Policy Regret in Repeated Games
Authors: Raman Arora, Michael Dinitz, Teodor Vanislavov Marinov, Mehryar Mohri
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | The notion of policy regret in online learning is a well defined performance measure for the common scenario of adaptive adversaries, which more traditional quantities such as external regret do not take into account. We revisit the notion of policy regret and first show that there are online learning settings in which policy regret and external regret are incompatible: any sequence of play that achieves a favorable regret with respect to one definition must do poorly with respect to the other. We then focus on the game-theoretic setting where the adversary is a self-interested agent. In that setting, we show that external regret and policy regret are not in conflict and, in fact, that a wide class of algorithms can ensure a favorable regret with respect to both definitions, so long as the adversary is also using such an algorithm. We also show that the sequence of play of no-policy regret algorithms converges to a policy equilibrium, a new notion of equilibrium that we introduce. Relating this back to external regret, we show that coarse correlated equilibria, which no-external regret players converge to, are a strict subset of policy equilibria. Thus, in game-theoretic settings, every sequence of play with no external regret also admits no policy regret, but the converse does not hold. |
| Researcher Affiliation | Collaboration | Raman Arora Dept. of Computer Science Johns Hopkins University Baltimore, MD 21204 arora@cs.jhu.edu Michael Dinitz Dept. of Computer Science Johns Hopkins University Baltimore, MD 21204 mdinitz@cs.jhu.edu Teodor V. Marinov Dept. of Computer Science Johns Hopkins University Baltimore, MD 21204 tmarino2@jhu.edu Mehryar Mohri Courant Institute and Google Research New York, NY 10012 mohri@cims.nyu.edu |
| Pseudocode | No | The paper is theoretical and focuses on proofs and definitions; it does not provide any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not mention providing open-source code for the described methodology. |
| Open Datasets | No | The paper is theoretical and does not involve empirical studies with datasets. Therefore, it does not discuss public datasets or their availability. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical studies with datasets. Therefore, it does not discuss dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe any experiments that would require specific hardware. No hardware specifications are mentioned. |
| Software Dependencies | No | The paper is theoretical and does not describe any experiments that would require specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not describe any empirical experimental setups, hyperparameters, or training settings. |