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Moritz Graf

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4

AAMAS Conference 2026 Conference Paper

Solving Qualitative Multi-Objective Stochastic Games

  • Moritz Graf
  • Anthony Lin
  • Rupak Majumdar

Manyproblemsincompositionalsynthesisandverificationofmultiagent systems—such as rational verification and assume-guarantee verificationinprobabilisticsystems—reducetoreasoningabouttwoplayer multi-objective stochastic games. This motivates us to study the problem of characterizing the complexity and memory requirements for two-player stochastic games with Boolean combinations of qualitative reachability and safety objectives. Reachability objectives require that a given set of states is reached; safety requires that a given set is invariant. A qualitative winning condition asks that an objective is satisfied almost surely (AS) or (in negated form) with non-zero (NZ) probability. We study the determinacy and complexity landscape of the problem. We show that games with conjunctions of AS and NZ reachability and safety objectives are determined, and determining the winner is PSPACE-complete. The same holds for positive boolean combinations of AS reachability and safety, as well as for negations thereof. On the other hand, games with full Boolean combinations of qualitative objectives are not determined, and are NEXPTIMEhard. Our hardness results show a connection between stochastic games and logics with partially-ordered quantification. Our results shed light on the relationship between determinacy and complexity, and extend the complexity landscape for stochastic games in the multi-objective setting.

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IROS Conference 2025 Conference Paper

Model-Based External Wrench Estimation for Underwater Robots

  • Moritz Graf
  • Daniel A Duecker

Similarly to aerial drones, small-scale underwater robots are prone to external wrenches resulting from disturbances such as water currents or collisions. Estimating the external wrench acting on an underwater robot is challenging due to non-linear hydrodynamic effects and the bottleneck of being limited to onboard sensing. We build on a model-based approach for aerial wrench estimation and extend it to the underwater domain. Various modifications are applied, such as capturing hydrodynamic effects, and new sensory information is integrated, for example, via Doppler velocity log (DVL). We evaluate the performance of the proposed approach through a series of experiments. Moreover, we assess the effect of fusing various sensor configurations and their respective influence on the wrench estimate, including low-cost vs. high-end IMU and DVL. Our adapted approach from the aerial domain delivers good results in estimating external wrenches on underwater robots. While the IMU quality is found to be less important, considering the underwater domain-specific damping terms is critical.

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AAMAS Conference 2024 Conference Paper

Symbolic Computation of Sequential Equilibria

  • Moritz Graf
  • Thorsten Engesser
  • Bernhard Nebel

The sequential equilibrium is a standard solution concept for extensive-form games with imperfect information that includes an explicit representation of the players’ beliefs. An assessment consisting of a strategy and a belief is a sequential equilibrium if it satisfies the properties of sequential rationality and consistency. Our main result is that both properties together can be written as a single finite system of polynomial equations and inequalities. The solutions to this system are exactly the sequential equilibria of the game. We construct this system explicitly and describe an implementation that solves it using cylindrical algebraic decomposition. To write consistency as a finite system of equations, we need to compute the extreme directions of a set of polyhedral cones. We propose a modified version of the double description method, optimized for this specific purpose. To the best of our knowledge, our implementation is the first to symbolically solve general finite imperfect information games for sequential equilibria. 1

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