The Defender vs. The Attacker Game

The researcher proposes a game-theoretic approach to analyze the interaction between the model defender and attacker in trigger-based black-box model watermarking. 

They design payoff functions for both players and determine the optimal strategies for each player, which provides a theoretical foundation for future research on black-box model watermarking.

A framework where a watermark is embedded in a model by training it on a dataset containing both normal images and a set of “trigger” samples ensures the watermarked model maintains performance on normal data while exhibiting specific behavior on the trigger set, enabling ownership verification. 

By leveraging game theory, they analyze the interaction between the watermark embedder and a potential attacker and focus on a partial cooperation game, acknowledging that both parties have an interest in maintaining the model’s overall performance while the embedder seeks to establish ownership. 

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This novel approach extends existing game-theoretic analyses in adversarial machine learning by incorporating cooperative aspects, providing valuable insights for designing more secure and resilient watermarking strategies for deep neural networks.

The game analysis investigates the strategic interaction between a model defender and attacker, where the defender employs watermarking to protect models while the attacker aims to compromise them. 

By modeling this interaction as a game with payoffs for both players, it takes into consideration a variety of factors, including the accuracy of the model, the accuracy of the watermark detection, and the force of the attack. 

The key findings reveal that the defender’s optimal strategy depends on the difference in robustness between different watermarked models and the difference in strength between different attacks. 

Specifically, the analysis identifies conditions under which the defender’s optimal response involves a mixed strategy, where they probabilistically choose between different watermarking approaches based on the expected attack intensity and the robustness of their models to those attacks. 

Unlike existing studies that solely focus on cooperative or non-cooperative scenarios, the research acknowledges the presence of both cooperative and competitive interests for both the defender (model owner) and the attacker. 

The game model incorporates economic costs and benefits into the payoff function, considering the performance of the model on the original task while emphasizing competition in watermark detection. 

The study reveals that the defender’s optimal response is influenced by the robustness variation among watermarked models and the strength disparity between different attacks, which underscores the critical importance of enhancing the robustness of watermarked models against real-world attacks during system design. 

Future research directions include examining the impact of trigger set selection on DNN model performance in real-world applications, conducting practical implementations to validate and extend the proposed framework, and exploring watermarking games for generative models to further enrich the watermarking theory.

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