Optimal Attack against Autoregressive Models by Manipulating the Environment

TL;DR

This paper introduces an optimal adversarial attack framework against autoregressive models in dynamical environments, utilizing control theory techniques like LQR and MPC to manipulate forecasts effectively.

Contribution

It formulates the attack problem as an optimal control task and provides solutions for both linear and nonlinear models, including black-box scenarios.

Findings

Attacks successfully manipulate autoregressive forecasts in experiments.

LQR and MPC effectively optimize attack strategies.

Black-box approach combines system identification with MPC.

Abstract

We describe an optimal adversarial attack formulation against autoregressive time series forecast using Linear Quadratic Regulator (LQR). In this threat model, the environment evolves according to a dynamical system; an autoregressive model observes the current environment state and predicts its future values; an attacker has the ability to modify the environment state in order to manipulate future autoregressive forecasts. The attacker's goal is to force autoregressive forecasts into tracking a target trajectory while minimizing its attack expenditure. In the white-box setting where the attacker knows the environment and forecast models, we present the optimal attack using LQR for linear models, and Model Predictive Control (MPC) for nonlinear models. In the black-box setting, we combine system identification and MPC. Experiments demonstrate the effectiveness of our attacks.