This objective is similar to Maximum Entropy Correlated Equilibrium (MECE) [48], and the proofs here are similar to the framework set out there. A drawback of MECE is that it is not easy to determine the minimum p permissible. If we choose p that does not permit a valid solution, then the parameters will diverge. We can circumvent this problem by optimizing the distance to a target ˆ p. And µis for balancing the linear objective.

Game theory provides a powerful framework for the design and analysis of multiagent systems that involve strategic interactions [see, e.g.,16].

In this paper, we study last-iterate convergence of learning algorithms in bilinear saddle-point problems, a preferable notion of convergence that captures the day-to-day behavior of learning dynamics. We focus on the challenging setting where players select actions from compact convex sets and receive only bandit feedback. Our main contribution is the design of an uncoupled learning algorithm that guarantees last-iterate convergence to the Nash equilibrium with high probability. We establish a convergence rate of $\tilde{O}(T^{-1/4})$ up to polynomial factors in problem parameters. Crucially, our proposed algorithm is computationally efficient, requiring only an efficient linear optimization oracle over the players' compact action sets. The algorithm is obtained by combining techniques from experimental design and the classic Follow-The-Regularized-Leader (FTRL) framework, with a carefully chosen regularizer function tailored to the geometry of the action set of each learner.

We propose to view the outcomes of the agents' dynamics as inducing a "meta-game" between the users.

Our main observation is that the gap between λnt and the accumulated reward of agent n, which we call the QoS regret, behaves like a queue.

Data valuation is a class of techniques for quantitatively assessing the value of data for applications like pricing in data marketplaces.