1,226,303 research outputs found
Adaptive Consensus and Parameter Estimation of Multi-Agent Systems with An Uncertain Leader
In this note, the problem of simultaneous leader-following consensus and
parameter estimation is studied for a class of multi-agent systems subject to
an uncertain leader system. The leader system is described by a sum of
sinusoids with unknown amplitudes, frequencies and phases. A distributed
adaptive observer is established for each agent to estimate the unknown
frequencies of the leader. It is shown that if the signal of the leader is
sufficiently rich, the estimation errors of the unknown frequencies converge to
zero asymptotically for all the agents. Based on the designed distributed
adaptive observer, a distributed adaptive control law is synthesized for each
agent to solve the leader-following consensus problem.Comment: 8 pag
Corruption-robust offline two-player zero-sum Markov games
We study data corruption robustness in offline two-player zero-sum Markov games. Given a dataset of realized trajectories of two players, an adversary is allowed to modify an ε-fraction of it. The learner’s goal is to identify an approximate Nash Equilibrium policy pair from the corrupted data. We consider this problem in linear Markov games under different degrees of data coverage and corruption. We start by providing an information-theoretic lower bound on the suboptimality gap of any learner. Next, we propose robust versions of the Pessimistic Minimax Value Iteration algorithm (Zhong et al., 2022), both under coverage on the corrupted data and under coverage only on the clean data, and show that they achieve (near)-optimal suboptimality gap bounds with respect to ε. We note that we are the first to provide such a characterization of the problem of learning approximate Nash Equilibrium policies in offline two-player zero-sum Markov games under data corruption
Controlling a Random Population is EXPTIME-hard
Bertrand et al. [1] (LMCS 2019) describe two-player zero-sum games in which one player tries to achieve a reachability objective in games (on the same finite arena) simultaneously by broadcasting actions, and where the opponent has full control of resolving non-deterministic choices. They show EXPTIME completeness for the question if such games can be won for every number of games. We consider the almost-sure variant in which the opponent randomizes their actions, and where the player tries to achieve the reachability objective eventually with probability one. The lower bound construction in [1] does not directly carry over to this randomized setting. In this note we show EXPTIME hardness for the almost-sure problem by reduction from Countdown Games
A note on large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games
Finding equilibria points in continuous minimax games has become a key
problem within machine learning, in part due to its connection to the training
of generative adversarial networks. Because of existence and robustness issues,
recent developments have shifted from pure equilibria to focusing on mixed
equilibria points. In this note we consider a method proposed by Domingo-Enrich
et al. for finding mixed equilibria in two-layer zero-sum games. The method is
based on entropic regularisation and the two competing strategies are
represented by two sets of interacting particles. We show that the sequence of
empirical measures of the particle system satisfies a large deviation principle
as the number of particles grows to infinity, and how this implies convergence
of the empirical measure and the associated Nikaid\^o-Isoda error,
complementing existing law of large numbers results.Comment: Revised section
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