned data $T'_i$ on behalf of $P_i$ that is still "$(1-p)$-close" to the correct data $T_i$ (e.g., $1-p$ fraction of $T'_i$ is still honestly generated). We prove that for any "bad" property $B$ of the final trained hypothesis $h$ (e.g., $h$ failing on a particular test example or having "large" risk) that has an arbitrarily small constant probability of happening without the attack, there always is a $(k,p)$-poisoning attack that increases the probability of $B$ from $\mu$ to by $\mu^{1-p \cdot k/m} = \mu + \Omega(p \cdot k/m)$. Our attack only uses clean labels, and it is online.

More generally, we prove that for any bounded function $f(x_1,\dots,x_n) \in [0,1]$ defined over an $n$-step random process $x = (x_1,\dots,x_n)$, an adversary who can override each of the $n$ blocks with \emph{even dependent} probability $p$ can increase the expected output by at least $\Omega(p \cdot \mathrm{Var}[f(x)])$.

**Category / Keywords: **foundations / Biasing, Coin-Tossing, Poisoning, Multi-party learning

**Original Publication**** (with minor differences): **ICML 2019

**Date: **received 9 Sep 2018, last revised 4 Nov 2021

**Contact author: **mohammad at virginia edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20211104:192840 (All versions of this report)

**Short URL: **ia.cr/2018/854

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