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Reward-Rate Congestion Games and Replicator--Dinkelbach Dynamics
Hassan Abdelraouf, Vaibhav Srivastava, Vijay Gupta
Reward rate is a key performance criterion in cyber-physical and robotic systems where time, workload, and coordination costs are limiting resources. We introduce reward-rate conge…
Stabilization Limits of Payoff-Based Higher-Order Replicator Dynamics
Hassan Abdelraouf, Vijay Gupta, Jeff S. Shamma
Replicator dynamics (RD) is a fundamental model in learning in games, connecting evolutionary game theory and online learning. This paper studies payoff-based higher-order variants…
Convergence of Payoff-Based Higher-Order Replicator Dynamics in Contractive Games
Hassan Abdelraouf, Vijay Gupta, Jeff S. Shamma
We study the convergence properties of a payoff-based higher-order version of replicator dynamics, a widely studied model in evolutionary dynamics and game-theoretic learning, in c…
Can a Learner Regret Using a No-Regret Algorithm? A Control-Theoretic Study of Performance Dominance
Hassan Abdelraouf, Jeff S. Shamma
No-regret learning dynamics ensure that a learner asymptotically achieves an average reward no worse than that of any fixed strategy. This no-regret guarantee does not determine th…
Passivity, No-Regret, and Convergent Learning in Contractive Games
Hassan Abdelraouf, Georgios Piliouras, Jeff S. Shamma
We investigate the interplay between passivity, no-regret, and convergence in contractive games for various learning dynamic models and their higher-order variants. Our setting is…
Polynomial Lyapunov Functions and Invariant Sets from a New Hierarchy of Quadratic Lyapunov Functions for LTV Systems
Hassan Abdelraouf, Eric Feron, Jeff S. Shamma
We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also…
Computing Bounds on -induced Norm for Linear Time-Invariant Systems Using Homogeneous Lyapunov Functions
Hassan Abdelraouf, Gidado-Yisa Immanuel, Eric Feron
Quadratic Lyapunov function has been widely used in the analysis of linear time invariant (LTI) systems ever since it has shown that the existence of such quadratic Lyapunov functi…
On Linear Time-Invariant Systems Analysis via A Single Trajectory: A Linear Programming Approach
Hassan Abdelraouf, Fahad Albalawi, Eric Feron
In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is p…