We characterize offline data poisoning attacks on Multi-Agent Reinforcement Learning (MARL), where an attacker may change a data set in an attempt to install a (potentially fictitious) unique Markov-perfect Nash equilibrium for a two-player zero-sum Markov game. We propose the unique Nash set, namely the set of games, specified by their Q functions, with a specific joint policy being the unique Nash equilibrium. The unique Nash set is central to poisoning attacks because the attack is successful if and only if data poisoning pushes all plausible games inside it. The unique Nash set generalizes the reward polytope commonly used in inverse reinforcement learning to MARL. For zero-sum Markov games, both the inverse Nash set and the set of plausible games induced by data are polytopes in the Q function space. We exhibit a linear program to efficiently compute the optimal poisoning attack. Our work sheds light on the structure of data poisoning attacks on offline MARL, a necessary step before one can design more robust MARL algorithms.

Data Poisoning to Fake a Nash Equilibria for Markov Games

To ensure the usefulness of Reinforcement Learning (RL) in real systems, it is crucial to ensure they are robust to noise and adversarial attacks. In adversarial RL, an external attacker has the power to manipulate the victim agent's interaction with the environment. We study the full class of online manipulation attacks, which include (i) state attacks, (ii) observation attacks (which are a generalization of perceived-state attacks), (iii) action attacks, and (iv) reward attacks. We show the attacker's problem of designing a stealthy attack that maximizes its own expected reward, which often corresponds to minimizing the victim's value, is captured by a Markov Decision Process (MDP) that we call a meta-MDP since it is not the true environment but a higher level environment induced by the attacked interaction. We show that the attacker can derive optimal attacks by planning in polynomial time or learning with polynomial sample complexity using standard RL techniques. We argue that the optimal defense policy for the victim can be computed as the solution to a stochastic Stackelberg game, which can be further simplified into a partially-observable turn-based stochastic game (POTBSG). Neither the attacker nor the victim would benefit from deviating from their respective optimal policies, thus such solutions are truly robust. Although the defense problem is NP-hard, we show that optimal Markovian defenses can be computed (learned) in polynomial time (sample complexity) in many scenarios.

Optimal Attack and Defense for Reinforcement Learning

In offline multi-agent reinforcement learning (MARL), the agents estimate policies from a given dataset. We study reward-poisoning attack on offline MARL, where an exogenous attacker can modify the reward vectors in the dataset before the agents see the data. Similar to poisoning attacks on a single RL agent, the attacker wants to guide the agents to learn a nefarious target policy while minimizing the lp norm of reward modification. Unlike attacks on single-agent RL, the attacker takes advantage of the strategic interactions between the agents to install the target policy as a Markov Perfect Dominant Strategy Equilibrium (MPDSE) and can achieve lower reward modification costs compared to separate single-agent attacks. We then show that the attack works on various MARL agents including uncertainty-aware learners, and we exhibit linear programs to efficiently solve the offline MARL attack problem. Our work thus paves the way for studying defense in offline MARL in the future.

Reward Poisoning Attacks on Offline Multi-Agent Reinforcement Learning

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Data Poisoning to Fake a Nash Equilibria for Markov Games

Optimal Attack and Defense for Reinforcement Learning

Reward Poisoning Attacks on Offline Multi-Agent Reinforcement Learning

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