Machine Learning
Regret bounds for prediction problems
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Approximate solutions to markov decision processes
Approximate solutions to markov decision processes
No-regret learning and game-theoretic equilibria
No-regret learning and game-theoretic equilibria
From external to internal regret
COLT'05 Proceedings of the 18th annual conference on Learning Theory
On Fixed Convex Combinations of No-Regret Learners
MLDM '09 Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition
A sampling-based approach to computing equilibria in succinct extensive-form games
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Maximum causal entropy correlated equilibria for Markov games
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
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Quite a bit is known about minimizing different kinds of regret in experts problems, and how these regret types relate to types of equilibria in the multiagent setting of repeated matrix games. Much less is known about the possible kinds of regret in online convex programming problems (OCPs), or about equilibria in the analogous multiagent setting of repeated convex games. This gap is unfortunate, since convex games are much more expressive than matrix games, and since many important machine learning problems can be expressed as OCPs. In this paper, we work to close this gap: we analyze a spectrum of regret types which lie between external and swap regret, along with their corresponding equilibria, which lie between coarse correlated and correlated equilibrium. We also analyze algorithms for minimizing these regret types. As examples of our framework, we derive algorithms for learning correlated equilibria in polyhedral convex games and extensive-form correlated equilibria in extensive-form games. The former is exponentially more efficient than previous algorithms, and the latter is the first of its type.